HI, Wofgang,
thanks very much for your reply. It indeed helps. Now I can
get the gradient of the velocity of the previous solution, basically
\nabla u, which is a nonsymmetric second-order tensor, with 4 entries
in a 2D case.
std::vector<Tensor<2,dim> > grads_velocity (n_q_points);
for (; cell!=endc; ++cell, ++stokes_cell)
{
stokes_fe_values[velocities].get_function_gradients (stokes_solution,
grads_velocity);
}
where grads_velocity[0] is a second-order tensor for the 0-th (first)
quadrature point.
For a 2D problem, it should have 2*2=4 entries, corresponding to a matrix
like
{dudx, dvdx,
dudy, dvdy} .
In fact, I can also get access to the four entries of grads_velocity[0] as
grads_velocity[0][0][0], grads_velocity[0][0][1], grads_velocity[0][1][0],
grads_velocity[0][1][1]. Now the only thing I need to know what is the
one-to-one
correspondence between the above 2-by-2 matrix and the four entries
of the tensor?
Thanks in advance,
best,
lailai
On Sunday, December 11, 2016 at 9:58:49 PM UTC-5, Wolfgang Bangerth wrote:
>
> On 12/10/2016 05:18 PM, Lailai Zhu wrote:
> >
> > I started everything from the step-31, Stokes equations solving vector
> > field 'u' and scalar field 'p', and a temperature equation for 'T'.
> >
> > My problem is similar to this, namely I have a scalar field, say 'C',
> 'C'
> > is an explicit function of 'u' and 'p' (for example C=(\nabla u : \nabla
> u)
> > - p ), so i don't need to use fem to solve for 'C' like the example 31
> > solving for 'T'. 'C' can be directly expression by 'u' and 'p'.
> >
> > I would like to use 'C' a lot as intermediate variable (for example to
> > help define the volume force of the momentum equations), so I need to
> know
> > 'C' at every quadrature points. I also want to export 'C' in the .vtk
> > output.
> >
> > My question is what be the most reasonable or efficient way to define
> and
> > calculate such 'C'. Do I need to define 'C' as a solution variable,
> exactly
> > like 'T' even I don't really need to solve for it? Thanks in advance,
>
> The answer is different for the two contexts. For creating output in a
> .vtk
> file, you will want to compute the quantity in a postprocessor derived
> from
> DataPostprocessor. There are a number of tutorial programs that show how
> to do
> this.
>
> On the other hand, if you need this quantity in the assembly of another
> equation, then you will want to compute it at the quadrature points you
> care
> about, whenever that is necessary. That is no different than using the
> previous solution to define the coefficient in the current iteration in a
> nonlinear scheme. You probably want to look at step-15 to see how to do
> this.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
>
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