void LowMachNavierStokes<Mu,SH,TC>::assemble_thermo_press_elem_time_deriv( bool /*compute_jacobian*/,
AssemblyContext& context )
{
// Element Jacobian * quadrature weights for interior integration
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_T_var)->get_JxW();
// The number of local degrees of freedom in each variable
const unsigned int n_p0_dofs = context.get_dof_indices(this->_p0_var).size();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubVector<libMesh::Real> &F_p0 = context.get_elem_residual(this->_p0_var);
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp = 0; qp != n_qpoints; ++qp)
{
libMesh::Number T;
T = context.interior_value(this->_T_var, qp);
libMesh::Gradient grad_u, grad_v, grad_w;
grad_u = context.interior_gradient(this->_u_var, qp);
grad_v = context.interior_gradient(this->_v_var, qp);
if (this->_dim == 3)
grad_w = context.interior_gradient(this->_w_var, qp);
libMesh::Number divU = grad_u(0) + grad_v(1);
if(this->_dim==3)
divU += grad_w(2);
//libMesh::Number cp = this->_cp(T);
//libMesh::Number cv = cp + this->_R;
//libMesh::Number gamma = cp/cv;
//libMesh::Number gamma_ratio = gamma/(gamma-1.0);
libMesh::Number p0 = context.interior_value( this->_p0_var, qp );
for (unsigned int i = 0; i != n_p0_dofs; ++i)
{
F_p0(i) += (p0/T - this->_p0/this->_T0)*JxW[qp];
//F_p0(i) -= p0*gamma_ratio*divU*JxW[qp];
} // End DoF loop i
}
return;
}
void LowMachNavierStokesSPGSMStabilization<Mu,SH,TC>::assemble_energy_time_deriv( bool /*compute_jacobian*/,
AssemblyContext& context )
{
// The number of local degrees of freedom in each variable.
const unsigned int n_T_dofs = context.get_dof_indices(this->_temp_vars.T()).size();
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_temp_vars.T())->get_JxW();
// The temperature shape functions gradients at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi =
context.get_element_fe(this->_temp_vars.T())->get_dphi();
libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(this->_temp_vars.T()); // R_{T}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::Number u, v;
u = context.interior_value(this->_flow_vars.u(), qp);
v = context.interior_value(this->_flow_vars.v(), qp);
libMesh::Gradient grad_T = context.interior_gradient(this->_temp_vars.T(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->mesh_dim(context) == 3)
U(2) = context.interior_value(this->_flow_vars.w(), qp); // w
libMesh::Real T = context.interior_value( this->_temp_vars.T(), qp );
libMesh::Real rho = this->rho( T, this->get_p0_steady( context, qp ) );
libMesh::Real k = this->_k(T);
libMesh::Real cp = this->_cp(T);
libMesh::Number rho_cp = rho*this->_cp(T);
libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u());
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::Real tau_E = this->_stab_helper.compute_tau_energy( context, qp, g, G, rho, U, k, cp, this->_is_steady );
libMesh::Real RE_s = this->compute_res_energy_steady( context, qp );
for (unsigned int i=0; i != n_T_dofs; i++)
{
FT(i) -= rho_cp*tau_E*RE_s*U*T_gradphi[i][qp]*JxW[qp];
}
}
return;
}
void LowMachNavierStokes<Mu,SH,TC>::compute_element_time_derivative_cache( const AssemblyContext& context,
CachedValues& cache )
{
const unsigned int n_qpoints = context.get_element_qrule().n_points();
std::vector<libMesh::Real> u, v, w, T, p, p0;
u.resize(n_qpoints);
v.resize(n_qpoints);
if( this->_dim > 2 )
w.resize(n_qpoints);
T.resize(n_qpoints);
p.resize(n_qpoints);
p0.resize(n_qpoints);
std::vector<libMesh::Gradient> grad_u, grad_v, grad_w, grad_T;
grad_u.resize(n_qpoints);
grad_v.resize(n_qpoints);
if( this->_dim > 2 )
grad_w.resize(n_qpoints);
grad_T.resize(n_qpoints);
for (unsigned int qp = 0; qp != n_qpoints; ++qp)
{
u[qp] = context.interior_value(this->_u_var, qp);
v[qp] = context.interior_value(this->_v_var, qp);
grad_u[qp] = context.interior_gradient(this->_u_var, qp);
grad_v[qp] = context.interior_gradient(this->_v_var, qp);
if( this->_dim > 2 )
{
w[qp] = context.interior_value(this->_w_var, qp);
grad_w[qp] = context.interior_gradient(this->_w_var, qp);
}
T[qp] = context.interior_value(this->_T_var, qp);
grad_T[qp] = context.interior_gradient(this->_T_var, qp);
p[qp] = context.interior_value(this->_p_var, qp);
p0[qp] = this->get_p0_steady(context, qp);
}
cache.set_values(Cache::X_VELOCITY, u);
cache.set_values(Cache::Y_VELOCITY, v);
cache.set_gradient_values(Cache::X_VELOCITY_GRAD, grad_u);
cache.set_gradient_values(Cache::Y_VELOCITY_GRAD, grad_v);
if(this->_dim > 2)
{
cache.set_values(Cache::Z_VELOCITY, w);
cache.set_gradient_values(Cache::Z_VELOCITY_GRAD, grad_w);
}
cache.set_values(Cache::TEMPERATURE, T);
cache.set_gradient_values(Cache::TEMPERATURE_GRAD, grad_T);
cache.set_values(Cache::PRESSURE, p);
cache.set_values(Cache::THERMO_PRESSURE, p0);
return;
}
void AxisymmetricHeatTransfer<Conductivity>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("AxisymmetricHeatTransfer::element_time_derivative");
#endif
// The number of local degrees of freedom in each variable.
