Implicit numerical scheme based on SMAC method for

Authors: Zhenlin Li Yongxue Zhang

Publish Date: 2008/05/29

Volume: 5, Issue: 2, Pages: 172-178

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Abstract

An implicit numerical scheme is developed based on the simplified marker and cell SMAC method to solve Reynoldsaveraged equations in general curvilinear coordinates for threedimensional 3D unsteady incompressible turbulent flow The governing equations include the Reynoldsaveraged momentum equations in which contravariant velocities are unknown variables pressurecorrection Poisson equation and kɛturbulent equations The governing equations are discretized in a 3D MAC staggered grid system To improve the numerical stability of the implicit SMAC scheme the higherorder highresolution ChakravarthyOsher total variation diminishing TVD scheme is used to discretize the convective terms in momentum equations and kɛequations The discretized algebraic momentum equations and kɛequations are solved by the timediversion multiple access CTDMA method The algebraic Poisson equations are solved by the Tschebyscheff SLOR successive linear over relaxation method with alternating computational directions At the end of the paper the unsteady flow at high Reynolds numbers through a simplified cascade made up of NACA65410 blade are simulated with the program written according to the implicit numerical scheme The reliability and accuracy of the implicit numerical scheme are verified through the satisfactory agreement between the numerical results of the surface pressure coefficient and experimental data The numerical results indicate that Reynolds number and angle of attack are two primary factors affecting the characteristics of unsteady flow

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