void AveragedTurbine<Mu>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /* cache */ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("AveragedTurbine::element_time_derivative");
#endif
// Element Jacobian * quadrature weights for interior integration
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_flow_vars.u())->get_JxW();
// The shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& u_phi =
context.get_element_fe(this->_flow_vars.u())->get_phi();
const std::vector<libMesh::Point>& u_qpoint =
context.get_element_fe(this->_flow_vars.u())->get_xyz();
// The number of local degrees of freedom in each variable
const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u()).size();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.u()); // R_{u},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.v()); // R_{u},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.u()); // R_{v},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.v()); // R_{v},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kus =
context.get_elem_jacobian(this->_flow_vars.u(),
this->fan_speed_var()); // R_{u},{s}
libMesh::DenseSubMatrix<libMesh::Number> &Ksu =
context.get_elem_jacobian(this->fan_speed_var(),
this->_flow_vars.u()); // R_{s},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvs =
context.get_elem_jacobian(this->_flow_vars.v(),
this->fan_speed_var()); // R_{v},{s}
libMesh::DenseSubMatrix<libMesh::Number> &Ksv =
context.get_elem_jacobian(this->fan_speed_var(),
this->_flow_vars.v()); // R_{s},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kss =
context.get_elem_jacobian(this->fan_speed_var(),
this->fan_speed_var()); // R_{s},{s}
libMesh::DenseSubMatrix<libMesh::Number>* Kwu = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kwv = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kww = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kuw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kvw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Ksw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kws = NULL;
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v()); // R_{v}
libMesh::DenseSubVector<libMesh::Number>* Fw = NULL;
libMesh::DenseSubVector<libMesh::Number> &Fs = context.get_elem_residual(this->fan_speed_var()); // R_{s}
if( this->mesh_dim(context) == 3 )
{
Kuw = &context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.w()); // R_{u},{w}
Kvw = &context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.w()); // R_{v},{w}
Kwu = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.u()); // R_{w},{u}
Kwv = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.v()); // R_{w},{v}
Kww = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.w()); // R_{w},{w}
Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
Ksw = &context.get_elem_jacobian(this->fan_speed_var(), this->_flow_vars.w()); // R_{s},{w}
Kws = &context.get_elem_jacobian(this->_flow_vars.w(), this->fan_speed_var()); // R_{w},{s}
Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Compute the solution at the old Newton iterate.
libMesh::Number u, v, s;
u = context.interior_value(this->_flow_vars.u(), qp);
v = context.interior_value(this->_flow_vars.v(), qp);
s = context.interior_value(this->fan_speed_var(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->mesh_dim(context) == 3)
U(2) = context.interior_value(this->_flow_vars.w(), qp); // w
libMesh::NumberVectorValue U_B_1;
libMesh::NumberVectorValue F;
libMesh::NumberTensorValue dFdU;
libMesh::NumberTensorValue* dFdU_ptr =
compute_jacobian ? &dFdU : NULL;
libMesh::NumberVectorValue dFds;
libMesh::NumberVectorValue* dFds_ptr =
compute_jacobian ? &dFds : NULL;
if (!this->compute_force(u_qpoint[qp], context.time, U, s,
U_B_1, F, dFdU_ptr, dFds_ptr))
continue;
libMesh::Real jac = JxW[qp];
// Using this dot product to derive torque *depends* on s=1
// and U_B_1 corresponding to 1 rad/sec base velocity; this
// means that the length of U_B_1 is equal to radius.
// F is the force on the air, so *negative* F is the force on
// the turbine.
Fs(0) -= U_B_1 * F * jac;
if (compute_jacobian)
{
Kss(0,0) -= U_B_1 * dFds * jac;
for (unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::Real jac_j = JxW[qp] * u_phi[j][qp];
for (unsigned int d=0; d != 3; ++d)
{
Ksu(0,j) -= jac_j * U_B_1(d) * dFdU(d,0);
Ksv(0,j) -= jac_j * U_B_1(d) * dFdU(d,1);
}
if (this->mesh_dim(context) == 3)
{
for (unsigned int d=0; d != 3; ++d)
(*Ksw)(0,j) -= jac_j * U_B_1(d) * dFdU(d,2);
}
} // End j dof loop
}
for (unsigned int i=0; i != n_u_dofs; i++)
{
const libMesh::Number jac_i = jac * u_phi[i][qp];
Fu(i) += F(0)*jac_i;
Fv(i) += F(1)*jac_i;
if( this->mesh_dim(context) == 3 )
(*Fw)(i) += F(2)*jac_i;
if( compute_jacobian )
{
Kus(i,0) += dFds(0) * jac_i;
Kvs(i,0) += dFds(1) * jac_i;
if( this->mesh_dim(context) == 3 )
(*Kws)(i,0) += dFds(2) * jac_i;
for (unsigned int j=0; j != n_u_dofs; j++)
{
const libMesh::Number jac_ij = jac_i * u_phi[j][qp];
Kuu(i,j) += jac_ij * dFdU(0,0);
Kuv(i,j) += jac_ij * dFdU(0,1);
Kvu(i,j) += jac_ij * dFdU(1,0);
Kvv(i,j) += jac_ij * dFdU(1,1);
if( this->mesh_dim(context) == 3 )
{
(*Kuw)(i,j) += jac_ij * dFdU(0,2);
(*Kvw)(i,j) += jac_ij * dFdU(1,2);
(*Kwu)(i,j) += jac_ij * dFdU(2,0);
(*Kwv)(i,j) += jac_ij * dFdU(2,1);
(*Kww)(i,j) += jac_ij * dFdU(2,2);
}
}
}
}
}
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("AveragedTurbine::element_time_derivative");
#endif
return;
}
void ElasticCableRayleighDamping<StressStrainLaw>::damping_residual( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/)
{
// First, do the "mass" contribution
this->mass_residual_impl(compute_jacobian,
context,
&libMesh::FEMContext::interior_rate,
&libMesh::DiffContext::get_elem_solution_rate_derivative,
_mu_factor);
// Now do the stiffness contribution
const unsigned int n_u_dofs = context.get_dof_indices(this->_disp_vars.u()).size();
const std::vector<libMesh::Real> &JxW =
this->get_fe(context)->get_JxW();
// Residuals that we're populating
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_disp_vars.u());
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_disp_vars.v());
libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(this->_disp_vars.w());
//Grab the Jacobian matrix as submatrices
//libMesh::DenseMatrix<libMesh::Number> &K = context.get_elem_jacobian();
libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.v());
libMesh::DenseSubMatrix<libMesh::Number> &Kuw = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.v());
libMesh::DenseSubMatrix<libMesh::Number> &Kvw = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number> &Kwu = context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number> &Kwv = context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.v());
libMesh::DenseSubMatrix<libMesh::Number> &Kww = context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.w());
unsigned int n_qpoints = context.get_element_qrule().n_points();
// All shape function gradients are w.r.t. master element coordinates
const std::vector<std::vector<libMesh::Real> >& dphi_dxi = this->get_fe(context)->get_dphidxi();
const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( this->_disp_vars.u() );
const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( this->_disp_vars.v() );
const libMesh::DenseSubVector<libMesh::Number>& w_coeffs = context.get_elem_solution( this->_disp_vars.w() );
