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 ***
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.
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
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