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

Abstract

SUMMARYA 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.

Comparison of h-, p- and hp-adaptation for convective heat transfer

“…Results from the lower Ra number computations are essentially duplicative with results found in the literature. Results for Ra =10 5 All the adaptive results agree well with benchmark data available in the literature for both flow and thermal patterns [12]. Quantitative studies were also conducted for the hp-adaptive algorithm with Ra=10 6 .…”

“…This method is based on the Helmholtz-Hodge Decomposition Theorem (Chorin [4]), and detailed description of employment of projection method can be found in the work of Ramaswamy et al [5].…”

An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows

“…The characteristic based split (CBS) method [1,10,[24][25][26][27][28][29][30][31] for incompressible ows is a variant of the velocity correction method or split method reported by many authors [7][8][9]. However, the CBS procedure is e cient and exible due to many extra provisions to improve stability and accuracy of incompressible ow calculations.…”

A CBS-type stabilizing algorithm for the consolidation of saturated porous media

“…References [1][2][3][4][5][6][7][8][9][10], starting from the early 1990s. All these 1. extending the ideas of Chorin to compute density/pressure increments; 2. treating the individual momentum or energy transport equations by the scalar characteristic process, again leading to FEM optimality.…”