Numerical simulation of two‐dimensional laminar mixed‐convection in a lid‐driven cavity using the mixed finite element consistent splitting scheme

Abstract

Purpose

The purpose of this paper is to propose an efficient/robust numerical algorithm for solving the two‐dimensional laminar mixed‐convection in a lid‐driven cavity using the mixed finite element (FE) technique.

Design/methodology/approach

A numerical algorithm was based on the so‐called consistent splitting scheme, which improved the numerical accuracy of the primitive variables. In order to obtain a stable solution, two choices of mixed FEs, the Taylor‐Hood and Crouzeix‐Raviart types, were used. Two mesh layouts were considered; uniform and non‐uniform.

Findings

To verify that the proposed scheme had a second‐order accuracy, some numerical results are presented and compared with the known solution. The answer was confirmative. Numerically accurate solutions were obtained for a fixed Prandtl number, Pr=0.71, for a range of the Reynolds number, Re from 100 to 3,000, and for a range of the Richardson number, Ri from 0.001 to 100. The results from these calculations, using the mixed FE consistent splitting scheme, agreed with the existing ones.

Research limitations/implications

Further extensions of this work could include the influence of various choices of Reynolds numbers, Prandtl numbers and Richardson numbers, and the effect of aspect ratio.

Originality/value

The present work was the first to apply a mixed FE in association with the consistent splitting scheme to the mixed convection problem.

Citation

Wong, J.C.‐. (2007), "Numerical simulation of two‐dimensional laminar mixed‐convection in a lid‐driven cavity using the mixed finite element consistent splitting scheme", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 No. 1, pp. 46-93. https://doi.org/10.1108/09615530710716081