Semi‐implicit and explicit finite element schemes for coupled fluid/thermal problems

TLDR: In this paper, a comparative analysis of two purely explicit and one semi-implicit finite element methods used for incompressible flow computation is presented, where the fundamental concepts and characteristics of the formulations and the solution methodology used are described in technical detail.

Abstract: A comparative investigation, based on a series of numerical tests, of two purely explicit and one semi-implicit finite element methods used for incompressible flow computation is presented. The ‘segregated’ approach is followed and the equations of motion are considered sequentially. The fundamental concepts and characteristics of the formulations and the solution methodology used are described in technical detail. Various modifications to Chorin's projection algorithm are investigated, particularly with respect to their effects on stability and accuracy. The stability of the semi-implicit method is shown to be less restrictive when compared to the explicit methods as the Reynolds number increases. At large time steps the artificial viscosity is also reduced and higher accuracy is obtained. The performance of the methods discussed in this paper is illustrated by the numerical solutions obtained for the cavity flow and flow past a rearward-facing step problems at high Reynolds numbers, and free convection flow problem at high Rayleigh numbers. It is shown that the semi-implicit method needs fewer iterations than the explicit methods, and the accuracy of the present methods is guaranteed by comparison with the existing methods.