| The problem of multi-dimensional hyperbolic conservation is one of the important research topics in computational fluid dynamics.The entropy stable scheme for hyperbolic conservation laws relies on physical background and can avoid some non-physical phenomena.In this paper,the construction method and main idea of entropy stable scheme are studied in detail,and the entropy stable scheme of two-dimensional hyperbolic conservation laws in triangular grids is constructed according to the construction method of entropy stable scheme.The numerical simulation of cylindrical flow around two-dimensional Euler equation indicates that the format does not produce carbuncle phenomenon.The main work of this paper includes:(1)Based on the study of entropy conservative,entropy stable and entropy consistent schemes,several schemes are extended to two-dimensional problems directly,and several typical examples are calculated.The results we obtained indicate the promotion is feasible.(2)Constructing entropy stable scheme directly under unstructured grids.Firstly,the semi-discrete numerical scheme of two-dimensional hyperbolic conservation laws of unstructured grids is obtained.Then,a two-dimensional Euler equation is used to describe the concrete process of constructing the entropy stable scheme on the basis of this semi-discrete scheme.We construct the entropy conservative flux function,and then add a Roe type dissipation term to getting the entropy stable scheme.In order to improve the accuracy of the scheme,this paper constructs a new high-precision entropy stable scheme by reconstructing the entropy variables at the interface of the adjacent cells in the computing area,and the solution of the problem of cylindrical flow around the two-dimensional Euler equation is solved.(3)The validity of the entropy stable scheme under the triangular mesh structure is verified by numerical examples,which is characterized by high precision and high resolution. |
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