Numerical solution of the Euler equations by finite volume methods: Central versus upwind schemes

Abstract

Euler equations are solved by means of three efficient and robust finite volume schemes, namely, central scheme of Jameson-Schmidt-Turkel (JST) and upwind schemes of Roe's Approximate Riemann Solver and Convective Upwind Split Pressure (CUSP) Scheme. Cell-centered discretization technique is employed. Multistage time-stepping algorithm is used to advance the solution in time. Acceleration techniques including local time stepping and implicit residual smoothing are applied for faster convergence to steady state. The flux at the cell faces is computed using MUSCL approach in upwind schemes and simple averaging procedure in JST scheme. MUSCL is enhanced by employing Van Albada limiter to suppress oscillations in regions of sharp gradients. Attention is directed towards the accuracy, convergence, and computational performance of the schemes. All schemes yield good convergence rates for a wide range of flow speeds.