This class corresponds to the viscous part of the "natural" boundary condition for the energy equation, i.e. More...

#include <NSEnergyViscousBC.h>

Inheritance diagram for NSEnergyViscousBC:

Public Member Functions
	NSEnergyViscousBC (const InputParameters &parameters)

Protected Member Functions
virtual Real	computeQpResidual ()
	Just like other kernels, we must overload the Residual and Jacobian contributions... More...

virtual Real	computeQpJacobian ()

virtual Real	computeQpOffDiagJacobian (unsigned jvar)

bool	isNSVariable (unsigned var)

unsigned	mapVarNumber (unsigned var)

Protected Attributes
const VariableGradient &	_grad_temperature

const MaterialProperty< Real > &	_thermal_conductivity

NSViscStressTensorDerivs< NSEnergyViscousBC >	_vst_derivs

NSTemperatureDerivs< NSEnergyViscousBC >	_temp_derivs

std::vector< const VariableGradient * >	_gradU

const VariableValue &	_u_vel

const VariableValue &	_v_vel

const VariableValue &	_w_vel

const VariableValue &	_rho

const VariableValue &	_rho_u

const VariableValue &	_rho_v

const VariableValue &	_rho_w

const VariableValue &	_rho_E

const VariableGradient &	_grad_rho

const VariableGradient &	_grad_rho_u

const VariableGradient &	_grad_rho_v

const VariableGradient &	_grad_rho_w

const VariableGradient &	_grad_rho_E

unsigned	_rho_var_number

unsigned	_rhou_var_number

unsigned	_rhov_var_number

unsigned	_rhow_var_number

unsigned	_rhoE_var_number

const MaterialProperty< Real > &	_dynamic_viscosity

const MaterialProperty< RealTensorValue > &	_viscous_stress_tensor

const IdealGasFluidProperties &	_fp

Friends
template<class U >
class	NSViscStressTensorDerivs

template<class U >
class	NSTemperatureDerivs

Detailed Description

This class corresponds to the viscous part of the "natural" boundary condition for the energy equation, i.e.

int_{Gamma} n . (- k*grad(T) - tau*u) v

A typical use for this kernel would be a subsonic outflow BC in which the pressure is specified. In this case, the residual and Jacobian contrbutions of the k*grad(T) and n.tau*u terms are computed and added to the matrix/rhs.

Definition at line 33 of file NSEnergyViscousBC.h.

Constructor & Destructor Documentation

◆ NSEnergyViscousBC()

NSEnergyViscousBC::NSEnergyViscousBC ( const InputParameters & parameters )

Definition at line 25 of file NSEnergyViscousBC.C.

   : NSIntegratedBC(parameters),
     _grad_temperature(coupledGradient(NS::temperature)),
     _thermal_conductivity(getMaterialProperty<Real>("thermal_conductivity")),
     // Viscous stress tensor derivative computing object
     _vst_derivs(*this),
     // Temperature derivative computing object
     _temp_derivs(*this)
 {
   // Store pointers to all variable gradients in a single vector.
   _gradU.resize(5);
   _gradU[0] = &_grad_rho;
   _gradU[1] = &_grad_rho_u;
   _gradU[2] = &_grad_rho_v;
   _gradU[3] = &_grad_rho_w;
   _gradU[4] = &_grad_rho_E;
 }

Member Function Documentation

◆ computeQpJacobian()

Real NSEnergyViscousBC::computeQpJacobian ( )

protectedvirtual

Definition at line 62 of file NSEnergyViscousBC.C.

 {
   // See notes for this term, involves temperature Hessian
   Real thermal_term = 0.0;
  
   for (unsigned int ell = 0; ell < LIBMESH_DIM; ++ell)
   {
     Real intermediate_result = 0.;
  
     // The temperature Hessian contribution
     for (unsigned n = 0; n < 5; ++n)
       intermediate_result += _temp_derivs.get_hess(/*m=*/4, n) * (*_gradU[n])[_qp](ell);
  
     // Hit Hessian contribution with test function
     intermediate_result *= _phi[_j][_qp];
  
     // Add in the temperature gradient contribution
     intermediate_result += _temp_derivs.get_grad(/*rhoE=*/4) * _grad_phi[_j][_qp](ell);
  
     // Hit the result with the normal component, accumulate in thermal_term
     thermal_term += intermediate_result * _normals[_qp](ell);
   }
  
   // Hit thermal_term with thermal conductivity
   thermal_term *= _thermal_conductivity[_qp];
  
   return (-thermal_term) * _test[_i][_qp];
 }

◆ computeQpOffDiagJacobian()

Real NSEnergyViscousBC::computeQpOffDiagJacobian ( unsigned jvar )

protectedvirtual

Definition at line 92 of file NSEnergyViscousBC.C.