const unsigned int n_T_dofs = context.get_dof_indices(_T_var).size();
const unsigned int n_u_dofs = context.get_dof_indices(_u_r_var).size();
//TODO: check n_T_dofs is same as n_u_dofs, n_v_dofs, n_w_dofs
// We get some references to cell-specific data that
// will be used to assemble the linear system.
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(_T_var)->get_JxW();
// The temperature shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& T_phi =
context.get_element_fe(_T_var)->get_phi();
// The velocity shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& vel_phi =
context.get_element_fe(_u_r_var)->get_phi();
// The temperature shape function gradients (in global coords.)
// at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi =
context.get_element_fe(_T_var)->get_dphi();
// Physical location of the quadrature points
const std::vector<libMesh::Point>& u_qpoint =
context.get_element_fe(_u_r_var)->get_xyz();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(_T_var); // R_{T}
libMesh::DenseSubMatrix<libMesh::Number> &KTT = context.get_elem_jacobian(_T_var, _T_var); // R_{T},{T}
libMesh::DenseSubMatrix<libMesh::Number> &KTr = context.get_elem_jacobian(_T_var, _u_r_var); // R_{T},{r}
libMesh::DenseSubMatrix<libMesh::Number> &KTz = context.get_elem_jacobian(_T_var, _u_z_var); // R_{T},{z}
// 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();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
const libMesh::Number r = u_qpoint[qp](0);
// Compute the solution & its gradient at the old Newton iterate.
libMesh::Number u_r, u_z;
u_r = context.interior_value(_u_r_var, qp);
u_z = context.interior_value(_u_z_var, qp);
libMesh::Gradient grad_T;
grad_T = context.interior_gradient(_T_var, qp);
libMesh::NumberVectorValue U (u_r,u_z);
libMesh::Number k = this->_k( context, qp );
// FIXME - once we have T-dependent k, we'll need its
// derivatives in Jacobians
// libMesh::Number dk_dT = this->_k.deriv( T );
// First, an i-loop over the degrees of freedom.
for (unsigned int i=0; i != n_T_dofs; i++)
{
FT(i) += JxW[qp]*r*
(-_rho*_Cp*T_phi[i][qp]*(U*grad_T) // convection term
-k*(T_gradphi[i][qp]*grad_T) ); // diffusion term
if (compute_jacobian)
{
libmesh_assert (context.get_elem_solution_derivative() == 1.0);
for (unsigned int j=0; j != n_T_dofs; j++)
{
// TODO: precompute some terms like:
// _rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*T_grad_phi[j][qp])
KTT(i,j) += JxW[qp] * context.get_elem_solution_derivative() *r*
(-_rho*_Cp*T_phi[i][qp]*(U*T_gradphi[j][qp]) // convection term
-k*(T_gradphi[i][qp]*T_gradphi[j][qp])); // diffusion term
} // end of the inner dof (j) loop
#if 0
if( dk_dT != 0.0 )
{
for (unsigned int j=0; j != n_T_dofs; j++)
{
// TODO: precompute some terms like:
KTT(i,j) -= JxW[qp] * context.get_elem_solution_derivative() *r*( dk_dT*T_phi[j][qp]*T_gradphi[i][qp]*grad_T );
}
}
#endif
// Matrix contributions for the Tu, Tv and Tw couplings (n_T_dofs same as n_u_dofs, n_v_dofs and n_w_dofs)
for (unsigned int j=0; j != n_u_dofs; j++)
{
KTr(i,j) += JxW[qp] * context.get_elem_solution_derivative() *r*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(0)));
KTz(i,j) += JxW[qp] * context.get_elem_solution_derivative() *r*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(1)));
} // end of the inner dof (j) loop
} // end - if (compute_jacobian && context.get_elem_solution_derivative())
} // end of the outer dof (i) loop
} // end of the quadrature point (qp) loop
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("AxisymmetricHeatTransfer::element_time_derivative");
#endif
return;
}
void SpalartAllmarasSPGSMStabilization<Mu>::element_time_derivative
( bool compute_jacobian,
AssemblyContext & context )
{
// Get a pointer to the current element, we need this for computing the distance to wall for the
// quadrature points
libMesh::Elem &elem_pointer = context.get_elem();
// The number of local degrees of freedom in each variable.
