Solution of the Euler Equations Based on Flux Vector Splitting

Ge Xinfeng,Su Keqin,Sun Gang

doi:10.19026/rjaset.5.4240

Abstract

The basic properties of the Euler equations are learned by studying hyperbolic PDEs and the Steger-Warming flux vector splitting approach and the NND scheme are given. The NND scheme based on improved Steger-Warming flux vector splitting is used for the solution of 1-D and shown that the numerical oscillation is restrained .The finite difference method has higher order of accuracy and better efficiency.

Highlights

Building an effective method to capture shock waves that has been an important part of the study in Computational Fluid Dynamics (CFD) field (Van der Geer et al, 2000; Strunk and White, 1979; Baghlani, 2011)
For the non-physical oscillations problems generated near the shock wave, Hearten proposed the total variation difference schemethe concept of Total Variation Difference (TVD) scheme, which the total variation is decreasing and constructed the TVD scheme with second order accuracy
The algorithm maintained the characteristics of high efficiency and easy to program that Steger-Warming splitting method have had and overcome the numerical oscillation near the shock wave that in Steger-Warming splitting method and had accuracy and manoeuvrability

Summary

INTRODUCTION

Building an effective method to capture shock waves that has been an important part of the study in Computational Fluid Dynamics (CFD) field (Van der Geer et al, 2000; Strunk and White, 1979; Baghlani, 2011). For the non-physical oscillations problems generated near the shock wave, Hearten proposed the total variation difference schemethe concept of TVD scheme, which the total variation is decreasing and constructed the TVD scheme with second order accuracy. Steger-Warming splitting method are often used by other schemes to better capture the shock wave for its characteristics of high efficiency and easy to program. The difference method that can automatically capture the shock wave is proposed based on the combination of improved Steger-Warming splitting method and NND scheme. The algorithm maintained the characteristics of high efficiency and easy to program that Steger-Warming splitting method have had and overcome the numerical oscillation near the shock wave that in Steger-Warming splitting method and had accuracy and manoeuvrability. Method proposed in this study has some reference value to the calculation of vector splitting

Which ρ

NND SCHEME AND THE NEW SCHEME

Test ρL uL pL

CONCLUSION