Оne-dimensional gas dynamics problems and their solution based on high-resolution finite difference schemes

Abstract

One-dimensional unsteady gas dynamics problems are revealing tests for the accuracy estimation of numerical solution with respect to simulation of supersonic flows of inviscid compressible gas. Numerical solution of Euler equations describing flows of inviscid compressible gas and conceding continuous and discontinuous solutions is considered. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes. The numerical solutions computed are compared with the exact solution of Riemann problem. Monotonic correction of derivatives makes possible avoiding new extremes and ensures monotonicity of the numerical solution near the discontinuity, but it leads to the smoothness of the existing minimums and maximums and to the accuracy loss. Calculations with the use of WENO schemes give the possibility for obtaining accurate and monotonic solution with the presence of weak and strong gas dynamical discontinuities.