SOME THEORETICAL AND PRACTICAL ASPECTS OF EFFICIENT MODELLING OF HEAT TRANSFER PHENOMENA ON A FINITE-ELEMENT GRID

Abstract

A review of the contemporary numerical techniques, commonly used in a computer simulation of practical engineering problems, involving the fluid flow and coupled heat transfer, is given in terms of comparison of their accuracy and computational economy. Particularly, some aspects of the utilization of two different formulations of the Finite Element Method (FEM), i.e.: the one based on the weighted residual approach (PGFEM) and the one where the control-volume method is exploited (CVFEM), are discussed to find the answer to the question of how to improve the economy of the FEM calculations. In this context, the accuracy of both methods is considered through verifying a physical correctness of the solution obtained. Some simple and no-time consuming means are discussed to reduce inaccuracy resulting from a violation of the physically meaningful conservation and maximum principles as well as from the improper modelling of convection over a sparse grid. Furthermore, to speed up the FEM calculations it is shown here how to adopt the time-split and factorization techniques, which take their origin from the finite difference methods, in the Control-Volume based FEM. The encouraging preliminary results are reported here for three pertinent test problems, involving the recirculated flow and coupled heat transfer.