 {
   if (isNSVariable(jvar))
   {
     // Note: This function requires both _vst_derivs *and* _temp_derivs
  
     // Convenience variables
     const RealTensorValue & tau = _viscous_stress_tensor[_qp];
  
     Real rho = _rho[_qp];
     Real phij = _phi[_j][_qp];
     RealVectorValue U(_rho_u[_qp], _rho_v[_qp], _rho_w[_qp]);
  
     // Map jvar into the variable m for our problem, regardless of
     // how Moose has numbered things.
     unsigned m = mapVarNumber(jvar);
  
     //
     // 1.) Thermal term derivatives
     //
  
     // See notes for this term, involves temperature Hessian
     Real thermal_term = 0.;
  
     for (unsigned ell = 0; ell < LIBMESH_DIM; ++ell)
     {
       Real intermediate_result = 0.;
  
       // The temperature Hessian contribution
       for (unsigned n = 0; n < 5; ++n)
         intermediate_result += _temp_derivs.get_hess(m, n) * (*_gradU[n])[_qp](ell);
  
       // Hit Hessian contribution with test function
       intermediate_result *= _phi[_j][_qp];
  
       // Add in the temperature gradient contribution
       intermediate_result += _temp_derivs.get_grad(m) * _grad_phi[_j][_qp](ell);
  
       // Hit the result with the normal component, accumulate in thermal_term
       thermal_term += intermediate_result * _normals[_qp](ell);
     }
  
     // Hit thermal_term with thermal conductivity
     thermal_term *= _thermal_conductivity[_qp];
  
     //
     // 2.) Viscous term derivatives
     //
  
     // Compute viscous term derivatives
     Real visc_term = 0.;
  
     switch (m)
     {
       case 0: // density
       {
         // Loop over k and ell as in the notes...
         for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
         {
           Real intermediate_value = 0.0;
           for (unsigned int ell = 0; ell < LIBMESH_DIM; ++ell)
             intermediate_value +=
                 (U(ell) / rho * (-tau(k, ell) * phij / rho + _vst_derivs.dtau(k, ell, m)));
  
           // Hit accumulated value with normal component k.  We will multiply by test function at
           // the end of this routine...
           visc_term += intermediate_value * _normals[_qp](k);
         } // end for k
  
         break;
       } // end case 0
  
       case 1:
       case 2:
       case 3: // momentums
       {
         // Map m -> 0,1,2 as usual...
         unsigned int m_local = m - 1;
  
         // Loop over k and ell as in the notes...
         for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
         {
           Real intermediate_value = tau(k, m_local) * phij / rho;
  
           for (unsigned int ell = 0; ell < LIBMESH_DIM; ++ell)
             intermediate_value += _vst_derivs.dtau(k, ell, m) * U(ell) /
                                   rho; // Note: pass 'm' to dtau, it will convert it internally
  
           // Hit accumulated value with normal component k.
           visc_term += intermediate_value * _normals[_qp](k);
         } // end for k
  
         break;
       } // end case 1,2,3
  
       case 4: // energy
         mooseError("Shouldn't get here, this is the on-diagonal entry!");
         break;
  
       default:
         mooseError("Invalid m value.");
         break;
     }
  
     // Finally, sum up the different contributions (with appropriate
     // sign) multiply by the test function, and return.
     return (-thermal_term - visc_term) * _test[_i][_qp];
   }
   else
     return 0.0;
 }

◆ computeQpResidual()

Real NSEnergyViscousBC::computeQpResidual ( )

protectedvirtual

Just like other kernels, we must overload the Residual and Jacobian contributions...

Definition at line 44 of file NSEnergyViscousBC.C.

 {
   // n . (- k*grad(T) - tau*u) v
  
   // Velocity vector object
   RealVectorValue vel(_u_vel[_qp], _v_vel[_qp], _w_vel[_qp]);
  
   // k*grad(T)
   RealVectorValue thermal_vec = _thermal_conductivity[_qp] * _grad_temperature[_qp];
  
   // tau*u
   RealVectorValue visc_vec = _viscous_stress_tensor[_qp] * vel;
  
   // Add everything up, dot with normal, hit with test function.
   return ((-thermal_vec - visc_vec) * _normals[_qp]) * _test[_i][_qp];
 }

◆ isNSVariable()

bool NSIntegratedBC::isNSVariable ( unsigned var )

protectedinherited

Definition at line 80 of file NSIntegratedBC.C.

 {
   if (var == _rho_var_number || var == _rhou_var_number || var == _rhov_var_number ||
       var == _rhow_var_number || var == _rhoE_var_number)
     return true;
   else
     return false;
 }

◆ mapVarNumber()

unsigned NSIntegratedBC::mapVarNumber ( unsigned var )

protectedinherited

Definition at line 90 of file NSIntegratedBC.C.

 {
   // Convert the Moose numbering to:
   // 0 for rho
   // 1 for rho*u
   // 2 for rho*v
   // 3 for rho*w
   // 4 for rho*e
   // regardless of the problem dimension, etc.
   unsigned int mapped_var_number;
  
   if (var == _rho_var_number)
     mapped_var_number = 0;
   else if (var == _rhou_var_number)
     mapped_var_number = 1;
   else if (var == _rhov_var_number)
     mapped_var_number = 2;
   else if (var == _rhow_var_number)
     mapped_var_number = 3;
   else if (var == _rhoE_var_number)
     mapped_var_number = 4;
   else
     mooseError("Invalid var!");
  
   return mapped_var_number;
 }