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Date of Publication:2022-10-09

Journal:浙江大学学报 工学版

Issue:5

Page Number:1032-1043

ISSN No.:1008-973X

Abstract:Generally upwind information cannot be clearly defined on unstructured mesh,thus a total variation diminishing (TVD) is difficult to be directly applied in such a mesh.An improved TVD scheme was proposed based on the gradient smoothing method (GSM) using unstructured mesh in order to solve the above problem.Using different smoothing domains,there are three types of GSM,i.e.node gradient smoothing method (nGSM)、midpoint gradient smoothing method (mGSM) and centre gradient smoothing method (cGSM).According to the above GSM models,three types of improved TVD were developed.In each scheme,locations of upwind points were to be found out and the variables at these points were calculated through interpolation operation.The improved TVD schemes were used to solve hyperbolic partial differential equation discontinuous problems and the results were compared with those by other methods,where three classical flux limiters (Superbee,Van leer and Minmod) were used.Numerical results show that the improved TVD based on GSM can effectively avoid the numerical oscillation and reduce the numerical diffusion,which can obtain good numerical results for both continuous and discontinuous problems.

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