A NOVEL SEGREGATED ALGORITHM FOR INCOMPRESSIBLE FLUID FLOW AND HEAT TRANSFER PROBLEMS—CLEAR (COUPLED AND LINKED EQUATIONS ALGORITHM REVISED) PART I: MATHEMATICAL FORMULATION AND SOLUTION PROCEDURE

Abstract

A novel segregated solution procedure for incompressible fluid flow and heat transfer problems is proposed. The new algorithm is called CLEAR (Coupled and Linked Equations Algorithm Revised). It differs from all SIMPLE-like algorithms in that it solves the improved pressure directly, rather than by adding a correction term, and no term is dropped in the derivation of the pressure equation. Thus the effects of the neighboring velocity values are fully taken into account, and the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate of the iteration process. Its robustness is improved by introducing a second relaxation factor. The mathematical formulation and the solution procedure of the CLEAR algorithm are described in detail in this article. Comprehensive discussion is conducted to describe the difference between the CLEAR algorithm and all other existing algorithms of the SIMPLE family. In Part II, six numerical application examples with available numerical solutions are provided to show the feasibility of the new algorithm.

The work reported here is supported by the National Key Project of R & D of China (G2000026303), and the National Natural Science Foundation of China (50076034, 50236010, 50276046).