High accuracy methods for solving non-linear compressible gas dynamics flow problem

Abstract

Euler equations are hyperbolic conservation law in compressible gas dynamics flow problem. In the non-linear problem, discontinuities or jump conditions may appear in the solutions. The numerical solutions typically produce oscillation near jump conditions because of truncation error. Weighted essentially non-oscillatory (WENO) scheme are adaptive high order method that suitable for the discontinuous function to minimize truncation error and diminish the oscillations. In this research, we use high order scheme to reduce numerical dissipation in hyperbolic conservation laws using WENO scheme that adopted as slope limiter in the finite volume coupled with Harten, Lax, van Leer-Contact (HLLC) flux to solve Euler equations. By some simple numerical tests in non-linear compressible flow problem, we found that the numerical results are non-oscillatory and very accurate. Numerical results show that the WENO scheme successfully implemented in finite volume methods to simulate non-linear compressible gas dynamics flow problem with satisfactory accuracy.