const unsigned int n_nu_dofs = context.get_dof_indices(this->_turbulence_vars.nu()).size();
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_turbulence_vars.nu())->get_JxW();
// The viscosity shape function gradients (in global coords.)
// at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& nu_gradphi =
context.get_element_fe(this->_turbulence_vars.nu())->get_dphi();
// Quadrature point locations
//const std::vector<libMesh::Point>& nu_qpoint =
//context.get_element_fe(this->_turbulence_vars.nu())->get_xyz();
//libMesh::DenseSubMatrix<libMesh::Number> &Knunu = context.get_elem_jacobian(this->_turbulence_vars.nu(), this->_turbulence_vars.nu()); // R_{nu},{nu}
libMesh::DenseSubVector<libMesh::Number> &Fnu = context.get_elem_residual(this->_turbulence_vars.nu()); // R_{nu}
libMesh::FEBase* fe = context.get_element_fe(this->_turbulence_vars.nu());
unsigned int n_qpoints = context.get_element_qrule().n_points();
// Auto pointer to distance fcn evaluated at quad points
std::unique_ptr< libMesh::DenseVector<libMesh::Real> > distance_qp;
// Fill the vector of distances to quadrature points
distance_qp = this->distance_function->interpolate(&elem_pointer, context.get_element_qrule().get_points());
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::Gradient grad_nu;
grad_nu = context.interior_gradient(this->_turbulence_vars.nu(), qp);
libMesh::Real jac = JxW[qp];
// The physical viscosity
libMesh::Real _mu_qp = this->_mu(context, qp);
// To be fixed
// For the channel flow we will just set the distance function analytically
//(*distance_qp)(qp) = std::min(fabs(y),fabs(1 - y));
// The flow velocity
libMesh::Number u,v;
u = context.interior_value(this->_flow_vars.u(), qp);
v = context.interior_value(this->_flow_vars.v(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->_flow_vars.dim() == 3)
U(2) = context.interior_value(this->_flow_vars.w(), qp);
// Stabilization terms
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::Real tau_spalart = this->_stab_helper.compute_tau_spalart( context, qp, g, G, this->_rho, U, _mu_qp, this->_is_steady );
libMesh::Number RM_spalart = this->_stab_helper.compute_res_spalart_steady( context, qp, this->_rho, _mu_qp, (*distance_qp)(qp), this->_infinite_distance );
for (unsigned int i=0; i != n_nu_dofs; i++)
{
Fnu(i) += jac*( -tau_spalart*RM_spalart*this->_rho*(U*nu_gradphi[i][qp]) );
}
if( compute_jacobian )
{
libmesh_not_implemented();
}
}
}
void ReactingLowMachNavierStokesStabilizationBase<Mixture,Evaluator>::compute_res_steady( AssemblyContext& context,
unsigned int qp,
libMesh::Real& RP_s,
libMesh::RealGradient& RM_s,
libMesh::Real& RE_s,
std::vector<libMesh::Real>& Rs_s )
{
Rs_s.resize(this->n_species(),0.0);
// Grab r-coordinate for axisymmetric terms
// We're assuming all variables are using the same quadrature rule
libMesh::Real r = (context.get_element_fe(this->_flow_vars.u())->get_xyz())[qp](0);
libMesh::RealGradient grad_p = context.interior_gradient(this->_press_var.p(), qp);
libMesh::RealGradient grad_u = context.interior_gradient(this->_flow_vars.u(), qp);
libMesh::RealGradient grad_v = context.interior_gradient(this->_flow_vars.v(), qp);
libMesh::RealGradient U( context.interior_value(this->_flow_vars.u(), qp),
context.interior_value(this->_flow_vars.v(), qp) );
libMesh::Real divU = grad_u(0) + grad_v(1);
if( this->_is_axisymmetric )
divU += U(0)/r;
if(this->mesh_dim(context) == 3)
{
U(2) = context.interior_value(this->_flow_vars.w(), qp);