const libMesh::DenseSubVector<libMesh::Number>& dudt_coeffs = context.get_elem_solution_rate( this->_disp_vars.u() );
const libMesh::DenseSubVector<libMesh::Number>& dvdt_coeffs = context.get_elem_solution_rate( this->_disp_vars.v() );
const libMesh::DenseSubVector<libMesh::Number>& dwdt_coeffs = context.get_elem_solution_rate( this->_disp_vars.w() );
// Need these to build up the covariant and contravariant metric tensors
const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi();
const unsigned int dim = 1; // The cable dimension is always 1 for this physics
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Gradients are w.r.t. master element coordinates
libMesh::Gradient grad_u, grad_v, grad_w;
libMesh::Gradient dgradu_dt, dgradv_dt, dgradw_dt;
for( unsigned int d = 0; d < n_u_dofs; d++ )
{
libMesh::RealGradient u_gradphi( dphi_dxi[d][qp] );
grad_u += u_coeffs(d)*u_gradphi;
grad_v += v_coeffs(d)*u_gradphi;
grad_w += w_coeffs(d)*u_gradphi;
dgradu_dt += dudt_coeffs(d)*u_gradphi;
dgradv_dt += dvdt_coeffs(d)*u_gradphi;
dgradw_dt += dwdt_coeffs(d)*u_gradphi;
}
libMesh::RealGradient grad_x( dxdxi[qp](0) );
libMesh::RealGradient grad_y( dxdxi[qp](1) );
libMesh::RealGradient grad_z( dxdxi[qp](2) );
libMesh::TensorValue<libMesh::Real> a_cov, a_contra, A_cov, A_contra;
libMesh::Real lambda_sq = 0;
this->compute_metric_tensors( qp, *(this->get_fe(context)), context,
grad_u, grad_v, grad_w,
a_cov, a_contra, A_cov, A_contra,
lambda_sq );
// Compute stress tensor
libMesh::TensorValue<libMesh::Real> tau;
ElasticityTensor C;
this->_stress_strain_law.compute_stress_and_elasticity(dim,a_contra,a_cov,A_contra,A_cov,tau,C);
libMesh::Real jac = JxW[qp];
for (unsigned int i=0; i != n_u_dofs; i++)
{
libMesh::RealGradient u_gradphi( dphi_dxi[i][qp] );
libMesh::Real u_diag_factor = _lambda_factor*this->_A*jac*tau(0,0)*dgradu_dt(0)*u_gradphi(0);
libMesh::Real v_diag_factor = _lambda_factor*this->_A*jac*tau(0,0)*dgradv_dt(0)*u_gradphi(0);
libMesh::Real w_diag_factor = _lambda_factor*this->_A*jac*tau(0,0)*dgradw_dt(0)*u_gradphi(0);
const libMesh::Real C1 = _lambda_factor*this->_A*jac*C(0,0,0,0)*u_gradphi(0);
const libMesh::Real gamma_u = (grad_x(0)+grad_u(0));
const libMesh::Real gamma_v = (grad_y(0)+grad_v(0));
const libMesh::Real gamma_w = (grad_z(0)+grad_w(0));
const libMesh::Real x_term = C1*gamma_u;
const libMesh::Real y_term = C1*gamma_v;
const libMesh::Real z_term = C1*gamma_w;
const libMesh::Real dt_term = dgradu_dt(0)*gamma_u + dgradv_dt(0)*gamma_v + dgradw_dt(0)*gamma_w;
Fu(i) += u_diag_factor + x_term*dt_term;
Fv(i) += v_diag_factor + y_term*dt_term;
Fw(i) += w_diag_factor + z_term*dt_term;
}
if( compute_jacobian )
{
for(unsigned int i=0; i != n_u_dofs; i++)
{
libMesh::RealGradient u_gradphi_I( dphi_dxi[i][qp] );
for(unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::RealGradient u_gradphi_J( dphi_dxi[j][qp] );
libMesh::Real common_factor = _lambda_factor*this->_A*jac*u_gradphi_I(0);
const libMesh::Real diag_term_1 = common_factor*tau(0,0)*u_gradphi_J(0)*context.get_elem_solution_rate_derivative();
const libMesh::Real dgamma_du = ( u_gradphi_J(0)*(grad_x(0)+grad_u(0)) );
const libMesh::Real dgamma_dv = ( u_gradphi_J(0)*(grad_y(0)+grad_v(0)) );
const libMesh::Real dgamma_dw = ( u_gradphi_J(0)*(grad_z(0)+grad_w(0)) );
const libMesh::Real diag_term_2_factor = common_factor*C(0,0,0,0)*context.get_elem_solution_derivative();
Kuu(i,j) += diag_term_1 + dgradu_dt(0)*diag_term_2_factor*dgamma_du;
Kuv(i,j) += dgradu_dt(0)*diag_term_2_factor*dgamma_dv;
Kuw(i,j) += dgradu_dt(0)*diag_term_2_factor*dgamma_dw;
Kvu(i,j) += dgradv_dt(0)*diag_term_2_factor*dgamma_du;
Kvv(i,j) += diag_term_1 + dgradv_dt(0)*diag_term_2_factor*dgamma_dv;
Kvw(i,j) += dgradv_dt(0)*diag_term_2_factor*dgamma_dw;
Kwu(i,j) += dgradw_dt(0)*diag_term_2_factor*dgamma_du;
Kwv(i,j) += dgradw_dt(0)*diag_term_2_factor*dgamma_dv;
Kww(i,j) += diag_term_1 + dgradw_dt(0)*diag_term_2_factor*dgamma_dw;
const libMesh::Real C1 = common_factor*C(0,0,0,0);
const libMesh::Real gamma_u = (grad_x(0)+grad_u(0));
const libMesh::Real gamma_v = (grad_y(0)+grad_v(0));
const libMesh::Real gamma_w = (grad_z(0)+grad_w(0));
const libMesh::Real x_term = C1*gamma_u;
const libMesh::Real y_term = C1*gamma_v;
const libMesh::Real z_term = C1*gamma_w;
const libMesh::Real ddtterm_du = u_gradphi_J(0)*(gamma_u*context.get_elem_solution_rate_derivative()
+ dgradu_dt(0)*context.get_elem_solution_derivative());
const libMesh::Real ddtterm_dv = u_gradphi_J(0)*(gamma_v*context.get_elem_solution_rate_derivative()
+ dgradv_dt(0)*context.get_elem_solution_derivative());
const libMesh::Real ddtterm_dw = u_gradphi_J(0)*(gamma_w*context.get_elem_solution_rate_derivative()
+ dgradw_dt(0)*context.get_elem_solution_derivative());
Kuu(i,j) += x_term*ddtterm_du;
Kuv(i,j) += x_term*ddtterm_dv;
Kuw(i,j) += x_term*ddtterm_dw;
Kvu(i,j) += y_term*ddtterm_du;
Kvv(i,j) += y_term*ddtterm_dv;
Kvw(i,j) += y_term*ddtterm_dw;
Kwu(i,j) += z_term*ddtterm_du;
Kwv(i,j) += z_term*ddtterm_dv;
Kww(i,j) += z_term*ddtterm_dw;
const libMesh::Real dt_term = dgradu_dt(0)*gamma_u + dgradv_dt(0)*gamma_v + dgradw_dt(0)*gamma_w;
// Here, we're missing derivatives of C(0,0,0,0) w.r.t. strain
// Nonzero for hyperelasticity models
const libMesh::Real dxterm_du = C1*u_gradphi_J(0)*context.get_elem_solution_derivative();
const libMesh::Real dyterm_dv = dxterm_du;
const libMesh::Real dzterm_dw = dxterm_du;
Kuu(i,j) += dxterm_du*dt_term;
Kvv(i,j) += dyterm_dv*dt_term;
Kww(i,j) += dzterm_dw*dt_term;
} // end j-loop
} // end i-loop
} // end if(compute_jacobian)
} // end qp loop
}
void ElasticMembranePressure<PressureType>::element_time_derivative
( bool compute_jacobian, AssemblyContext & context )
{
unsigned int u_var = this->_disp_vars.u();
unsigned int v_var = this->_disp_vars.v();
unsigned int w_var = this->_disp_vars.w();
const unsigned int n_u_dofs = context.get_dof_indices(u_var).size();
const std::vector<libMesh::Real> &JxW =
this->get_fe(context)->get_JxW();
const std::vector<std::vector<libMesh::Real> >& u_phi =
this->get_fe(context)->get_phi();
const MultiphysicsSystem & system = context.get_multiphysics_system();
unsigned int u_dot_var = system.get_second_order_dot_var(u_var);
unsigned int v_dot_var = system.get_second_order_dot_var(v_var);
unsigned int w_dot_var = system.get_second_order_dot_var(w_var);
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(u_dot_var);
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(v_dot_var);
libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(w_dot_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kuv = context.get_elem_jacobian(u_dot_var,v_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kuw = context.get_elem_jacobian(u_dot_var,w_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kvu = context.get_elem_jacobian(v_dot_var,u_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kvw = context.get_elem_jacobian(v_dot_var,w_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kwu = context.get_elem_jacobian(w_dot_var,u_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kwv = context.get_elem_jacobian(w_dot_var,v_var);
unsigned int n_qpoints = context.get_element_qrule().n_points();
// All shape function gradients are w.r.t. master element coordinates
const std::vector<std::vector<libMesh::Real> >& dphi_dxi =
