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;
}
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;
}
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));
}