divU += (context.interior_gradient(this->_flow_vars.w(), qp))(2);
}
// We don't add axisymmetric terms here since we don't directly use hess_{u,v}
// axisymmetric terms are built into divGradU, etc. functions below
libMesh::RealTensor hess_u = context.interior_hessian(this->_flow_vars.u(), qp);
libMesh::RealTensor hess_v = context.interior_hessian(this->_flow_vars.v(), qp);
libMesh::Real T = context.interior_value(this->_temp_vars.T(), qp);
libMesh::Gradient grad_T = context.interior_gradient(this->_temp_vars.T(), qp);
libMesh::Tensor hess_T = context.interior_hessian(this->_temp_vars.T(), qp);
libMesh::Real hess_T_term = hess_T(0,0) + hess_T(1,1);
#if LIBMESH_DIM > 2
hess_T_term += hess_T(2,2);
#endif
// Add axisymmetric terms, if needed
if( this->_is_axisymmetric )
hess_T_term += grad_T(0)/r;
std::vector<libMesh::Real> ws(this->n_species());
std::vector<libMesh::RealGradient> grad_ws(this->n_species());
std::vector<libMesh::RealTensor> hess_ws(this->n_species());
for(unsigned int s=0; s < this->_n_species; s++ )
{
ws[s] = context.interior_value(this->_species_vars.species(s), qp);
grad_ws[s] = context.interior_gradient(this->_species_vars.species(s), qp);
hess_ws[s] = context.interior_hessian(this->_species_vars.species(s), qp);
}
Evaluator gas_evaluator( this->_gas_mixture );
const libMesh::Real R_mix = gas_evaluator.R_mix(ws);
const libMesh::Real p0 = this->get_p0_steady(context,qp);
libMesh::Real rho = this->rho(T, p0, R_mix );
libMesh::Real cp = gas_evaluator.cp(T,p0,ws);
libMesh::Real M = gas_evaluator.M_mix( ws );
std::vector<libMesh::Real> D( this->n_species() );
libMesh::Real mu, k;
gas_evaluator.mu_and_k_and_D( T, rho, cp, ws, mu, k, D );
// grad_rho = drho_dT*gradT + \sum_s drho_dws*grad_ws
const libMesh::Real drho_dT = -p0/(R_mix*T*T);
libMesh::RealGradient grad_rho = drho_dT*grad_T;
for(unsigned int s=0; s < this->_n_species; s++ )
{
libMesh::Real Ms = gas_evaluator.M(s);
libMesh::Real R_uni = Constants::R_universal/1000.0; /* J/kmol-K --> J/mol-K */
// drho_dws = -p0/(T*R_mix*R_mix)*dR_dws
// dR_dws = R_uni*d_dws(1/M)
// d_dws(1/M) = d_dws(\sum_s w_s/Ms) = 1/Ms
const libMesh::Real drho_dws = -p0/(R_mix*R_mix*T)*R_uni/Ms;
grad_rho += drho_dws*grad_ws[s];
}
libMesh::RealGradient rhoUdotGradU;
libMesh::RealGradient divGradU;
libMesh::RealGradient divGradUT;
libMesh::RealGradient divdivU;
if( this->mesh_dim(context) < 3 )
{
rhoUdotGradU = rho*_stab_helper.UdotGradU( U, grad_u, grad_v );
// Call axisymmetric versions if we are doing an axisymmetric run
if( this->_is_axisymmetric )
{
divGradU = _stab_helper.div_GradU_axi( r, U, grad_u, grad_v, hess_u, hess_v );
divGradUT = _stab_helper.div_GradU_T_axi( r, U, grad_u, hess_u, hess_v );
divdivU = _stab_helper.div_divU_I_axi( r, U, grad_u, hess_u, hess_v );
}
else
{
divGradU = _stab_helper.div_GradU( hess_u, hess_v );
divGradUT = _stab_helper.div_GradU_T( hess_u, hess_v );
divdivU = _stab_helper.div_divU_I( hess_u, hess_v );
}
}
else
{
libMesh::RealGradient grad_w = context.interior_gradient(this->_flow_vars.w(), qp);
libMesh::RealTensor hess_w = context.interior_hessian(this->_flow_vars.w(), qp);
rhoUdotGradU = rho*_stab_helper.UdotGradU( U, grad_u, grad_v, grad_w );
divGradU = _stab_helper.div_GradU( hess_u, hess_v, hess_w );
divGradUT = _stab_helper.div_GradU_T( hess_u, hess_v, hess_w );
divdivU = _stab_helper.div_divU_I( hess_u, hess_v, hess_w );
}
// Terms if we have vicosity derivatives w.r.t. temp.