this->get_fe(context)->get_dphidxi();
const std::vector<std::vector<libMesh::Real> >& dphi_deta =
this->get_fe(context)->get_dphideta();
const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( u_var );
const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( v_var );
const libMesh::DenseSubVector<libMesh::Number>& w_coeffs = context.get_elem_solution( w_var );
const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi();
const std::vector<libMesh::RealGradient>& dxdeta = this->get_fe(context)->get_dxyzdeta();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// sqrt(det(a_cov)), a_cov being the covariant metric tensor of undeformed body
libMesh::Real sqrt_a = sqrt( dxdxi[qp]*dxdxi[qp]*dxdeta[qp]*dxdeta[qp]
- dxdxi[qp]*dxdeta[qp]*dxdeta[qp]*dxdxi[qp] );
// Gradients are w.r.t. master element coordinates
libMesh::Gradient grad_u, grad_v, grad_w;
for( unsigned int d = 0; d < n_u_dofs; d++ )
{
libMesh::RealGradient u_gradphi( dphi_dxi[d][qp], dphi_deta[d][qp] );
grad_u += u_coeffs(d)*u_gradphi;
grad_v += v_coeffs(d)*u_gradphi;
grad_w += w_coeffs(d)*u_gradphi;
}
libMesh::RealGradient dudxi( grad_u(0), grad_v(0), grad_w(0) );
libMesh::RealGradient dudeta( grad_u(1), grad_v(1), grad_w(1) );
libMesh::RealGradient A_1 = dxdxi[qp] + dudxi;
libMesh::RealGradient A_2 = dxdeta[qp] + dudeta;
libMesh::RealGradient A_3 = A_1.cross(A_2);
// Compute pressure at this quadrature point
libMesh::Real press = (*_pressure)(context,qp);
// Small optimization
libMesh::Real p_over_sa = press/sqrt_a;
/* The formula here is actually
P*\sqrt{\frac{A}{a}}*A_3, where A_3 is a unit vector
But, |A_3| = \sqrt{A} so the normalizing part kills
the \sqrt{A} in the numerator, so we can leave it out
and *not* normalize A_3.
*/
libMesh::RealGradient traction = p_over_sa*A_3;
for (unsigned int i=0; i != n_u_dofs; i++)
{
// Small optimization
libMesh::Real phi_times_jac = u_phi[i][qp]*JxW[qp];
Fu(i) -= traction(0)*phi_times_jac;
Fv(i) -= traction(1)*phi_times_jac;
Fw(i) -= traction(2)*phi_times_jac;
if( compute_jacobian )
{
for (unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::RealGradient u_gradphi( dphi_dxi[j][qp], dphi_deta[j][qp] );
const libMesh::Real dt0_dv = p_over_sa*(u_gradphi(0)*A_2(2) - A_1(2)*u_gradphi(1));
const libMesh::Real dt0_dw = p_over_sa*(A_1(1)*u_gradphi(1) - u_gradphi(0)*A_2(1));
const libMesh::Real dt1_du = p_over_sa*(A_1(2)*u_gradphi(1) - u_gradphi(0)*A_2(2));
const libMesh::Real dt1_dw = p_over_sa*(u_gradphi(0)*A_2(0) - A_1(0)*u_gradphi(1));
const libMesh::Real dt2_du = p_over_sa*(u_gradphi(0)*A_2(1) - A_1(1)*u_gradphi(1));
const libMesh::Real dt2_dv = p_over_sa*(A_1(0)*u_gradphi(1) - u_gradphi(0)*A_2(0));
Kuv(i,j) -= dt0_dv*phi_times_jac;
Kuw(i,j) -= dt0_dw*phi_times_jac;
Kvu(i,j) -= dt1_du*phi_times_jac;
Kvw(i,j) -= dt1_dw*phi_times_jac;
Kwu(i,j) -= dt2_du*phi_times_jac;
Kwv(i,j) -= dt2_dv*phi_times_jac;
}
}
}
}
}
void VelocityPenalty<Mu>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /* cache */ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("VelocityPenalty::element_time_derivative");
#endif
// Element Jacobian * quadrature weights for interior integration
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_flow_vars.u_var())->get_JxW();
// The shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& u_phi =
context.get_element_fe(this->_flow_vars.u_var())->get_phi();
const std::vector<libMesh::Point>& u_qpoint =
context.get_element_fe(this->_flow_vars.u_var())->get_xyz();
// The number of local degrees of freedom in each variable
const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u_var()).size();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_flow_vars.u_var(), this->_flow_vars.u_var()); // R_{u},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_flow_vars.u_var(), this->_flow_vars.v_var()); // R_{u},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_flow_vars.v_var(), this->_flow_vars.u_var()); // R_{v},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_flow_vars.v_var(), this->_flow_vars.v_var()); // R_{v},{v}
libMesh::DenseSubMatrix<libMesh::Number>* Kwu = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kwv = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kww = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kuw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kvw = NULL;
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u_var()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v_var()); // R_{v}
libMesh::DenseSubVector<libMesh::Number>* Fw = NULL;
if( this->_dim == 3 )
{
Kuw = &context.get_elem_jacobian(this->_flow_vars.u_var(), this->_flow_vars.w_var()); // R_{u},{w}
Kvw = &context.get_elem_jacobian(this->_flow_vars.v_var(), this->_flow_vars.w_var()); // R_{v},{w}
Kwu = &context.get_elem_jacobian(this->_flow_vars.w_var(), this->_flow_vars.u_var()); // R_{w},{u}
Kwv = &context.get_elem_jacobian(this->_flow_vars.w_var(), this->_flow_vars.v_var()); // R_{w},{v}
Kww = &context.get_elem_jacobian(this->_flow_vars.w_var(), this->_flow_vars.w_var()); // R_{w},{w}
Fw = &context.get_elem_residual(this->_flow_vars.w_var()); // R_{w}
}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Compute the solution at the old Newton iterate.
libMesh::Number u, v;
u = context.interior_value(this->_flow_vars.u_var(), qp);
v = context.interior_value(this->_flow_vars.v_var(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->_dim == 3)
U(2) = context.interior_value(this->_flow_vars.w_var(), qp); // w
libMesh::NumberVectorValue F;
libMesh::NumberTensorValue dFdU;
libMesh::NumberTensorValue* dFdU_ptr =
compute_jacobian ? &dFdU : NULL;
if (!this->compute_force(u_qpoint[qp], context, U, F, dFdU_ptr))
continue;
const libMesh::Real jac = JxW[qp];
for (unsigned int i=0; i != n_u_dofs; i++)
{
const libMesh::Number jac_i = jac * u_phi[i][qp];
Fu(i) += F(0)*jac_i;
Fv(i) += F(1)*jac_i;
if( this->_dim == 3 )
{
(*Fw)(i) += F(2)*jac_i;
}
if( compute_jacobian )
{
for (unsigned int j=0; j != n_u_dofs; j++)
{
const libMesh::Number jac_ij = context.get_elem_solution_derivative() * jac_i * u_phi[j][qp];
Kuu(i,j) += jac_ij * dFdU(0,0);
Kuv(i,j) += jac_ij * dFdU(0,1);
Kvu(i,j) += jac_ij * dFdU(1,0);
Kvv(i,j) += jac_ij * dFdU(1,1);
if( this->_dim == 3 )
{
(*Kuw)(i,j) += jac_ij * dFdU(0,2);
(*Kvw)(i,j) += jac_ij * dFdU(1,2);
(*Kwu)(i,j) += jac_ij * dFdU(2,0);
(*Kwv)(i,j) += jac_ij * dFdU(2,1);
(*Kww)(i,j) += jac_ij * dFdU(2,2);
}
}
}
}
}
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("VelocityPenalty::element_time_derivative");
#endif
return;
}
// The matrix assembly function to be called at each time step to
// prepare for the linear solve.
void assemble_solid (EquationSystems& es,
const std::string& system_name)
{
//es.print_info();
#if LOG_ASSEMBLE_PERFORMANCE
PerfLog perf_log("Assemble");
perf_log.push("assemble stiffness");
#endif
// Get a reference to the auxiliary system
//TransientExplicitSystem& aux_system = es.get_system<TransientExplicitSystem>("Newton-update");
// It is a good idea to make sure we are assembling
// the proper system.
libmesh_assert (system_name == "Newton-update");
// Get a constant reference to the mesh object.
const MeshBase& mesh = es.get_mesh();
// The dimension that we are running
const unsigned int dim = mesh.mesh_dimension();
// Get a reference to the Stokes system object.
