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

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.