/*
if( this->_mu.deriv(T) != 0.0 )
{
libMesh::Gradient gradTgradu( grad_T*grad_u, grad_T*grad_v );
libMesh::Gradient gradTgraduT( grad_T(0)*grad_u(0) + grad_T(1)*grad_u(1),
grad_T(0)*grad_v(0) + grad_T(1)*grad_v(1) );
libMesh::Real divU = grad_u(0) + grad_v(1);
libMesh::Gradient gradTdivU( grad_T(0)*divU, grad_T(1)*divU );
if(this->mesh_dim(context) == 3)
{
libMesh::Gradient grad_w = context.interior_gradient(this->_flow_vars.w(), qp);
gradTgradu(2) = grad_T*grad_w;
gradTgraduT(0) += grad_T(2)*grad_u(2);
gradTgraduT(1) += grad_T(2)*grad_v(2);
gradTgraduT(2) = grad_T(0)*grad_w(0) + grad_T(1)*grad_w(1) + grad_T(2)*grad_w(2);
divU += grad_w(2);
gradTdivU(0) += grad_T(0)*grad_w(2);
gradTdivU(1) += grad_T(1)*grad_w(2);
gradTdivU(2) += grad_T(2)*divU;
}
divT += this->_mu.deriv(T)*( gradTgradu + gradTgraduT - 2.0/3.0*gradTdivU );
}
*/
// Axisymmetric terms already built in
libMesh::RealGradient div_stress = mu*(divGradU + divGradUT - 2.0/3.0*divdivU);
std::vector<libMesh::Real> omega_dot(this->n_species());
gas_evaluator.omega_dot(T,rho,ws,omega_dot);
libMesh::Real chem_term = 0.0;
libMesh::Gradient mass_term(0.0,0.0,0.0);
for(unsigned int s=0; s < this->_n_species; s++ )
{
// Start accumulating chemistry term for energy residual
libMesh::Real h_s=gas_evaluator.h_s(T,s);
chem_term += h_s*omega_dot[s];
/* Accumulate mass term for continuity residual
mass_term = grad_M/M */
mass_term += grad_ws[s]/this->_gas_mixture.M(s);
libMesh::Real hess_s_term = hess_ws[s](0,0) + hess_ws[s](1,1);
#if LIBMESH_DIM > 2
hess_s_term += hess_ws[s](2,2);
#endif
// Add axisymmetric terms, if needed
if( this->_is_axisymmetric )
hess_s_term += grad_ws[s](0)/r;
// Species residual
/*! \todo Still missing derivative of species diffusion coefficient.
rho*grad_D[s]*grad_ws[s] */
Rs_s[s] = rho*U*grad_ws[s] - rho*D[s]*hess_s_term - grad_rho*D[s]*grad_ws[s]
- omega_dot[s];
}
mass_term *= M;
// Continuity residual
RP_s = divU - (U*grad_T)/T - U*mass_term;
// Momentum residual
RM_s = rhoUdotGradU + grad_p - div_stress - rho*(this->_g);
// Energy residual
// - this->_k.deriv(T)*(grad_T*grad_T)
RE_s = rho*U*cp*grad_T - k*(hess_T_term) + chem_term;
return;
}
void LowMachNavierStokesSPGSMStabilization<Mu,SH,TC>::assemble_momentum_time_deriv( bool /*compute_jacobian*/,
AssemblyContext& context )
{
// 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();
// Check number of dofs is same for _flow_vars.u(), v_var and w_var.
