libMesh::Real SpalartAllmarasStabilizationHelper::compute_res_spalart_steady( AssemblyContext& context,
unsigned int qp, const libMesh::Real rho, const libMesh::Real mu, const libMesh::Real distance_qp, const bool infinite_distance) const
{
// 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);
libMesh::RealGradient grad_u = context.fixed_interior_gradient(this->_flow_vars.u(), qp);
libMesh::RealGradient grad_v = context.fixed_interior_gradient(this->_flow_vars.v(), qp);
libMesh::Number nu_value = context.interior_value(this->_turbulence_vars.nu(), qp);
libMesh::RealGradient grad_nu = context.fixed_interior_gradient(this->_turbulence_vars.nu(), qp);
libMesh::RealTensor hess_nu = context.fixed_interior_hessian(this->_turbulence_vars.nu(), qp);
// The convection term
libMesh::Number rhoUdotGradnu = rho*(U*grad_nu);
// The diffusion term
libMesh::Number inv_sigmadivnuplusnuphysicalGradnu = (1./this->_sa_params.get_sigma())*(grad_nu*grad_nu + ((nu_value + mu)*(hess_nu(0,0) + hess_nu(1,1) + (this->_flow_vars.dim() == 3)?hess_nu(2,2):0)) + this->_sa_params.get_cb2()*grad_nu*grad_nu);
// The source term
libMesh::Real vorticity_value_qp = this->_spalart_allmaras_helper.vorticity(context, qp);
libMesh::Real S_tilde = this->_sa_params.source_fn(nu_value, mu, distance_qp, vorticity_value_qp, infinite_distance);
libMesh::Real source_term = this->_sa_params.get_cb1()*S_tilde*nu_value;
libMesh::Real kappa2 = (this->_sa_params.get_kappa())*(this->_sa_params.get_kappa());
libMesh::Real cw1 = this->_sa_params.get_cb1()/kappa2 + (1.0 + this->_sa_params.get_cb2())/this->_sa_params.get_sigma();
// The destruction term
libMesh::Real fw = this->_sa_params.destruction_fn(nu_value, distance_qp, S_tilde, infinite_distance);
libMesh::Real destruction_term = 0.0;
if(infinite_distance)
{
destruction_term = 0.0;
}
else
{
destruction_term = cw1*fw*pow(nu_value/distance_qp, 2.);
}
return rhoUdotGradnu + source_term + inv_sigmadivnuplusnuphysicalGradnu - destruction_term;
}
void HeatTransferStabilizationHelper::compute_res_energy_steady_and_derivs
( AssemblyContext& context,
unsigned int qp,
const libMesh::Real rho,
const libMesh::Real Cp,
const libMesh::Real k,
libMesh::Real &res,
libMesh::Real &d_res_dT,
libMesh::Gradient &d_res_dgradT,
libMesh::Tensor &d_res_dhessT,
libMesh::Gradient &d_res_dU
) const
{
libMesh::Gradient grad_T = context.fixed_interior_gradient(this->_temp_vars.T(), qp);
libMesh::Tensor hess_T = context.fixed_interior_hessian(this->_temp_vars.T(), qp);
libMesh::RealGradient rhocpU( rho*Cp*context.fixed_interior_value(this->_flow_vars.u(), qp),
rho*Cp*context.fixed_interior_value(this->_flow_vars.v(), qp) );
if(this->_flow_vars.dim() == 3)
rhocpU(2) = rho*Cp*context.fixed_interior_value(this->_flow_vars.w(), qp);
res = rhocpU*grad_T - k*(hess_T(0,0) + hess_T(1,1) + hess_T(2,2));
d_res_dT = 0;
d_res_dgradT = rhocpU;
d_res_dhessT = 0;
d_res_dhessT(0,0) = -k;
d_res_dhessT(1,1) = -k;
d_res_dhessT(2,2) = -k;
d_res_dU = rho * Cp * grad_T;
}