TransientLinearImplicitSystem & newton_update =
es.get_system<TransientLinearImplicitSystem> ("Newton-update");
// New
TransientLinearImplicitSystem & last_non_linear_soln =
es.get_system<TransientLinearImplicitSystem> ("Last-non-linear-soln");
TransientLinearImplicitSystem & fluid_system_vel =
es.get_system<TransientLinearImplicitSystem> ("fluid-system-vel");
#if VELOCITY
TransientLinearImplicitSystem& velocity = es.get_system<TransientLinearImplicitSystem>("velocity-system");
#endif
#if UN_MINUS_ONE
TransientLinearImplicitSystem & unm1 =
es.get_system<TransientLinearImplicitSystem> ("unm1-system");
#endif
test(62);
const System & ref_sys = es.get_system("Reference-Configuration");
test(63);
// Numeric ids corresponding to each variable in the system
const unsigned int u_var = last_non_linear_soln .variable_number ("u");
const unsigned int v_var = last_non_linear_soln .variable_number ("v");
const unsigned int w_var = last_non_linear_soln .variable_number ("w");
#if INCOMPRESSIBLE
const unsigned int p_var = last_non_linear_soln .variable_number ("p");
#endif
#if FLUID_P_CONST
const unsigned int m_var = fluid_system_vel.variable_number ("fluid_M");
std::vector<unsigned int> dof_indices_m;
#endif
// Get the Finite Element type for "u". Note this will be
// the same as the type for "v".
FEType fe_vel_type = last_non_linear_soln.variable_type(u_var);
test(64);
#if INCOMPRESSIBLE
// Get the Finite Element type for "p".
FEType fe_pres_type = last_non_linear_soln .variable_type(p_var);
#endif
// Build a Finite Element object of the specified type for
// the velocity variables.
AutoPtr<FEBase> fe_vel (FEBase::build(dim, fe_vel_type));
#if INCOMPRESSIBLE
// Build a Finite Element object of the specified type for
// the pressure variables.
AutoPtr<FEBase> fe_pres (FEBase::build(dim, fe_pres_type));
#endif
// A Gauss quadrature rule for numerical integration.
// Let the \p FEType object decide what order rule is appropriate.
QGauss qrule (dim, fe_vel_type.default_quadrature_order());
// Tell the finite element objects to use our quadrature rule.
fe_vel->attach_quadrature_rule (&qrule);
test(65);
// AutoPtr<QBase> qrule2(fe_vel_type.default_quadrature_rule(dim));
// fe_vel->attach_quadrature_rule (qrule2.get());
#if INCOMPRESSIBLE
fe_pres->attach_quadrature_rule (&qrule);
#endif
// The element Jacobian * quadrature weight at each integration point.
const std::vector<Real>& JxW = fe_vel->get_JxW();
// The element shape functions evaluated at the quadrature points.
const std::vector<std::vector<Real> >& phi = fe_vel->get_phi();
// The element shape function gradients for the velocity
// variables evaluated at the quadrature points.
const std::vector<std::vector<RealGradient> >& dphi = fe_vel->get_dphi();
test(66);
#if INCOMPRESSIBLE
// The element shape functions for the pressure variable
// evaluated at the quadrature points.
const std::vector<std::vector<Real> >& psi = fe_pres->get_phi();
#endif
const std::vector<Point>& coords = fe_vel->get_xyz();
// A reference to the \p DofMap object for this system. The \p DofMap
// object handles the index translation from node and element numbers
// to degree of freedom numbers. We will talk more about the \p DofMap
// in future examples.
const DofMap & dof_map = last_non_linear_soln .get_dof_map();
#if FLUID_P_CONST
const DofMap & dof_map_fluid = fluid_system_vel .get_dof_map();
#endif
// K will be the jacobian
// F will be the Residual
DenseMatrix<Number> Ke;
DenseVector<Number> Fe;
DenseSubMatrix<Number>
Kuu(Ke), Kuv(Ke), Kuw(Ke),
Kvu(Ke), Kvv(Ke), Kvw(Ke),
Kwu(Ke), Kwv(Ke), Kww(Ke);
#if INCOMPRESSIBLE
DenseSubMatrix<Number> Kup(Ke),Kvp(Ke),Kwp(Ke), Kpu(Ke), Kpv(Ke), Kpw(Ke), Kpp(Ke);
#endif;
DenseSubVector<Number>
Fu(Fe), Fv(Fe), Fw(Fe);
#if INCOMPRESSIBLE
DenseSubVector<Number> Fp(Fe);
#endif
// This vector will hold the degree of freedom indices for
// the element. These define where in the global system
// the element degrees of freedom get mapped.
