void AveragedTurbine<Mu>::nonlocal_time_derivative(bool compute_jacobian,
AssemblyContext& context,
CachedValues& /* cache */ )
{
libMesh::DenseSubMatrix<libMesh::Number> &Kss =
context.get_elem_jacobian(this->fan_speed_var(), this->fan_speed_var()); // R_{s},{s}
libMesh::DenseSubVector<libMesh::Number> &Fs =
context.get_elem_residual(this->fan_speed_var()); // R_{s}
const std::vector<libMesh::dof_id_type>& dof_indices =
context.get_dof_indices(this->fan_speed_var());
const libMesh::Number fan_speed =
context.get_system().current_solution(dof_indices[0]);
const libMesh::Number output_torque =
this->torque_function(libMesh::Point(0), fan_speed);
Fs(0) += output_torque;
if (compute_jacobian)
{
// FIXME: we should replace this FEM with a hook to the AD fparser stuff
const libMesh::Number epsilon = 1e-6;
const libMesh::Number output_torque_deriv =
(this->torque_function(libMesh::Point(0), fan_speed+epsilon) -
this->torque_function(libMesh::Point(0), fan_speed-epsilon)) / (2*epsilon);
Kss(0,0) += output_torque_deriv * context.get_elem_solution_derivative();
}
return;
}
void ScalarODE::nonlocal_constraint(bool compute_jacobian,
AssemblyContext& context,
CachedValues& /* cache */ )
{
libMesh::DenseSubMatrix<libMesh::Number> &Kss =
context.get_elem_jacobian(_scalar_ode_var, _scalar_ode_var); // R_{s},{s}
libMesh::DenseSubVector<libMesh::Number> &Fs =
context.get_elem_residual(_scalar_ode_var); // R_{s}
const libMesh::Number constraint =
(*constraint_function)(context, libMesh::Point(0),
context.get_time());
Fs(0) += constraint;
if (compute_jacobian)
{
// FIXME: we should replace this hacky FDM with a hook to the
// AD fparser stuff
libMesh::DenseSubVector<libMesh::Number> &Us =
const_cast<libMesh::DenseSubVector<libMesh::Number>&>
(context.get_elem_solution(_scalar_ode_var)); // U_{s}
const libMesh::Number s = Us(0);
Us(0) = s + this->_epsilon;
libMesh::Number constraint_jacobian =
(*constraint_function)(context, libMesh::Point(0),
context.get_time());
Us(0) = s - this->_epsilon;
constraint_jacobian -=
(*constraint_function)(context, libMesh::Point(0),
context.get_time());
Us(0) = s;
constraint_jacobian /= (2*this->_epsilon);
Kss(0,0) += constraint_jacobian *
context.get_elem_solution_derivative();
}
return;
}
void AveragedTurbine<Mu>::nonlocal_mass_residual( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /* cache */ )
{
libMesh::DenseSubMatrix<libMesh::Number> &Kss =
context.get_elem_jacobian(this->fan_speed_var(), this->fan_speed_var()); // R_{s},{s}
libMesh::DenseSubVector<libMesh::Number> &Fs =
context.get_elem_residual(this->fan_speed_var()); // R_{s}
const libMesh::DenseSubVector<libMesh::Number> &Us =
context.get_elem_solution_rate(this->fan_speed_var());
const libMesh::Number& fan_speed = Us(0);
Fs(0) -= this->moment_of_inertia * fan_speed;
if (compute_jacobian)
{
Kss(0,0) -= this->moment_of_inertia * context.get_elem_solution_rate_derivative();
}
return;
}
bool DifferentiablePhysics::nonlocal_mass_residual(bool request_jacobian,
DiffContext &c)
{
FEMContext &context = cast_ref<FEMContext&>(c);
for (unsigned int var = 0; var != context.n_vars(); ++var)
{
if (!this->is_time_evolving(var))
continue;
if (c.get_system().variable(var).type().family != SCALAR)
continue;
const std::vector<dof_id_type>& dof_indices =
context.get_dof_indices(var);
const unsigned int n_dofs = cast_int<unsigned int>
(dof_indices.size());
DenseSubVector<Number> &Fs = context.get_elem_residual(var);
DenseSubMatrix<Number> &Kss = context.get_elem_jacobian( var, var );
const libMesh::DenseSubVector<libMesh::Number> &Us =
context.get_elem_solution(var);
for (unsigned int i=0; i != n_dofs; ++i)
{
Fs(i) -= Us(i);
if (request_jacobian)
Kss(i,i) -= context.elem_solution_rate_derivative;
}
}
return request_jacobian;
}
void AveragedTurbine<Mu>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /* cache */ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("AveragedTurbine::element_time_derivative");
#endif
// Element Jacobian * quadrature weights for interior integration
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_flow_vars.u())->get_JxW();
// The shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& u_phi =
context.get_element_fe(this->_flow_vars.u())->get_phi();
const std::vector<libMesh::Point>& u_qpoint =
context.get_element_fe(this->_flow_vars.u())->get_xyz();
// 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();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.u()); // R_{u},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.v()); // R_{u},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.u()); // R_{v},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.v()); // R_{v},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kus =
