Solution of Navier‐Stokes equations by fourth‐order compact schemes and AUSM flux splitting

Abstract

Purpose

To develop a high‐order compact finite‐difference method for solving flow problems containing shock waves.

Design/methodology/approach

A numerical algorithm based on high‐order compact finite‐difference schemes is developed for solving Navier‐Stokes equations in two‐dimensional space. The convective flux terms are discretized by using advection upstream splitting method (AUSM). The developed method is then used to compute some example laminar flow problems. The problems considered have a range of Mach number that corresponds to subsonic incompressible flow to hypersonic compressible flows that contain shock waves and shock/boundary‐layer interaction.

Findings

The paper shows that the AUSM flux splitting and high‐order compact finite‐difference methods can be used accurately and robustly in resolving shear layers and capturing shock waves. The highly diffusive nature of conventional flux splitting especially on coarse grids makes them inaccurate for boundary layers even with high‐order discretization.

Originality/value

This paper presents a high‐order numerical method that can accurately and robustly capture shock waves without deteriorating oscillations and resolve boundary layers and shock/boundary layer interaction.

Citation

Mawlood, M.K., Basri, S., Asrar, W., Omar, A.A., Mokhtar, A.S. and Ahmad, M.M.H.M. (2006), "Solution of Navier‐Stokes equations by fourth‐order compact schemes and AUSM flux splitting", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 16 No. 1, pp. 107-120. https://doi.org/10.1108/09615530610636982