Hi. I have a question on how we can impose external force term, or right
hand side, in Stokes flow.
My governing equation is same with that of step-22, stokes flow
-nabla^2 u + grad p = f
-grad u = 0
but I want to impose 'f',
To do this, I made function that gives me f value on each point.
For example, if I want function of f thats looks like f=(x^2,y^2);
I would make function like this...
template <int dim>
class RightHandSide : public Function<dim>
{
public:
RightHandSide () : Function<dim>(dim+1) {}
virtual void vector_value (const Point<dim> &p,
Vector<double> &value) const;
};
template <int dim>
void
RightHandSide<dim>::vector_value (const Point<dim> &p,
Vector<double> &values) const
{
values(0) = pow(p[0],2);
values(1) = pow(p[1],2);
values(2) = 0.0;
}
After that I may consider this 'f' term when I assemble system.
but I don't see a way to how I should try modify following read lines of
the code from step-22
for (; cell!=endc; ++cell)
{
fe_values.reinit (cell);
local_matrix = 0;
local_rhs = 0;
right_hand_side.vector_value_list(fe_values.get_quadrature_points(),
rhs_values);
for (unsigned int q=0; q<n_q_points; ++q)
{
for (unsigned int k=0; k<dofs_per_cell; ++k)
{
phi_grads_u[k] = fe_values[velocities].symmetric_gradient (k, q);
div_phi_u[k] = fe_values[velocities].divergence (k, q);
phi_p[k] = fe_values[pressure].value (k, q);
}
for (unsigned int i=0; i<dofs_per_cell; ++i)
{
for (unsigned int j=0; j<=i; ++j)
{
local_matrix(i,j) += (phi_grads_u[i] * phi_grads_u[j]
- div_phi_u[i] * phi_p[j]
- phi_p[i] * div_phi_u[j]
+ phi_p[i] * phi_p[j])
* fe_values.JxW(q);
}
*const unsigned int component_i =*
* fe.system_to_component_index(i).first;*
* local_rhs(i) += fe_values.shape_value(i,q) **
* rhs_values[q](component_i) **
* fe_values.JxW(q);*
}
}
My 'f' is not '0' any more but it has multiple components.
in fact, the weak form of the governing equation '-nabla^2 u + grad p = f '
also should have two components,..(x and y) ....
How can I achieve this....?
Thank you
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