PROPOSAL OF OPTIMAL SCHEME FOR HIGHLY ACCURATE FINITE-DIFFERENCE APPROXIMATION METHOD OF CONVECTION DIFFUSION EQUATIONS

Abstract

A novel OPTIMAL scheme based on the second-order interpolation tecnique is proposed for highly accurate and non-oscillatory simulation of convection. The effectiveness of this scheme is demonstrated through applications of several scalar transport problems in two-dimensional laminar and turbulent recirculating flow. The results are compared to currently avaiable schemes such as PLDS, QUICK, LODA, ULTRA- SHARP etc., and these results demonstrate that the bounded OPTIMAL and the bounded LODA with local full upwinding can give accurate and wiggle free solutions with properly designed coarse mesh layout. However, the OPTIMAL evidently appears advantageous for practical applications because of its computational simplicity and stable convergent process.