Real
INSSplitMomentum::computeQpOffDiagJacobian(unsigned jvar)
{
if ((jvar == _u_vel_var_number) || (jvar == _v_vel_var_number) || (jvar == _w_vel_var_number))
{
// Derivative of viscous stress tensor
RealTensorValue dtau;
// Initialize to invalid value, then determine correct value.
unsigned vel_index = 99;
// Set index and build dtau for that index
if (jvar == _u_vel_var_number)
{
vel_index = 0;
dtau(0, 0) = 2. * _grad_phi[_j][_qp](0);
dtau(0, 1) = _grad_phi[_j][_qp](1);
dtau(0, 2) = _grad_phi[_j][_qp](2);
dtau(1, 0) = _grad_phi[_j][_qp](1);
dtau(2, 0) = _grad_phi[_j][_qp](2);
}
else if (jvar == _v_vel_var_number)
{
vel_index = 1;
/* */ dtau(0, 1) = _grad_phi[_j][_qp](0);
dtau(1, 0) = _grad_phi[_j][_qp](0);
dtau(1, 1) = 2. * _grad_phi[_j][_qp](1);
dtau(1, 2) = _grad_phi[_j][_qp](2);
/* */ dtau(2, 1) = _grad_phi[_j][_qp](2);
}
else if (jvar == _w_vel_var_number)
{
vel_index = 2;
/* */ dtau(0, 2) =
_grad_phi[_j][_qp](0);
/* */ dtau(1, 2) =
_grad_phi[_j][_qp](1);
dtau(2, 0) = _grad_phi[_j][_qp](0);
dtau(2, 1) = _grad_phi[_j][_qp](1);
dtau(2, 2) = 2. * _grad_phi[_j][_qp](2);
}
// Vector object for test function
RealVectorValue test;
test(_component) = _test[_i][_qp];
// Vector object for U
RealVectorValue U(_u_vel[_qp], _v_vel[_qp], _w_vel[_qp]);
// Tensor object for test function gradient
RealTensorValue grad_test;
for (unsigned k = 0; k < 3; ++k)
grad_test(_component, k) = _grad_test[_i][_qp](k);
// Compute the convective part
RealVectorValue convective_jac = _phi[_j][_qp] * RealVectorValue(_grad_u_vel[_qp](vel_index),
_grad_v_vel[_qp](vel_index),
_grad_w_vel[_qp](vel_index));
// Extra contribution in vel_index component
convective_jac(vel_index) += U * _grad_phi[_j][_qp];
Real convective_part = convective_jac * test;
// Compute the viscous part
Real viscous_part = (_mu[_qp] / _rho[_qp]) * dtau.contract(grad_test);
// Return the result
return convective_part + viscous_part;
}
else
return 0;
}
Real INSChorinPredictor::computeQpOffDiagJacobian(unsigned jvar)
{
switch (_predictor_enum)
{
case OLD:
{
return 0.;
}
case NEW:
{
if ((jvar == _u_vel_var_number) || (jvar == _v_vel_var_number) || (jvar == _w_vel_var_number))
{
// Derivative of grad_U wrt the velocity component
RealTensorValue dgrad_U;
// Initialize to invalid value, then determine correct value.
unsigned vel_index = 99;
// Map jvar into the indices (0,1,2)
if (jvar == _u_vel_var_number)
vel_index = 0;
else if (jvar == _v_vel_var_number)
vel_index = 1;
else if (jvar == _w_vel_var_number)
vel_index = 2;
// Fill in the vel_index'th row of dgrad_U with _grad_phi[_j][_qp]
for (unsigned k=0; k<3; ++k)
dgrad_U(vel_index,k) = _grad_phi[_j][_qp](k);
// Vector object for test function
RealVectorValue test;
test(_component) = _test[_i][_qp];
// Vector object for U
RealVectorValue U(_u_vel[_qp], _v_vel[_qp], _w_vel[_qp]);
// Tensor object for test function gradient
RealTensorValue grad_test;
for (unsigned k=0; k<3; ++k)
grad_test(_component, k) = _grad_test[_i][_qp](k);
// Compute the convective part
RealVectorValue convective_jac = _phi[_j][_qp] * RealVectorValue(_grad_u_vel[_qp](vel_index),
_grad_v_vel[_qp](vel_index),
_grad_w_vel[_qp](vel_index));
// Extra contribution in vel_index component
convective_jac(vel_index) += U*_grad_phi[_j][_qp];
// Be sure to scale by _dt!
Real convective_part = _dt * (convective_jac * test);
// Compute the viscous part, be sure to scale by _dt. Note: the contracted
// value should be zero unless vel_index and _component match.
Real viscous_part = _dt * (_mu/_rho) * dgrad_U.contract(grad_test);
// Return the result
return convective_part + viscous_part;
}
else
return 0;
}
case STAR:
{
if (jvar == _u_vel_star_var_number)
{
return _dt * _phi[_j][_qp] * _grad_u[_qp](0) * _test[_i][_qp];
}
else if (jvar == _v_vel_star_var_number)
{
return _dt * _phi[_j][_qp] * _grad_u[_qp](1) * _test[_i][_qp];
}
else if (jvar == _w_vel_star_var_number)
{
return _dt * _phi[_j][_qp] * _grad_u[_qp](2) * _test[_i][_qp];
}
else
return 0;
}
default:
mooseError("Unrecognized Chorin predictor type requested.");
}
}