std::vector<unsigned int> dof_indices;
std::vector<unsigned int> dof_indices_u;
std::vector<unsigned int> dof_indices_v;
std::vector<unsigned int> dof_indices_w;
#if INCOMPRESSIBLE
std::vector<unsigned int> dof_indices_p;
#endif
#if INERTIA
test(67);
const unsigned int a_var = last_non_linear_soln.variable_number ("a");
const unsigned int b_var = last_non_linear_soln.variable_number ("b");
const unsigned int c_var = last_non_linear_soln.variable_number ("c");
//B block
DenseSubMatrix<Number>
Kua(Ke), Kub(Ke), Kuc(Ke),
Kva(Ke), Kvb(Ke), Kvc(Ke),
Kwa(Ke), Kwb(Ke), Kwc(Ke);
//C block
DenseSubMatrix<Number>
Kau(Ke), Kav(Ke), Kaw(Ke),
Kbu(Ke), Kbv(Ke), Kbw(Ke),
Kcu(Ke), Kcv(Ke), Kcw(Ke);
//D block
DenseSubMatrix<Number>
Kaa(Ke), Kab(Ke), Kac(Ke),
Kba(Ke), Kbb(Ke), Kbc(Ke),
Kca(Ke), Kcb(Ke), Kcc(Ke);
DenseSubVector<Number>
Fa(Fe), Fb(Fe), Fc(Fe);
std::vector<unsigned int> dof_indices_a;
std::vector<unsigned int> dof_indices_b;
std::vector<unsigned int> dof_indices_c;
test(68);
#endif
DenseMatrix<Real> stiff;
DenseVector<Real> res;
VectorValue<Gradient> grad_u_mat;
VectorValue<Gradient> grad_u_mat_old;
const Real dt = es.parameters.get<Real>("dt");
const Real progress = es.parameters.get<Real>("progress");
#if PORO
DenseVector<Real> p_stiff;
DenseVector<Real> p_res;
PoroelasticConfig material(dphi,psi);
#endif
// Just calculate jacobian contribution when we need to
material.calculate_linearized_stiffness = true;
MeshBase::const_element_iterator el = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator end_el = mesh.active_local_elements_end();
for ( ; el != end_el; ++el)
{
test(69);
const Elem* elem = *el;
dof_map.dof_indices (elem, dof_indices);
dof_map.dof_indices (elem, dof_indices_u, u_var);
dof_map.dof_indices (elem, dof_indices_v, v_var);
dof_map.dof_indices (elem, dof_indices_w, w_var);
#if INCOMPRESSIBLE
dof_map.dof_indices (elem, dof_indices_p, p_var);
#endif
const unsigned int n_dofs = dof_indices.size();
const unsigned int n_u_dofs = dof_indices_u.size();
const unsigned int n_v_dofs = dof_indices_v.size();
const unsigned int n_w_dofs = dof_indices_w.size();
#if INCOMPRESSIBLE
const unsigned int n_p_dofs = dof_indices_p.size();
#endif
#if FLUID_P_CONST
dof_map_fluid.dof_indices (elem, dof_indices_m, m_var);
#endif
//elem->print_info();
fe_vel->reinit (elem);
#if INCOMPRESSIBLE
fe_pres->reinit (elem);
#endif
Ke.resize (n_dofs, n_dofs);
Fe.resize (n_dofs);
Kuu.reposition (u_var*n_u_dofs, u_var*n_u_dofs, n_u_dofs, n_u_dofs);
Kuv.reposition (u_var*n_u_dofs, v_var*n_u_dofs, n_u_dofs, n_v_dofs);
Kuw.reposition (u_var*n_u_dofs, w_var*n_u_dofs, n_u_dofs, n_w_dofs);
#if INCOMPRESSIBLE
Kup.reposition (u_var*n_u_dofs, p_var*n_u_dofs, n_u_dofs, n_p_dofs);
#endif
Kvu.reposition (v_var*n_v_dofs, u_var*n_v_dofs, n_v_dofs, n_u_dofs);
Kvv.reposition (v_var*n_v_dofs, v_var*n_v_dofs, n_v_dofs, n_v_dofs);
Kvw.reposition (v_var*n_v_dofs, w_var*n_v_dofs, n_v_dofs, n_w_dofs);
#if INCOMPRESSIBLE
Kvp.reposition (v_var*n_v_dofs, p_var*n_v_dofs, n_v_dofs, n_p_dofs);
#endif
Kwu.reposition (w_var*n_w_dofs, u_var*n_w_dofs, n_w_dofs, n_u_dofs);
Kwv.reposition (w_var*n_w_dofs, v_var*n_w_dofs, n_w_dofs, n_v_dofs);
Kww.reposition (w_var*n_w_dofs, w_var*n_w_dofs, n_w_dofs, n_w_dofs);
#if INCOMPRESSIBLE
Kwp.reposition (w_var*n_w_dofs, p_var*n_w_dofs, n_w_dofs, n_p_dofs);
Kpu.reposition (p_var*n_u_dofs, u_var*n_u_dofs, n_p_dofs, n_u_dofs);
Kpv.reposition (p_var*n_u_dofs, v_var*n_u_dofs, n_p_dofs, n_v_dofs);
Kpw.reposition (p_var*n_u_dofs, w_var*n_u_dofs, n_p_dofs, n_w_dofs);
Kpp.reposition (p_var*n_u_dofs, p_var*n_u_dofs, n_p_dofs, n_p_dofs);
#endif
Fu.reposition (u_var*n_u_dofs, n_u_dofs);
Fv.reposition (v_var*n_u_dofs, n_v_dofs);
Fw.reposition (w_var*n_u_dofs, n_w_dofs);
#if INCOMPRESSIBLE
Fp.reposition (p_var*n_u_dofs, n_p_dofs);
#endif
#if INERTIA
//B block
Kua.reposition (u_var*n_u_dofs, 3*n_u_dofs + n_p_dofs, n_u_dofs, n_u_dofs);
Kub.reposition (u_var*n_u_dofs, 4*n_u_dofs + n_p_dofs, n_u_dofs, n_v_dofs);
Kuc.reposition (u_var*n_u_dofs, 5*n_u_dofs + n_p_dofs, n_u_dofs, n_w_dofs);
Kva.reposition (v_var*n_v_dofs, 3*n_u_dofs + n_p_dofs, n_v_dofs, n_u_dofs);
Kvb.reposition (v_var*n_v_dofs, 4*n_u_dofs + n_p_dofs, n_v_dofs, n_v_dofs);
Kvc.reposition (v_var*n_v_dofs, 5*n_u_dofs + n_p_dofs, n_v_dofs, n_w_dofs);
Kwa.reposition (w_var*n_w_dofs, 3*n_u_dofs + n_p_dofs, n_w_dofs, n_u_dofs);
Kwb.reposition (w_var*n_w_dofs, 4*n_u_dofs + n_p_dofs, n_w_dofs, n_v_dofs);
Kwc.reposition (w_var*n_w_dofs, 5*n_u_dofs + n_p_dofs, n_w_dofs, n_w_dofs);
test(701);
//C block
Kau.reposition (3*n_u_dofs + n_p_dofs, u_var*n_u_dofs, n_u_dofs, n_u_dofs);
Kav.reposition (3*n_u_dofs + n_p_dofs, v_var*n_u_dofs, n_u_dofs, n_v_dofs);
Kaw.reposition (3*n_u_dofs + n_p_dofs, w_var*n_u_dofs, n_u_dofs, n_w_dofs);
Kbu.reposition (4*n_u_dofs + n_p_dofs, u_var*n_v_dofs, n_v_dofs, n_u_dofs);
Kbv.reposition (4*n_u_dofs + n_p_dofs, v_var*n_v_dofs, n_v_dofs, n_v_dofs);
Kbw.reposition (4*n_u_dofs + n_p_dofs, w_var*n_v_dofs, n_v_dofs, n_w_dofs);
Kcu.reposition (5*n_u_dofs + n_p_dofs, u_var*n_w_dofs, n_w_dofs, n_u_dofs);
Kcv.reposition (5*n_u_dofs + n_p_dofs, v_var*n_w_dofs, n_w_dofs, n_v_dofs);
Kcw.reposition (5*n_u_dofs + n_p_dofs, w_var*n_w_dofs, n_w_dofs, n_w_dofs);
//D block
Kaa.reposition (3*n_u_dofs + n_p_dofs, 3*n_u_dofs + n_p_dofs, n_u_dofs, n_u_dofs);
Kab.reposition (3*n_u_dofs + n_p_dofs, 4*n_u_dofs + n_p_dofs, n_u_dofs, n_v_dofs);
Kac.reposition (3*n_u_dofs + n_p_dofs, 5*n_u_dofs + n_p_dofs, n_u_dofs, n_w_dofs);
Kba.reposition (4*n_u_dofs + n_p_dofs, 3*n_u_dofs + n_p_dofs, n_v_dofs, n_u_dofs);
