Flux Formulation using a Fully 2D Approximate Roe Riemann Solver

Abstract

Computational Fluid Dynamics (CFD) calculations are mostly performed on very complicated geometries. This implies that 2D and 3D (two and three space Dimensions) numerical methods are often developed on unstructured grids. In this paper, we present a purely two dimensional numerical scheme that canbe applied on both nonlinear hyperbolic equations and systems of conservation laws such as Euler’s or Navier-Stokes’ equations. Our numerical method is capable of building a 2D flux that does not depend on any direction linked to the mesh; is second order accurate by local two dimensional”Monotonic Upstream Scheme for Conservation Laws” (MUSCL) [6, 10] upwind extrapolation-interpolation technique ; and is built on a three state Roe Riemann Solver (RS) [3], The building flux is based on the Local Lax-Friedrichs (LLF) and R.oe Fix (RF) algorithms introduced by C.W. Shu and S. Osher in [8] but extended to a three state solution prescribed at the gravity center of each triangle in order to satisfy locally the entropy increase condition across shock waves.