libmesh_assert (n_u_dofs == context.get_dof_indices(this->_flow_vars.v()).size());
if (this->mesh_dim(context) == 3)
libmesh_assert (n_u_dofs == context.get_dof_indices(this->_flow_vars.w()).size());
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_flow_vars.u())->get_JxW();
// The velocity shape function gradients at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& u_gradphi =
context.get_element_fe(this->_flow_vars.u())->get_dphi();
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::Real>* Fw = NULL;
if( this->mesh_dim(context) == 3 )
{
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++)
{
libMesh::Real T = context.interior_value( this->_temp_vars.T(), qp );
libMesh::Real rho = this->rho( T, this->get_p0_steady( context, qp ) );
libMesh::RealGradient U( context.interior_value(this->_flow_vars.u(), qp),
context.interior_value(this->_flow_vars.v(), qp) );
libMesh::RealGradient grad_u = context.interior_gradient(this->_flow_vars.u(), qp);
libMesh::RealGradient grad_v = context.interior_gradient(this->_flow_vars.v(), qp);
libMesh::RealGradient grad_w;
if( this->mesh_dim(context) == 3 )
{
U(2) = context.interior_value(this->_flow_vars.w(), qp);
grad_w = context.interior_gradient(this->_flow_vars.w(), qp);
}
libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u());
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::Real mu = this->_mu(T);
libMesh::Real tau_M = this->_stab_helper.compute_tau_momentum( context, qp, g, G, rho, U, mu, this->_is_steady );
libMesh::Real tau_C = this->_stab_helper.compute_tau_continuity( tau_M, g );
libMesh::Real RC_s = this->compute_res_continuity_steady( context, qp );
libMesh::RealGradient RM_s = this->compute_res_momentum_steady( context, qp );
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) += ( - tau_C*RC_s*u_gradphi[i][qp](0)
- tau_M*RM_s(0)*rho*U*u_gradphi[i][qp] )*JxW[qp];
Fv(i) += ( - tau_C*RC_s*u_gradphi[i][qp](1)
- tau_M*RM_s(1)*rho*U*u_gradphi[i][qp] )*JxW[qp];
if( this->mesh_dim(context) == 3 )
{
(*Fw)(i) += ( - tau_C*RC_s*u_gradphi[i][qp](2)
- tau_M*RM_s(2)*rho*U*u_gradphi[i][qp] )*JxW[qp];
}
}
}
return;
}
void HeatTransfer::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("HeatTransfer::element_time_derivative");
#endif
// The number of local degrees of freedom in each variable.
const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size();
const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.u_var()).size();
//TODO: check n_T_dofs is same as n_u_dofs, n_v_dofs, n_w_dofs
// We get some references to cell-specific data that
// will be used to assemble the linear system.
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(_temp_vars.T_var())->get_JxW();
// The temperature shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& T_phi =
context.get_element_fe(_temp_vars.T_var())->get_phi();
// The velocity shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& vel_phi =
context.get_element_fe(_flow_vars.u_var())->get_phi();
// The temperature shape function gradients (in global coords.)
// at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi =
context.get_element_fe(_temp_vars.T_var())->get_dphi();
const std::vector<libMesh::Point>& u_qpoint =
context.get_element_fe(this->_flow_vars.u_var())->get_xyz();
libMesh::DenseSubMatrix<libMesh::Number> &KTT = context.get_elem_jacobian(_temp_vars.T_var(), _temp_vars.T_var()); // R_{T},{T}
libMesh::DenseSubMatrix<libMesh::Number> &KTu = context.get_elem_jacobian(_temp_vars.T_var(), _flow_vars.u_var()); // R_{T},{u}
libMesh::DenseSubMatrix<libMesh::Number> &KTv = context.get_elem_jacobian(_temp_vars.T_var(), _flow_vars.v_var()); // R_{T},{v}
libMesh::DenseSubMatrix<libMesh::Number>* KTw = NULL;
libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(_temp_vars.T_var()); // R_{T}
if( this->_dim == 3 )
{
KTw = &context.get_elem_jacobian(_temp_vars.T_var(), _flow_vars.w_var()); // R_{T},{w}
}
// 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();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Compute the solution & its gradient at the old Newton iterate.
libMesh::Number u, v;
u = context.interior_value(_flow_vars.u_var(), qp);
v = context.interior_value(_flow_vars.v_var(), qp);
libMesh::Gradient grad_T;
grad_T = context.interior_gradient(_temp_vars.T_var(), qp);
libMesh::NumberVectorValue U (u,v);
if (_dim == 3)
U(2) = context.interior_value(_flow_vars.w_var(), qp);
const libMesh::Number r = u_qpoint[qp](0);
libMesh::Real jac = JxW[qp];
if( _is_axisymmetric )
{
jac *= r;
}
// First, an i-loop over the degrees of freedom.
