[ConvectionDiffusionApplication] Adding crosswind stabilization to Eulerian Convection–Diffusion element

[Marco1410]

📝 Description
This pull request introduces a crosswind stabilization term in the EulerianConvectionDiffusionElement of Kratos.

The implementation follows the discontinuity-capturing approach proposed in A discontinuity‑capturing crosswind‑dissipation for the finite element solution of the convection‑diffusion equation by Ramon Codina. The method adds a nonlinear diffusion in the direction orthogonal to the flow in order to reduce the spurious oscillations that may still appear when using streamline-based stabilization techniques.

The stabilization term can be activated through the element settings.
By default CROSS_WIND_STABILIZATION_FACTOR is zero.

 "transient_parameters" : {
        "dynamic_tau" : 1.0,
        "theta"       : 0.5,
        "cross_wind_stabilization_factor" : 0.0
   }

Additionally, a unit test has been included to verify the correct behaviour of the implementation.

To illustrate the effect of the stabilization, two example simulations are shown below:

• Without crosswind stabilization:
  Spurious oscillations appear near steep gradients.
  

• With crosswind stabilization:
  The oscillations are significantly reduced.
  

🆕 Changelog

• eulerian_conv_diff.cpp
• convection_diffusion_transient_solver.py
• test_eulerian_conv_diff.cpp

[rubenzorrilla]

I'm not fully convinced about the elemental cross wind factor calculation. Aside of this, the others are minors.

[rubenzorrilla]

You are allocating this for each Gauss pt.

[rubenzorrilla]

Access once outside the Gauss pt. loop. Besides avoiding accessing the ProcessInfo many times, you can use it to check if the cross wind stabilization is active and avoid all these operations.

[rubenzorrilla]

Suggested change

	const double disc_capturing_coeff = 0.5*C*h*fabs(res/norm_grad);
	const double disc_capturing_coeff = 0.5*C*h*std::abs(res/norm_grad);

[rubenzorrilla]

Are you sure about this? Shouldn't it involve the viscosity besides the tau?

[rubenzorrilla]

Make it more strict. In order to output the values, you can use std::setprecision (you can find some examples in the FluidDynamicsApplication).

[rubenzorrilla]

Shouldn't it automatically add it when validating the defaults?