Kbb.reposition (4*n_u_dofs + n_p_dofs, 4*n_u_dofs + n_p_dofs, n_v_dofs, n_v_dofs);
Kbc.reposition (4*n_u_dofs + n_p_dofs, 5*n_u_dofs + n_p_dofs, n_v_dofs, n_w_dofs);
Kca.reposition (5*n_u_dofs + n_p_dofs, 3*n_u_dofs + n_p_dofs, n_w_dofs, n_u_dofs);
Kcb.reposition (5*n_u_dofs + n_p_dofs, 4*n_u_dofs + n_p_dofs, n_w_dofs, n_v_dofs);
Kcc.reposition (5*n_u_dofs + n_p_dofs, 5*n_u_dofs + n_p_dofs, n_w_dofs, n_w_dofs);
Fa.reposition (3*n_u_dofs + n_p_dofs, n_u_dofs);
Fb.reposition (4*n_u_dofs + n_p_dofs, n_v_dofs);
Fc.reposition (5*n_u_dofs + n_p_dofs, n_w_dofs);
dof_map.dof_indices (elem, dof_indices_a, a_var);
dof_map.dof_indices (elem, dof_indices_b, b_var);
dof_map.dof_indices (elem, dof_indices_c, c_var);
test(71);
#endif
System& aux_system = es.get_system<System>("Reference-Configuration");
std::vector<unsigned int> undefo_index;
std::vector<unsigned int> vel_index;
for (unsigned int qp=0; qp<qrule.n_points(); qp++)
{
Point rX;
for (unsigned int l=0; l<n_u_dofs; l++)
{
rX(0) += phi[l][qp]*ref_sys.current_local_solution->el(dof_indices_u[l]);
rX(1) += phi[l][qp]*ref_sys.current_local_solution->el(dof_indices_v[l]);
rX(2) += phi[l][qp]*ref_sys.current_local_solution->el(dof_indices_w[l]);
}
#if INERTIA || DT
test(72);
Real rho_s=15;
Point current_x;
for (unsigned int l=0; l<n_u_dofs; l++)
{
current_x(0) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_u[l]);
current_x(1) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_v[l]);
current_x(2) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_w[l]);
}
Point old_x;
for (unsigned int l=0; l<n_u_dofs; l++)
{
old_x(0) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_u[l]);
old_x(1) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_v[l]);
old_x(2) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_w[l]);
}
#if INERTIA
Point old_vel;
for (unsigned int l=0; l<n_u_dofs; l++)
{
old_vel(0) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_a[l]);
old_vel(1) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_b[l]);
old_vel(2) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_c[l]);
}
Point current_vel;
for (unsigned int l=0; l<n_u_dofs; l++)
{
current_vel(0) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_a[l]);
current_vel(1) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_b[l]);
current_vel(2) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_c[l]);
}
#endif
#if UN_MINUS_ONE
Point unm1_x;
for (unsigned int l=0; l<n_u_dofs; l++)
{
unm1_x(0) += phi[l][qp]*unm1.old_local_solution->el(dof_indices_u[l]);
unm1_x(1) += phi[l][qp]*unm1.old_local_solution->el(dof_indices_v[l]);
unm1_x(2) += phi[l][qp]*unm1.old_local_solution->el(dof_indices_w[l]);
}
#endif
Point value_acc;
Point value_acc_alt;
#if DT
for (unsigned int d = 0; d < dim; ++d) {
value_acc_alt(d) = (rho_s)*( ((current_x(d)-rX(d))-(old_x(d)-rX(d)))-((old_x(d)-rX(d))- (unm1_x(d)-rX(d))) );
value_acc(d) = (rho_s)*((current_x(d))-2*(old_x(d))+ (unm1_x(d)));
value_acc(d) = (rho_s)*((current_x(d))-(old_x(d)));
}
#endif
Point res_1;
Point res_2;
#if INERTIA
for (unsigned int d = 0; d < dim; ++d) {
res_1(d) = (rho_s)*((current_vel(d))-(old_vel(d)));
res_2(d) = current_x(d)-dt*current_vel(d)-old_x(d);
}
/*
std::cout<<" current_vel "<<current_vel<<std::endl;
std::cout<<" res_1 "<<res_1<<std::endl;
std::cout<<" res_2 "<<res_2<<std::endl;
*/
#endif
test(73);
#endif
Number p_solid = 0.;
#if MOVING_MESH
grad_u_mat(0) = grad_u_mat(1) = grad_u_mat(2) = 0;
for (unsigned int d = 0; d < dim; ++d) {
std::vector<Number> u_undefo;
//Fills the vector di with the global degree of freedom indices for the element. :dof_indicies
aux_system.get_dof_map().dof_indices(elem, undefo_index,d);
aux_system.current_local_solution->get(undefo_index, u_undefo);
for (unsigned int l = 0; l != n_u_dofs; l++)
grad_u_mat(d).add_scaled(dphi[l][qp], u_undefo[l]);
}
#endif
//#include "fixed_mesh_in_solid_assemble_code.txt"
#if INCOMPRESSIBLE
for (unsigned int l=0; l<n_p_dofs; l++)
{
p_solid += psi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_p[l]);
}
#endif
#if INCOMPRESSIBLE
Real m=0;
Real p_fluid=0;
#if FLUID_VEL
for (unsigned int l=0; l<n_p_dofs; l++)
{
p_fluid += psi[l][qp]*fluid_system_vel.current_local_solution->el(dof_indices_p[l]);
}
//As outlined in Chappel p=(p_curr-p_old)/2
Real p_fluid_old=0;
for (unsigned int l=0; l<n_p_dofs; l++)
{
p_fluid_old += psi[l][qp]*fluid_system_vel.old_local_solution->el(dof_indices_p[l]);
}
p_fluid=0.5*p_fluid+0.5*p_fluid_old;
Real m_old=0;
#if FLUID_P_CONST
for (unsigned int l=0; l<n_p_dofs; l++)
{
m += psi[l][qp]*fluid_system_vel.current_local_solution->el(dof_indices_m[l]);
}
for (unsigned int l=0; l<n_p_dofs; l++)
{
m_old += psi[l][qp]*fluid_system_vel.old_local_solution->el(dof_indices_m[l]);
}
#endif
material.init_for_qp(grad_u_mat, p_solid, qp, 1.0*m+0.0*m_old, p_fluid);
#endif
#endif //#if INCOMPRESSIBLE
#if INCOMPRESSIBLE && ! PORO
material.init_for_qp(grad_u_mat, p_solid, qp);
#endif
for (unsigned int i=0; i<n_u_dofs; i++)
{
res.resize(dim);
material.get_residual(res, i);
res.scale(JxW[qp]);
#if INERTIA
res.scale(dt);
#endif
#if DT
res.scale(dt);
#endif
//std::cout<< "res "<<res<<std::endl;
Fu(i) += res(0);
Fv(i) += res(1) ;
Fw(i) += res(2);
#if GRAVITY
Real grav=0.0;
Fu(i) += progress*grav*JxW[qp]*phi[i][qp];
#endif
#if INERTIA
Fu(i) += JxW[qp]*phi[i][qp]*res_1(0);
Fv(i) += JxW[qp]*phi[i][qp]*res_1(1);
Fw(i) += JxW[qp]*phi[i][qp]*res_1(2);
Fa(i) += JxW[qp]*phi[i][qp]*res_2(0);
Fb(i) += JxW[qp]*phi[i][qp]*res_2(1);
Fc(i) += JxW[qp]*phi[i][qp]*res_2(2);
#endif
// Matrix contributions for the uu and vv couplings.
