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