for (unsigned int i=0; i != n_T_dofs; i++)
{
FT(i) += jac *
(-_rho*_Cp*T_phi[i][qp]*(U*grad_T) // convection term
-_k*(T_gradphi[i][qp]*grad_T) ); // diffusion term
if (compute_jacobian)
{
for (unsigned int j=0; j != n_T_dofs; j++)
{
// TODO: precompute some terms like:
// _rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*T_grad_phi[j][qp])
KTT(i,j) += jac *
(-_rho*_Cp*T_phi[i][qp]*(U*T_gradphi[j][qp]) // convection term
-_k*(T_gradphi[i][qp]*T_gradphi[j][qp])); // diffusion term
} // end of the inner dof (j) loop
// Matrix contributions for the Tu, Tv and Tw couplings (n_T_dofs same as n_u_dofs, n_v_dofs and n_w_dofs)
for (unsigned int j=0; j != n_u_dofs; j++)
{
KTu(i,j) += jac*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(0)));
KTv(i,j) += jac*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(1)));
if (_dim == 3)
(*KTw)(i,j) += jac*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(2)));
} // end of the inner dof (j) loop
} // end - if (compute_jacobian && context.get_elem_solution_derivative())
} // end of the outer dof (i) loop
} // end of the quadrature point (qp) loop
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("HeatTransfer::element_time_derivative");
#endif
return;
}
void PracticeCDRinv::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/ ){
// The number of local degrees of freedom in each variable.
const unsigned int n_c_dofs = context.get_dof_indices(_c_var).size();
// We get some references to cell-specific data that
// will be used to assemble the linear system.
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(_c_var)->get_JxW();
// The temperature shape function gradients (in global coords.)
// at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& dphi =
context.get_element_fe(_c_var)->get_dphi();
const std::vector<std::vector<libMesh::Real> >& phi = context.get_element_fe(_c_var)->get_phi();
const std::vector<libMesh::Point>& q_points =
context.get_element_fe(_c_var)->get_xyz();
libMesh::DenseSubMatrix<libMesh::Number> &J_c_zc = context.get_elem_jacobian(_c_var, _zc_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_c_c = context.get_elem_jacobian(_c_var, _c_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_zc_c = context.get_elem_jacobian(_zc_var, _c_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_zc_fc = context.get_elem_jacobian(_zc_var, _fc_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_fc_zc = context.get_elem_jacobian(_fc_var, _zc_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_fc_fc = context.get_elem_jacobian(_fc_var, _fc_var);
libMesh::DenseSubVector<libMesh::Number> &Rc = context.get_elem_residual( _c_var );;
libMesh::DenseSubVector<libMesh::Number> &Rzc = context.get_elem_residual( _zc_var );
libMesh::DenseSubVector<libMesh::Number> &Rfc = context.get_elem_residual( _fc_var );
// 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();
for (unsigned int qp=0; qp != n_qpoints; qp++){
libMesh::Number
c = context.interior_value(_c_var, qp),
zc = context.interior_value(_zc_var, qp),
fc = context.interior_value(_fc_var, qp);
libMesh::Gradient
grad_c = context.interior_gradient(_c_var, qp),
grad_zc = context.interior_gradient(_zc_var, qp),
grad_fc = context.interior_gradient(_fc_var, qp);
//location of quadrature point
const libMesh::Real ptx = q_points[qp](0);
const libMesh::Real pty = q_points[qp](1);
int xind, yind;
libMesh::Real xdist = 1.e10; libMesh::Real ydist = 1.e10;
for(int ii=0; ii<x_pts.size(); ii++){
libMesh::Real tmp = std::abs(ptx - x_pts[ii]);
if(xdist > tmp){
xdist = tmp;
xind = ii;
}
else
break;
}
for(int jj=0; jj<y_pts[xind].size(); jj++){
libMesh::Real tmp = std::abs(pty - y_pts[xind][jj]);
if(ydist > tmp){
ydist = tmp;
yind = jj;
}
else
break;
}
libMesh::Real u = vel_field[xind][yind](0);
libMesh::Real v = vel_field[xind][yind](1);
libMesh::NumberVectorValue U (u, v);
// First, an i-loop over the degrees of freedom.
