Momentum-based approximation of incompressible multiphase fluid flows
Résumé
We introduce a time stepping technique using the momentum as dependent variable to solve incompressible multiphase problems. The main advantage of this approach is that the mass matrix is time-independent making this tech- nique suitable for spectral methods. A level set method is applied to reconstruct the fluid properties such as density. We also introduce a stabilization method using an entropy-viscosity technique and a compression technique to limit the flattening of the level set function. We extend our algorithm to immiscible con- ducting fluids by coupling the incompressible Navier-Stokes and the Maxwell equations. We validate the proposed algorithm against analytical and manufac- tured solutions. Results on test cases such as Newton's bucket problem and a variation thereof are provided. Surface tension effects are tested on benchmark problems involving bubbles. A numerical simulation of a phenomenon related to the industrial production of aluminium is presented at the end of the paper.