void LowMachNavierStokesSPGSMStabilization<Mu,SH,TC>::assemble_energy_mass_residual( 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.fixed_interior_value(this->_flow_vars.u(), qp);
v = context.fixed_interior_value(this->_flow_vars.v(), qp);
libMesh::Gradient grad_T = context.fixed_interior_gradient(this->_temp_vars.T(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->mesh_dim(context) == 3)
U(2) = context.fixed_interior_value(this->_flow_vars.w(), qp); // w
libMesh::Real T = context.fixed_interior_value( this->_temp_vars.T(), qp );
libMesh::Real rho = this->rho( T, this->get_p0_transient( 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, false );
libMesh::Real RE_t = this->compute_res_energy_transient( context, qp );
for (unsigned int i=0; i != n_T_dofs; i++)
{
FT(i) -= rho_cp*tau_E*RE_t*U*T_gradphi[i][qp]*JxW[qp];
}
}
return;
}
libMesh::Real HeatTransferStabilizationHelper::compute_res_energy_steady( AssemblyContext& context,
unsigned int qp,
const libMesh::Real rho,
const libMesh::Real Cp,
const libMesh::Real k ) const
{
libMesh::Gradient grad_T = context.fixed_interior_gradient(this->_temp_vars.T(), qp);
libMesh::Tensor hess_T = context.fixed_interior_hessian(this->_temp_vars.T(), qp);
libMesh::RealGradient rhocpU( rho*Cp*context.fixed_interior_value(this->_flow_vars.u(), qp),
rho*Cp*context.fixed_interior_value(this->_flow_vars.v(), qp) );
if(this->_flow_vars.dim() == 3)
rhocpU(2) = rho*Cp*context.fixed_interior_value(this->_flow_vars.w(), qp);
return rhocpU*grad_T - k*(hess_T(0,0) + hess_T(1,1) + hess_T(2,2));
}
void LowMachNavierStokesSPGSMStabilization<Mu,SH,TC>::assemble_momentum_mass_residual( 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.fixed_interior_value( this->_temp_vars.T(), qp );
libMesh::Real rho = this->rho( T, this->get_p0_transient( context, qp ) );
libMesh::Real mu = this->_mu(T);
libMesh::RealGradient U( context.fixed_interior_value(this->_flow_vars.u(), qp),
context.fixed_interior_value(this->_flow_vars.v(), qp) );
libMesh::RealGradient grad_u = context.fixed_interior_gradient(this->_flow_vars.u(), qp);
libMesh::RealGradient grad_v = context.fixed_interior_gradient(this->_flow_vars.v(), qp);
libMesh::RealGradient grad_w;
if( this->mesh_dim(context) == 3 )
{
U(2) = context.fixed_interior_value(this->_flow_vars.w(), qp);
grad_w = context.fixed_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 tau_M = this->_stab_helper.compute_tau_momentum( context, qp, g, G, rho, U, mu, false );
libMesh::Real tau_C = this->_stab_helper.compute_tau_continuity( tau_M, g );
libMesh::Real RC_t = this->compute_res_continuity_transient( context, qp );
libMesh::RealGradient RM_s = this->compute_res_momentum_steady( context, qp );
libMesh::RealGradient RM_t = this->compute_res_momentum_transient( context, qp );
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) -= ( tau_C*RC_t*u_gradphi[i][qp](0)
+ tau_M*RM_t(0)*rho*U*u_gradphi[i][qp] )*JxW[qp];
Fv(i) -= ( tau_C*RC_t*u_gradphi[i][qp](1)
+ tau_M*RM_t(1)*rho*U*u_gradphi[i][qp] )*JxW[qp];
if( this->mesh_dim(context) == 3 )
{
(*Fw)(i) -= ( tau_C*RC_t*u_gradphi[i][qp](2)
+ tau_M*RM_t(2)*rho*U*u_gradphi[i][qp] )*JxW[qp];
}
}
}
return;
}