for (unsigned int i=0; i != n_c_dofs; i++){
Rc(i) += JxW[qp]*(-_k*grad_zc*dphi[i][qp] + U*grad_zc*phi[i][qp] + 2*_R*zc*c*phi[i][qp]);
Rzc(i) += JxW[qp]*(-_k*grad_c*dphi[i][qp] - U*grad_c*phi[i][qp] + _R*c*c*phi[i][qp] + fc*phi[i][qp]);
Rfc(i) += JxW[qp]*(_beta*grad_fc*dphi[i][qp] + zc*phi[i][qp]);
if (compute_jacobian){
for (unsigned int j=0; j != n_c_dofs; j++){
J_c_zc(i,j) += JxW[qp]*(-_k*dphi[j][qp]*dphi[i][qp] + U*dphi[j][qp]*phi[i][qp]
+ 2*_R*phi[j][qp]*c*phi[i][qp]);
J_c_c(i,j) += JxW[qp]*(2*_R*zc*phi[j][qp]*phi[i][qp]);
J_zc_c(i,j) += JxW[qp]*(-_k*dphi[j][qp]*dphi[i][qp] - U*dphi[j][qp]*phi[i][qp]
+ 2*_R*c*phi[j][qp]*phi[i][qp]);
J_zc_fc(i,j) += JxW[qp]*(phi[j][qp]*phi[i][qp]);
J_fc_zc(i,j) += JxW[qp]*(phi[j][qp]*phi[i][qp]);
J_fc_fc(i,j) += JxW[qp]*(_beta*dphi[j][qp]*dphi[i][qp]);
} // end of the inner dof (j) loop
} // end - if (compute_jacobian && context.get_elem_solution_derivative())
} // end of the outer dof (i) loop
} // end of the quadrature point (qp) loop
for(unsigned int dnum=0; dnum<datavals.size(); dnum++){
libMesh::Point data_point = datapts[dnum];
if(context.get_elem().contains_point(data_point)){
libMesh::Number cpred = context.point_value(_c_var, data_point);
libMesh::Number cstar = datavals[dnum];
unsigned int dim = context.get_system().get_mesh().mesh_dimension();
libMesh::FEType fe_type = context.get_element_fe(_c_var)->get_fe_type();
//go between physical and reference element
libMesh::Point c_master = libMesh::FEInterface::inverse_map(dim, fe_type, &context.get_elem(), data_point);
std::vector<libMesh::Real> point_phi(n_c_dofs);
for (unsigned int i=0; i != n_c_dofs; i++){
//get value of basis function at mapped point in reference (master) element
point_phi[i] = libMesh::FEInterface::shape(dim, fe_type, &context.get_elem(), i, c_master);
}
for (unsigned int i=0; i != n_c_dofs; i++){
Rc(i) += (cpred - cstar)*point_phi[i];
if (compute_jacobian){
for (unsigned int j=0; j != n_c_dofs; j++)
J_c_c(i,j) += point_phi[j]*point_phi[i] ;
}
}
}
}
return;
}
void HeatConduction<K>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/ )
{
// The number of local degrees of freedom in each variable.
const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size();
// We get some references to cell-specific data that
// will be used to assemble the linear system.
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(_temp_vars.T_var())->get_JxW();
// The temperature shape function gradients (in global coords.)
// at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi =
context.get_element_fe(_temp_vars.T_var())->get_dphi();
// The subvectors and submatrices we need to fill:
//
// K_{\alpha \beta} = R_{\alpha},{\beta} = \partial{ R_{\alpha} } / \partial{ {\beta} } (where R denotes residual)
// e.g., for \alpha = T and \beta = v we get: K_{Tu} = R_{T},{u}
//
libMesh::DenseSubMatrix<libMesh::Number> &KTT = context.get_elem_jacobian(_temp_vars.T_var(), _temp_vars.T_var()); // R_{T},{T}
libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(_temp_vars.T_var()); // R_{T}
// 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();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Compute the solution & its gradient at the old Newton iterate.
libMesh::Gradient grad_T;
grad_T = context.interior_gradient(_temp_vars.T_var(), qp);
// Compute the conductivity at this qp
libMesh::Real _k_qp = this->_k(context, qp);
// First, an i-loop over the degrees of freedom.
for (unsigned int i=0; i != n_T_dofs; i++)
{
FT(i) += JxW[qp]*(-_k_qp*(T_gradphi[i][qp]*grad_T));
if (compute_jacobian)
{
for (unsigned int j=0; j != n_T_dofs; j++)
{
// TODO: precompute some terms like:
// _rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*T_grad_phi[j][qp])
KTT(i,j) += JxW[qp] * context.get_elem_solution_derivative() *
( -_k_qp*(T_gradphi[i][qp]*T_gradphi[j][qp]) ); // diffusion term
} // end of the inner dof (j) loop
} // end - if (compute_jacobian && context.get_elem_solution_derivative())
} // end of the outer dof (i) loop
} // end of the quadrature point (qp) loop
return;
}
