ON THE CONSTRUCTION OF A THIRD‐ORDER ACCURATE MONOTONE CONVECTION SCHEME WITH APPLICATION TO TURBULENT FLOWS IN GENERAL DOMAINS

A formally third-order accurate finite volume upwind scheme which preserves monotonicity is constructed. It is based on a third-order polynomial interpolant in Leonard's normalized variable space. A flux limiter is derived using the fact that there exists a one-to-one map between normalized variable and TVD spaces. This scheme, which is relatively simple and quite compact, is implemented in a staggered general co-ordinates finite volume algorithm including the standard k-e model and applied to the turbulence transport equations. A number of test problems demonstrate the utility of the proposed scheme. It is shown that in cases where turbulence convection is dominant, the application of a higher-order monotone convection scheme to the turbulence equations leads to results which are more accurate than those obtained using the first-order upwind scheme.

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