context.get_elem_jacobian(this->_flow_vars.u(),
this->fan_speed_var()); // R_{u},{s}
libMesh::DenseSubMatrix<libMesh::Number> &Ksu =
context.get_elem_jacobian(this->fan_speed_var(),
this->_flow_vars.u()); // R_{s},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvs =
context.get_elem_jacobian(this->_flow_vars.v(),
this->fan_speed_var()); // R_{v},{s}
libMesh::DenseSubMatrix<libMesh::Number> &Ksv =
context.get_elem_jacobian(this->fan_speed_var(),
this->_flow_vars.v()); // R_{s},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kss =
context.get_elem_jacobian(this->fan_speed_var(),
this->fan_speed_var()); // R_{s},{s}
libMesh::DenseSubMatrix<libMesh::Number>* Kwu = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kwv = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kww = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kuw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kvw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Ksw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kws = NULL;
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::Number>* Fw = NULL;
libMesh::DenseSubVector<libMesh::Number> &Fs = context.get_elem_residual(this->fan_speed_var()); // R_{s}
if( this->mesh_dim(context) == 3 )
{
Kuw = &context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.w()); // R_{u},{w}
Kvw = &context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.w()); // R_{v},{w}
Kwu = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.u()); // R_{w},{u}
Kwv = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.v()); // R_{w},{v}
Kww = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.w()); // R_{w},{w}
Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
Ksw = &context.get_elem_jacobian(this->fan_speed_var(), this->_flow_vars.w()); // R_{s},{w}
Kws = &context.get_elem_jacobian(this->_flow_vars.w(), this->fan_speed_var()); // R_{w},{s}
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++)
{
// Compute the solution at the old Newton iterate.
libMesh::Number u, v, s;
u = context.interior_value(this->_flow_vars.u(), qp);
v = context.interior_value(this->_flow_vars.v(), qp);
s = context.interior_value(this->fan_speed_var(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->mesh_dim(context) == 3)
U(2) = context.interior_value(this->_flow_vars.w(), qp); // w
libMesh::NumberVectorValue U_B_1;
libMesh::NumberVectorValue F;
libMesh::NumberTensorValue dFdU;
libMesh::NumberTensorValue* dFdU_ptr =
compute_jacobian ? &dFdU : NULL;
libMesh::NumberVectorValue dFds;
libMesh::NumberVectorValue* dFds_ptr =
compute_jacobian ? &dFds : NULL;
if (!this->compute_force(u_qpoint[qp], context.time, U, s,
U_B_1, F, dFdU_ptr, dFds_ptr))
continue;
libMesh::Real jac = JxW[qp];
// Using this dot product to derive torque *depends* on s=1
// and U_B_1 corresponding to 1 rad/sec base velocity; this
// means that the length of U_B_1 is equal to radius.
// F is the force on the air, so *negative* F is the force on
// the turbine.
Fs(0) -= U_B_1 * F * jac;
if (compute_jacobian)
{
Kss(0,0) -= U_B_1 * dFds * jac;
for (unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::Real jac_j = JxW[qp] * u_phi[j][qp];
for (unsigned int d=0; d != 3; ++d)
{
Ksu(0,j) -= jac_j * U_B_1(d) * dFdU(d,0);
Ksv(0,j) -= jac_j * U_B_1(d) * dFdU(d,1);
}
if (this->mesh_dim(context) == 3)
{
for (unsigned int d=0; d != 3; ++d)
(*Ksw)(0,j) -= jac_j * U_B_1(d) * dFdU(d,2);
}
} // End j dof loop
}
for (unsigned int i=0; i != n_u_dofs; i++)
{
const libMesh::Number jac_i = jac * u_phi[i][qp];
Fu(i) += F(0)*jac_i;
Fv(i) += F(1)*jac_i;
if( this->mesh_dim(context) == 3 )
(*Fw)(i) += F(2)*jac_i;
if( compute_jacobian )
{
Kus(i,0) += dFds(0) * jac_i;
Kvs(i,0) += dFds(1) * jac_i;
if( this->mesh_dim(context) == 3 )
(*Kws)(i,0) += dFds(2) * jac_i;
for (unsigned int j=0; j != n_u_dofs; j++)
{
const libMesh::Number jac_ij = jac_i * u_phi[j][qp];
Kuu(i,j) += jac_ij * dFdU(0,0);
Kuv(i,j) += jac_ij * dFdU(0,1);
Kvu(i,j) += jac_ij * dFdU(1,0);
Kvv(i,j) += jac_ij * dFdU(1,1);
if( this->mesh_dim(context) == 3 )
{
(*Kuw)(i,j) += jac_ij * dFdU(0,2);
(*Kvw)(i,j) += jac_ij * dFdU(1,2);
(*Kwu)(i,j) += jac_ij * dFdU(2,0);
(*Kwv)(i,j) += jac_ij * dFdU(2,1);
(*Kww)(i,j) += jac_ij * dFdU(2,2);
}
}
}
}
}
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("AveragedTurbine::element_time_derivative");
#endif
return;
}
