A simple FORCE-type centred scheme accurate for contact discontinuities: Application to compressible Euler flows

Abstract

The FORCE-type centred schemes are simple and efficient and do not explicitly require the wave propagation information of the system to calculate the numerical flux. However, their poor resolution for contact discontinuities seriously affects their applications. In the present work, a simple FORCE-type centred scheme accurate for contact discontinuities is proposed and applied to calculations of compressible Euler flows. The missing contact wave of the original FORCE centred scheme is restored with an algebraic method and the resolution for contact discontinuities is further improved by using the boundary variation diminishing (BVD) algorithm to minimize the density jump in the numerical diffusion term of the original FORCE centred scheme. Numerical results of several one- and two-dimensional benchmark test problems fully demonstrate that the proposed centred scheme is capable of capturing contact discontinuities more sharply than the complete-wave HLLC upwind scheme. In addition, another advantage of the proposed centred scheme is that it is free from the carbuncle phenomenon which afflicts many contact-capturing upwind schemes (e.g. Roe and HLLC) in calculations of multidimensional flow problems involving strong shock waves.