Question about plotting the solution.

[Najwa Alshehri]

Dear team,

I am seeking your help in understanding how few things work in dealii.

I am solving Stokes interface problem where viscosity differs in two parts of the domain ( outer part and immersed circle). I am solving using unfitted boundary approach ( boundary between domains do not align with the mesh). I am using Q2-Q1 Finite element.

I use the following data_out:

std::vector<std::string> solution_names(dim, "velocity");

solution_names.emplace_back("pressure");

std::vector<DataComponentInterpretation::DataComponentInterpretation>

data_component_interpretation(

dim, DataComponentInterpretation::component_is_part_of_vector);

data_component_interpretation.push_back(

DataComponentInterpretation::component_is_scalar);

const MappingQ<dim> mapping(1);

DataOut<dim> data_out;

data_out.attach_dof_handler(dof_handler);

data_out.add_data_vector(error_u, "error_u");

data_out.add_data_vector(error_p, "error_p");

data_out.add_data_vector(solution,

solution_names,

DataOut<dim>::type_dof_data,

data_component_interpretation);

data_out.add_data_vector(error_per_cell_omega, "error_indicator_omega");

data_out.build_patches(mapping, fe.degree + 1, DataOut<dim>::curved_inner_cells);

I removed the mean value of the approximated pressure in different ways. One of them is just like in step-56

const double mean_pressure = VectorTools::compute_mean_value(

dof_handler, QGauss<dim>(2 * pressure_degree + 10), solution, dim);

solution.block(1).add(-mean_pressure);

I noticed that the solution of the pressure have some (unexpected) oscillations at the interface even though the exact solution of the pressure is a smooth function (x^2-y^2). In fact, if I just look at the solution in 2d using heat map, those oscillations are not clear. 

However, in ParaView, when I use Warp by a scalar filter, they are so clear.

My questions are,

Is this "compute mean value" works with any order of finite element?

Am I using "build batches" wrong?

Is this a common behaviour if the coefficients jumps?

Any other suggestions are appreciated.

Thank you so much,

Najwa

[Wolfgang Bangerth]

Najwa:
if you have a discontinuous viscosity in the Stokes equations, I think you
want to read this paper:
https://www.math.colostate.edu/~bangerth/publications/2017-boussinesq.pdf
Specifically, section 3.3 talks about this situation, and it shows in figures
2 and 4 that you do get spikes in the pressure.

Best
W.


On 4/24/25 05:17, Najwa Alshehri wrote:
> *** Caution: EXTERNAL Sender ***

> 2d_p.png
> However, in ParaView, when I use Warp by a scalar filter, they are so clear.

> 3d_p.png
>
>
> My questions are,
> Is this "compute mean value" works with any order of finite element?
> Am I using "build batches" wrong?
> Is this a common behaviour if the coefficients jumps?
>
> Any other suggestions are appreciated.
>
> Thank you so much,
> Najwa
>
>
>
>
>

> --
> The deal.II project is located at http://www.dealii.org/
> <http://www.dealii.org/>
> For mailing list/forum options, see
> https://groups.google.com/d/forum/dealii?hl=en
> <https://groups.google.com/d/forum/dealii?hl=en>
> ---
> You received this message because you are subscribed to the Google Groups
> "deal.II User Group" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to dealii+un...@googlegroups.com
> <mailto:dealii+un...@googlegroups.com>.
> To view this discussion visit
> https://groups.google.com/d/msgid/dealii/d9a8c115-f363-42b5-bef2-9b26b62ae616n%40googlegroups.com <https://groups.google.com/d/msgid/dealii/d9a8c115-f363-42b5-bef2-9b26b62ae616n%40googlegroups.com?utm_medium=email&utm_source=footer>.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Najwa Alshehri]

Dear Professor Wolfgang,

Thank you very much for your answer. This is exactly what I wanted to confirm. I highly appreciate it.

Best,

Najwa