for (unsigned int j=0; j<n_u_dofs; j++)
{
material.get_linearized_stiffness(stiff, i, j);
stiff.scale(JxW[qp]);
#if DT
res.scale(dt);
#endif
#if INERTIA
stiff.scale(dt);
Kua(i,j)+= rho_s*JxW[qp]*phi[i][qp]*phi[j][qp];
Kvb(i,j)+= rho_s*JxW[qp]*phi[i][qp]*phi[j][qp];
Kwc(i,j)+= rho_s*JxW[qp]*phi[i][qp]*phi[j][qp];
Kau(i,j)+= JxW[qp]*phi[i][qp]*phi[j][qp];
Kbv(i,j)+= JxW[qp]*phi[i][qp]*phi[j][qp];
Kcw(i,j)+= JxW[qp]*phi[i][qp]*phi[j][qp];
Kaa(i,j)+= -dt*JxW[qp]*phi[i][qp]*phi[j][qp];
Kbb(i,j)+= -dt*JxW[qp]*phi[i][qp]*phi[j][qp];
Kcc(i,j)+= -dt*JxW[qp]*phi[i][qp]*phi[j][qp];
#endif
Kuu(i,j)+= stiff(u_var, u_var);
Kuv(i,j)+= stiff(u_var, v_var);
Kuw(i,j)+= stiff(u_var, w_var);
Kvu(i,j)+= stiff(v_var, u_var);
Kvv(i,j)+= stiff(v_var, v_var);
Kvw(i,j)+= stiff(v_var, w_var);
Kwu(i,j)+= stiff(w_var, u_var);
Kwv(i,j)+= stiff(w_var, v_var);
Kww(i,j)+= stiff(w_var, w_var);
#if GRAVITY
Kuu(i,j)+= 1*JxW[qp]*phi[i][qp]*phi[j][qp];
#endif
}
}
#if INCOMPRESSIBLE && FLUID_P_CONST
for (unsigned int i = 0; i < n_p_dofs; i++) {
material.get_p_residual(p_res, i);
p_res.scale(JxW[qp]);
Fp(i) += p_res(0);
}
for (unsigned int i = 0; i < n_u_dofs; i++) {
for (unsigned int j = 0; j < n_p_dofs; j++) {
material.get_linearized_uvw_p_stiffness(p_stiff, i, j);
p_stiff.scale(JxW[qp]);
Kup(i, j) += p_stiff(0);
Kvp(i, j) += p_stiff(1);
Kwp(i, j) += p_stiff(2);
}
}
for (unsigned int i = 0; i < n_p_dofs; i++) {
for (unsigned int j = 0; j < n_u_dofs; j++) {
material.get_linearized_p_uvw_stiffness(p_stiff, i, j);
p_stiff.scale(JxW[qp]);
Kpu(i, j) += p_stiff(0);
Kpv(i, j) += p_stiff(1);
Kpw(i, j) += p_stiff(2);
}
}
#endif
#if CHAP && ! FLUID_P_CONST
for (unsigned int i = 0; i < n_p_dofs; i++) {
Fp(i) += 0*JxW[qp]*psi[i][qp];
}
for (unsigned int i = 0; i < n_p_dofs; i++) {
for (unsigned int j = 0; j < n_p_dofs; j++) {
Kpp(i, j) += 1*JxW[qp]*psi[i][qp]*psi[j][qp];
}
}
#endif
}//end of qp loop
newton_update.matrix->add_matrix (Ke, dof_indices);
newton_update.rhs->add_vector (Fe, dof_indices);
} // end of element loop
// dof_map.constrain_element_matrix_and_vector (Ke, Fe, dof_indices);
newton_update.rhs->close();
newton_update.matrix->close();
#if LOG_ASSEMBLE_PERFORMANCE
perf_log.pop("assemble stiffness");
#endif
#if LOG_ASSEMBLE_PERFORMANCE
perf_log.push("assemble bcs");
#endif
//Assemble the boundary conditions.
assemble_bcs(es);
#if LOG_ASSEMBLE_PERFORMANCE
perf_log.pop("assemble bcs");
#endif
std::ofstream lhs_out("lhsoutS3.dat");
Ke.print(lhs_out);
lhs_out.close();
return;
}
void BoussinesqBuoyancyAdjointStabilization<Mu>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("BoussinesqBuoyancyAdjointStabilization::element_time_derivative");
#endif
// The number of local degrees of freedom in each variable.
const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.u_var()).size();
const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size();
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(_flow_vars.u_var())->get_JxW();
const std::vector<std::vector<libMesh::Real> >& T_phi =
context.get_element_fe(this->_temp_vars.T_var())->get_phi();
const std::vector<std::vector<libMesh::Real> >& u_phi =
context.get_element_fe(this->_flow_vars.u_var())->get_phi();
const std::vector<std::vector<libMesh::RealGradient> >& u_gradphi =
context.get_element_fe(this->_flow_vars.u_var())->get_dphi();
const std::vector<std::vector<libMesh::RealTensor> >& u_hessphi =
context.get_element_fe(this->_flow_vars.u_var())->get_d2phi();
// Get residuals and jacobians
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(_flow_vars.u_var()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(_flow_vars.v_var()); // R_{v}
libMesh::DenseSubVector<libMesh::Number> *Fw = NULL;
libMesh::DenseSubMatrix<libMesh::Number> &KuT =
context.get_elem_jacobian(_flow_vars.u_var(), _temp_vars.T_var()); // J_{uT}
libMesh::DenseSubMatrix<libMesh::Number> &KvT =
context.get_elem_jacobian(_flow_vars.v_var(), _temp_vars.T_var()); // J_{vT}
libMesh::DenseSubMatrix<libMesh::Number> &Kuu =
context.get_elem_jacobian(_flow_vars.u_var(), _flow_vars.u_var()); // J_{uu}
libMesh::DenseSubMatrix<libMesh::Number> &Kuv =
context.get_elem_jacobian(_flow_vars.u_var(), _flow_vars.v_var()); // J_{uv}
libMesh::DenseSubMatrix<libMesh::Number> &Kvu =
context.get_elem_jacobian(_flow_vars.v_var(), _flow_vars.u_var()); // J_{vu}
libMesh::DenseSubMatrix<libMesh::Number> &Kvv =
context.get_elem_jacobian(_flow_vars.v_var(), _flow_vars.v_var()); // J_{vv}
libMesh::DenseSubMatrix<libMesh::Number> *KwT = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kuw = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kvw = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kwu = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kwv = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kww = NULL;
if(this->_dim == 3)
{
Fw = &context.get_elem_residual(this->_flow_vars.w_var()); // R_{w}
KwT = &context.get_elem_jacobian
(_flow_vars.w_var(), _temp_vars.T_var()); // J_{wT}
Kuw = &context.get_elem_jacobian
(_flow_vars.u_var(), _flow_vars.w_var()); // J_{uw}
Kvw = &context.get_elem_jacobian
(_flow_vars.v_var(), _flow_vars.w_var()); // J_{vw}
Kwu = &context.get_elem_jacobian
(_flow_vars.w_var(), _flow_vars.u_var()); // J_{wu}
Kwv = &context.get_elem_jacobian
(_flow_vars.w_var(), _flow_vars.v_var()); // J_{wv}
Kww = &context.get_elem_jacobian
(_flow_vars.w_var(), _flow_vars.w_var()); // J_{ww}
}
// Now we will build the element Jacobian and residual.
// Constructing the residual requires the solution and its
// gradient from the previous timestep. This must be
// calculated at each quadrature point by summing the
// solution degree-of-freedom values by the appropriate
// weight functions.
unsigned int n_qpoints = context.get_element_qrule().n_points();
libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u_var());
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::RealGradient U( context.interior_value( this->_flow_vars.u_var(), qp ),
context.interior_value( this->_flow_vars.v_var(), qp ) );
if( this->_dim == 3 )
{
U(2) = context.interior_value( this->_flow_vars.w_var(), qp );
}
// Compute the viscosity at this qp
libMesh::Real mu_qp = this->_mu(context, qp);
libMesh::Real tau_M;
libMesh::Real d_tau_M_d_rho;
libMesh::Gradient d_tau_M_dU;
if (compute_jacobian)
this->_stab_helper.compute_tau_momentum_and_derivs
( context, qp, g, G, this->_rho, U, mu_qp,
tau_M, d_tau_M_d_rho, d_tau_M_dU,
this->_is_steady );
else
tau_M = this->_stab_helper.compute_tau_momentum
( context, qp, g, G, this->_rho, U, mu_qp,
this->_is_steady );
// Compute the solution & its gradient at the old Newton iterate.
