MODELLING AND NUMERICAL SIMULATION OF LOW-MACH-NUMBER COMPRESSIBLE FLOWS

Abstract

SUMMARY Based upon the operator-splitting method designed by the authors to solve the Navier-Stokes equations with variable density and viscosity, a segregated time-marching solution scheme is proposed for solving the low-Machnumber flow model with the acoustic waves being filtered out. This solution scheme does not rely on the correction for global mass conservation to maintain solution accuracy. With this advantage the scheme can be directly applied to general low-Mach-number flow problems with confidence.The scheme is validated by comparing the results for a number of test cases with known limiting exact solutions and published numerical solutions by other authors. Low-Mach-number compressible flows have a wide range of industrial applications, e.g. combustions, chemical reactions, natural convections. The numerical simulation of low-Mach-number flows is still a challenge to contemporary compressible flow algorithms. As is well lcn~wn,'~ time-marching compressible flow schemes become ineffective at low Mach numbers because of the wide disparity of time scales associated with convection and the rapid propagation of acoustic waves (or disturbances) which quickly contaminates the solutions and therefore reduces the stability of the scheme and destroys the convergence to steady state. In order to improve convergence and stability, one common approach is to use a modified compressible flow model (called the L-model in this paper) for the low-Mach-number case,335 which excludes acoustic waves by separating the pressure p into a thermodynamic part p~ which is spatially uniform and a hydrodynamic part p~ with Pd << p~ in the low-Mach-number case. The usual variable density model (called the V-model in this paper) and Boussinesq model (called the B-model in this paper) are particular cases of the L-model. The main purpose of this paper is to present a segregated time-marching solution algorithm for numerical solution of this modified model for low-Mach-number flows. This solution scheme does not rely on the correction for global mass conservation to maintain solution accuracy. With this advantage the scheme can be directly applied to general low-Mach-number flow problems with confidence, especially where such a correction is either impossible or unfeasible. The core of this algorithm is an CCC 0271-2091/96/020077-27 0 1996 by John Wiley & Sons, Ltd.