[FluidDynamicsApplication] Two-fluid Navier-Stokes formulation with fractional splitting approach

[uxuech]

📝 Description

This PR implements a Two-fluid Navier-Stokes formulation using the fractional splitting approach.
The momentum conservation equation has been split into two parts.
The first part solves a pure convection problem for a vector field, in this case, the fractional velocity, where the convection velocity is the vector field itself.
The second part solves the remaining terms of the momentum conservation equation, adding those terms with opposite signs to the ones included in the first part of the problem. This ensures that, in the continuum, the combination of both problems results in the original momentum conservation equation.

Additionally, the approach to mass conservation has been slightly modified. The original two-fluid Navier-Stokes elements include a mass source term that is added to cut elements. Now, the mass source term added to the cut elements differs depending on whether the cut part of the element is water or air.

🆕 Changelog

This translates into the implementation of two new symbolic elements with their corresponding templates and data containers, as well as the unit tests for the elements.

• vectorial convection fractional element.
• two fluid navier stokes fractional element.

[loumalouomega]

@uxuech take a look at the Linux compilation erros, a priori easy to fix:

In file included from /__w/Kratos/Kratos/applications/FluidDynamicsApplication/fluid_dynamics_application.cpp:28,
                 from /__w/Kratos/Kratos/build/Custom/applications/FluidDynamicsApplication/CMakeFiles/KratosFluidDynamicsCore.dir/Unity/unity_2_cxx.cxx:47:
/__w/Kratos/Kratos/applications/FluidDynamicsApplication/fluid_dynamics_application.h: In constructor 'Kratos::KratosFluidDynamicsApplication::KratosFluidDynamicsApplication()':
/__w/Kratos/Kratos/applications/FluidDynamicsApplication/fluid_dynamics_application.h:465:96: error: 'Kratos::KratosFluidDynamicsApplication::mVectorialConvectionFractionalElement2D3N' will be initialized after [-Werror=reorder]
     const VectorialConvectionFractionalElement<VectorialConvectionFractionalElementData<2, 3>> mVectorialConvectionFractionalElement2D3N;
                                                                                                ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/__w/Kratos/Kratos/applications/FluidDynamicsApplication/fluid_dynamics_application.h:464:96: error:   'const Kratos::VectorialConvectionFractionalElement<Kratos::VectorialConvectionFractionalElementData<3, 4> > Kratos::KratosFluidDynamicsApplication::mVectorialConvectionFractionalElement3D4N' [-Werror=reorder]
     const VectorialConvectionFractionalElement<VectorialConvectionFractionalElementData<3, 4>> mVectorialConvectionFractionalElement3D4N;
                                                                                                ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /__w/Kratos/Kratos/build/Custom/applications/FluidDynamicsApplication/CMakeFiles/KratosFluidDynamicsCore.dir/Unity/unity_2_cxx.cxx:47:
/__w/Kratos/Kratos/applications/FluidDynamicsApplication/fluid_dynamics_application.cpp:39:1: error:   when initialized here [-Werror=reorder]
 KratosFluidDynamicsApplication::KratosFluidDynamicsApplication():
 ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /__w/Kratos/Kratos/applications/FluidDynamicsApplication/fluid_dynamics_application.cpp:28,
                 from /__w/Kratos/Kratos/build/Custom/applications/FluidDynamicsApplication/CMakeFiles/KratosFluidDynamicsCore.dir/Unity/unity_2_cxx.cxx:47:
/__w/Kratos/Kratos/applications/FluidDynamicsApplication/fluid_dynamics_application.h:464:96: error: 'Kratos::KratosFluidDynamicsApplication::mVectorialConvectionFractionalElement3D4N' will be initialized after [-Werror=reorder]
     const VectorialConvectionFractionalElement<VectorialConvectionFractionalElementData<3, 4>> mVectorialConvectionFractionalElement3D4N;
                                                                                                ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/__w/Kratos/Kratos/applications/FluidDynamicsApplication/fluid_dynamics_application.h:462:84: error:   'const Kratos::TwoFluidNavierStokesFractional<Kratos::TwoFluidNavierStokesFractionalData<2, 3> > Kratos::KratosFluidDynamicsApplication::mTwoFluidNavierStokesFractional2D3N' [-Werror=reorder]
     const TwoFluidNavierStokesFractional<TwoFluidNavierStokesFractionalData<2, 3>> mTwoFluidNavierStokesFractional2D3N;
                                                                                    ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /__w/Kratos/Kratos/build/Custom/applications/FluidDynamicsApplication/CMakeFiles/KratosFluidDynamicsCore.dir/Unity/unity_2_cxx.cxx:47:
/__w/Kratos/Kratos/applications/FluidDynamicsApplication/fluid_dynamics_application.cpp:39:1: error:   when initialized here [-Werror=reorder]

[rubenzorrilla]

There are minor things to be corrected before merging. Note that most of my suggestions apply to many places. Please take them into account in all of them.

[uxuech]

I have reviewed everything, and I think that all suggestions and corrections have been done. Please let me know if there's anything else to modify. Thank you! @rubenzorrilla

[rubenzorrilla]

Ready to go 🚀