关键词: 多面体网格, 蜂窝网格, 径向基函数, 动能通量分裂, 非结构, 复杂外形, 可压缩流动

Abstract: A new algorithm for solving Euler equations on polyhedral grids is developed and validated in this paper. A general solver which supports arbitrary mesh topology and three-dimensional complex geometry is constructed by using Fortran 95 language. For spatial discretization, a new improved radial basis function method is proposed for gradient calculation. An accurate and robust second-order reconstruction is achieved by using the kinetic flux vector splitting scheme. The new method does not depend on the geometry of the grid. Thus it is much less sensitive to grid quality. With a point implicit relaxation time marching strategy, the solver remains stable at large time steps. The test cases indicate that the algorithm and the solver developed in this paper are stable, accurate while exhibiting good flexibility on mesh universality.

Key words: polyhedral grid, honeycomb grid, radial basis function, kinetic flux vector splitting, unstructured, complex geometry, compressible flow