A NEW HIGH-ORDER-ACCURATE AND BOUNDED SCHEME FOR INCOMPRESSIBLE FLOW

Abstract

The interpolative reasonableness is analyzed and the conditions for the construction of bounded, accurate scheme with interpolative reasonableness (BAIR) are presented. It is required that the interfacial variable have a positive response to the disturbance occurring at the main grid point and that the transportive property be kept (dynamic interpolate reasonableness, DIR). A new high-order-accurate and bounded (HOAB) scheme based on the BAIR is proposed for the calculation of incompressible flow. The new scheme, HOAB, istested by five problems: (1) pure convection of a stepwise profile in an oblique uniform velocity field, (2) pure convection of a double-step profile in an oblique uniform velocity field, (3) pure convection of an elliptical profile, (4) lid-driven cavity flow, and (5) turbulent flow over a backward-facing step. The computational results are compared with the results of five high-resolution schemes: Zhu and Rodi's MINMOD scheme, Van leer's CLAM scheme, Chakravarthy and Osher's OSHER scheme, Gaskell and Lau's SMART scheme, Darwish's STOIC scheme, and exact solution/benchmark solution or experimental data. The numerical tests show that the new scheme is capable of capturing steep gradients whilemaintaining boundedness of solutions and is more accurate than the other five high-resolutionschemes.