An Implicit Integral Formulation for the Modeling of Inviscid Fluid Flows in Domains Containing Obstacles

Abstract

We focus here on an integral approach to compute compressible inviscid fluid flows in physical domains cluttered up with many small obstacles. This approach is based on a multidimensional porous integral formulation of Euler system of equations. Its discretization uses a first order semi-implicit finite volume scheme with pressure-correction algorithm preserving the positivity of both density and pressure. Numerical tests are completed by simulating a 2D channel flow containing two aligned tubes. The results are compared to reference solutions obtained with a pure fluid approach on a fine mesh.