void HeatTransfer::element_time_derivative( bool compute_jacobian,
libMesh::FEMContext& 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.dof_indices_var[_T_var].size();
const unsigned int n_u_dofs = context.dof_indices_var[_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.element_fe_var[_T_var]->get_JxW();
// The temperature shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& T_phi =
context.element_fe_var[_T_var]->get_phi();
// The velocity shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& vel_phi =
context.element_fe_var[_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.element_fe_var[_T_var]->get_dphi();
const std::vector<libMesh::Point>& u_qpoint =
context.element_fe_var[this->_u_var]->get_xyz();
// We do this in the incompressible Navier-Stokes class and need to do it here too
// since _w_var won't have been defined in the global map.
if (_dim != 3)
_w_var = _u_var; // for convenience
libMesh::DenseSubMatrix<libMesh::Number> &KTT = *context.elem_subjacobians[_T_var][_T_var]; // R_{T},{T}
libMesh::DenseSubMatrix<libMesh::Number> &KTu = *context.elem_subjacobians[_T_var][_u_var]; // R_{T},{u}
libMesh::DenseSubMatrix<libMesh::Number> &KTv = *context.elem_subjacobians[_T_var][_v_var]; // R_{T},{v}
libMesh::DenseSubMatrix<libMesh::Number> &KTw = *context.elem_subjacobians[_T_var][_w_var]; // R_{T},{w}
libMesh::DenseSubVector<libMesh::Number> &FT = *context.elem_subresiduals[_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.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, w;
u = context.interior_value(_u_var, qp);
v = context.interior_value(_v_var, qp);
if (_dim == 3)
w = context.interior_value(_w_var, qp);
libMesh::Gradient grad_T;
grad_T = context.interior_gradient(_T_var, qp);
libMesh::NumberVectorValue U (u,v);
if (_dim == 3)
U(2) = w;
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.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 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 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;
}