libMesh::Number T;
T = context.interior_value(_temp_vars.T_var(), qp);
libMesh::RealGradient d_residual_dT = _rho_ref*_beta_T*_g;
// d_residual_dU = 0
libMesh::RealGradient residual = (T-_T_ref)*d_residual_dT;
for (unsigned int i=0; i != n_u_dofs; i++)
{
libMesh::Real test_func = this->_rho*U*u_gradphi[i][qp] +
mu_qp*( u_hessphi[i][qp](0,0) + u_hessphi[i][qp](1,1) + u_hessphi[i][qp](2,2) );
Fu(i) += -tau_M*residual(0)*test_func*JxW[qp];
Fv(i) += -tau_M*residual(1)*test_func*JxW[qp];
if (_dim == 3)
{
(*Fw)(i) += -tau_M*residual(2)*test_func*JxW[qp];
}
if (compute_jacobian)
{
libMesh::Gradient d_test_func_dU = this->_rho*u_gradphi[i][qp];
// d_test_func_dT = 0
for (unsigned int j=0; j != n_u_dofs; ++j)
{
Kuu(i,j) += -tau_M*residual(0)*d_test_func_dU(0)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
Kuu(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*residual(0)*test_func*JxW[qp] * context.get_elem_solution_derivative();
Kuv(i,j) += -tau_M*residual(0)*d_test_func_dU(1)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
Kuv(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*residual(0)*test_func*JxW[qp] * context.get_elem_solution_derivative();
Kvu(i,j) += -tau_M*residual(1)*d_test_func_dU(0)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
Kvu(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*residual(1)*test_func*JxW[qp] * context.get_elem_solution_derivative();
Kvv(i,j) += -tau_M*residual(1)*d_test_func_dU(1)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
Kvv(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*residual(1)*test_func*JxW[qp] * context.get_elem_solution_derivative();
}
for (unsigned int j=0; j != n_T_dofs; ++j)
{
// KuT(i,j) += -tau_M*residual(0)*dtest_func_dT[j]*JxW[qp] * context.get_elem_solution_derivative();
KuT(i,j) += -tau_M*d_residual_dT(0)*T_phi[j][qp]*test_func*JxW[qp] * context.get_elem_solution_derivative();
// KvT(i,j) += -tau_M*residual(1)*dtest_func_dT[j]*JxW[qp] * context.get_elem_solution_derivative();
KvT(i,j) += -tau_M*d_residual_dT(1)*T_phi[j][qp]*test_func*JxW[qp] * context.get_elem_solution_derivative();
}
if (_dim == 3)
{
for (unsigned int j=0; j != n_T_dofs; ++j)
{
// KwT(i,j) += -tau_M*residual(2)*dtest_func_dT[j]*JxW[qp] * context.get_elem_solution_derivative();
(*KwT)(i,j) += -tau_M*d_residual_dT(2)*T_phi[j][qp]*test_func*JxW[qp] * context.get_elem_solution_derivative();
}
for (unsigned int j=0; j != n_u_dofs; ++j)
{
(*Kuw)(i,j) += -tau_M*residual(0)*d_test_func_dU(2)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kuw)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*residual(0)*test_func*JxW[qp] * context.get_elem_solution_derivative();
(*Kvw)(i,j) += -tau_M*residual(1)*d_test_func_dU(2)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kvw)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*residual(1)*test_func*JxW[qp] * context.get_elem_solution_derivative();
(*Kwu)(i,j) += -tau_M*residual(2)*d_test_func_dU(0)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kwu)(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*residual(2)*test_func*JxW[qp] * context.get_elem_solution_derivative();
(*Kwv)(i,j) += -tau_M*residual(2)*d_test_func_dU(1)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kwv)(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*residual(2)*test_func*JxW[qp] * context.get_elem_solution_derivative();
(*Kww)(i,j) += -tau_M*residual(2)*d_test_func_dU(2)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kww)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*residual(2)*test_func*JxW[qp] * context.get_elem_solution_derivative();
}
}
} // End compute_jacobian check
} // End i dof loop
} // End quadrature loop
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("BoussinesqBuoyancyAdjointStabilization::element_time_derivative");
#endif
return;
}
void ElasticMembraneConstantPressure::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/ )
{
const unsigned int n_u_dofs = context.get_dof_indices(_disp_vars.u()).size();
const std::vector<libMesh::Real> &JxW =
this->get_fe(context)->get_JxW();
const std::vector<std::vector<libMesh::Real> >& u_phi =
this->get_fe(context)->get_phi();
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(_disp_vars.u());
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(_disp_vars.v());
libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number>& Kuv = context.get_elem_jacobian(_disp_vars.u(),_disp_vars.v());
libMesh::DenseSubMatrix<libMesh::Number>& Kuw = context.get_elem_jacobian(_disp_vars.u(),_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number>& Kvu = context.get_elem_jacobian(_disp_vars.v(),_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number>& Kvw = context.get_elem_jacobian(_disp_vars.v(),_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number>& Kwu = context.get_elem_jacobian(_disp_vars.w(),_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number>& Kwv = context.get_elem_jacobian(_disp_vars.w(),_disp_vars.v());
unsigned int n_qpoints = context.get_element_qrule().n_points();
// All shape function gradients are w.r.t. master element coordinates
const std::vector<std::vector<libMesh::Real> >& dphi_dxi =
this->get_fe(context)->get_dphidxi();
const std::vector<std::vector<libMesh::Real> >& dphi_deta =
this->get_fe(context)->get_dphideta();
const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( _disp_vars.u() );
const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( _disp_vars.v() );
const libMesh::DenseSubVector<libMesh::Number>& w_coeffs = context.get_elem_solution( _disp_vars.w() );
const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi();
const std::vector<libMesh::RealGradient>& dxdeta = this->get_fe(context)->get_dxyzdeta();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// sqrt(det(a_cov)), a_cov being the covariant metric tensor of undeformed body
libMesh::Real sqrt_a = sqrt( dxdxi[qp]*dxdxi[qp]*dxdeta[qp]*dxdeta[qp]
- dxdxi[qp]*dxdeta[qp]*dxdeta[qp]*dxdxi[qp] );
// Gradients are w.r.t. master element coordinates
libMesh::Gradient grad_u, grad_v, grad_w;
for( unsigned int d = 0; d < n_u_dofs; d++ )
{
libMesh::RealGradient u_gradphi( dphi_dxi[d][qp], dphi_deta[d][qp] );
grad_u += u_coeffs(d)*u_gradphi;
grad_v += v_coeffs(d)*u_gradphi;
grad_w += w_coeffs(d)*u_gradphi;
}
libMesh::RealGradient dudxi( grad_u(0), grad_v(0), grad_w(0) );
libMesh::RealGradient dudeta( grad_u(1), grad_v(1), grad_w(1) );
libMesh::RealGradient A_1 = dxdxi[qp] + dudxi;
libMesh::RealGradient A_2 = dxdeta[qp] + dudeta;
libMesh::RealGradient A_3 = A_1.cross(A_2);
/* The formula here is actually
P*\sqrt{\frac{A}{a}}*A_3, where A_3 is a unit vector
But, |A_3| = \sqrt{A} so the normalizing part kills
the \sqrt{A} in the numerator, so we can leave it out
and *not* normalize A_3.
*/
libMesh::RealGradient traction = _pressure/sqrt_a*A_3;
libMesh::Real jac = JxW[qp];
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) -= traction(0)*u_phi[i][qp]*jac;
Fv(i) -= traction(1)*u_phi[i][qp]*jac;
Fw(i) -= traction(2)*u_phi[i][qp]*jac;
if( compute_jacobian )
{
for (unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::RealGradient u_gradphi( dphi_dxi[j][qp], dphi_deta[j][qp] );
const libMesh::Real dt0_dv = _pressure/sqrt_a*(u_gradphi(0)*A_2(2) - A_1(2)*u_gradphi(1));
const libMesh::Real dt0_dw = _pressure/sqrt_a*(A_1(1)*u_gradphi(1) - u_gradphi(0)*A_2(1));
const libMesh::Real dt1_du = _pressure/sqrt_a*(A_1(2)*u_gradphi(1) - u_gradphi(0)*A_2(2));
const libMesh::Real dt1_dw = _pressure/sqrt_a*(u_gradphi(0)*A_2(0) - A_1(0)*u_gradphi(1));
const libMesh::Real dt2_du = _pressure/sqrt_a*(u_gradphi(0)*A_2(1) - A_1(1)*u_gradphi(1));
const libMesh::Real dt2_dv = _pressure/sqrt_a*(A_1(0)*u_gradphi(1) - u_gradphi(0)*A_2(0));
Kuv(i,j) -= dt0_dv*u_phi[i][qp]*jac;
Kuw(i,j) -= dt0_dw*u_phi[i][qp]*jac;
Kvu(i,j) -= dt1_du*u_phi[i][qp]*jac;
Kvw(i,j) -= dt1_dw*u_phi[i][qp]*jac;
Kwu(i,j) -= dt2_du*u_phi[i][qp]*jac;
Kwv(i,j) -= dt2_dv*u_phi[i][qp]*jac;
}
}
}
}
return;
}