An upwind method for incompressible flows with heat transfer

Abstract

Purpose

The purpose of this paper is to present a novel numerical method to solve incompressible flows with natural and mixed convections using pseudo‐compressibility formulation.

Design/methodology/approach

The present method is derived using the framework of Harten Lax and van Leer with contact (HLLC) method of Toro, Spruce and Spears, that was originally developed for compressible gas dynamics equations. This work generalizes the algorithm described in the previous paper to the case where heat transfer is involved. Here, the solution of the Riemann problem is approximated by a three‐wave system.

Findings

A few test cases involving incompressible laminar flows inside 2D square cavity for various Rayleigh and Reynolds numbers are considered for validating the present method. The computed results from the present method are found to be quite promising.

Originality/value

Although pseudo‐compressibility formulation has been found to have superior performance and has the potential to have numerical treatments similar to compressible flow equations, only two numerical methods have been applied so far; namely Jameson method and Roes flux difference splitting method. A new sophisticated numerical method, following the framework of HLLC method, is derived and implemented for solving pseudo‐compressibility‐based incompressible flow equations with heat transfer.

Citation

Chandra Mandal, J. and Iyer, A.S. (2011), "An upwind method for incompressible flows with heat transfer", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 5, pp. 518-534. https://doi.org/10.1108/09615531111135800