A New Kinetic-Based Solver for Solving Compressible Flow on Arbitrary Polyhedral Grids

摘要

A kinetic-based unstructured algorithm for obtaining the numerical solution to three-dimensional, inviscid, compressible flows is developed and implemented on arbitrary polyhedral grids. The algorithm is derived using a cell-centered finite volume formulation for arbitrary grids topology including honeycomb grids. A new improved radical basis function method is proposed for the accurate and robust gradient calculation. The new method does not depend on the geometry of cell. Thus it is much less sensitive to the shape of the grid especially for honeycomb mesh. After an accurate gradient computation, the spatial second order accuracy is achieved through the MUSCL approach along with the Kinetic Flux Vector Splitting scheme. With a point implicit relaxation time marching strategy, the solver remains stable at large courant number for high Mach number computation. Several test cases are being conducted on the accuracy and efficiency of the solver. The model test cases include two-dimensional unstructured mesh scramjet inlets computation and three-dimensional multi-block structured mesh M6 wing test case. The further evolution of the performance on honeycomb grids simulation is investigated. Fast convergence of honeycomb based computation is observed as expected. The test cases indicate that the algorithms and the solver developed in this paper exhibit good flexibility on mesh universality and robustness for high speed flow simulation. Finally, the solver is applied to a three-dimensional aircraft configuration successfully.