Orateur
Description
The approximation on incompressible flows with variable density and viscosity has many applications in engineering and geosciences (e.g. liquid metal batteries, aluminum production). First, we describe briefly some motivations, classic numerical methods used to the incompressible Navier-Stokes equations with variable density, and the main challenges we face when using pseudo-spectral methods. Second, we will introduce a novel artificial compressibility techniques which, unlike projection method, does not require to solve a Poisson problem to update the pressure and enforce the incompressibility constraints. The momentum, equal to the product of the density and velocity, and the pressure are chosen as primary unknowns which leads to a time independent mass matrix. We will discuss theoretical aspects (stability and convergence) of the proposed methods and its validation over various benchmarks.