A Gridless-Finite Volume Hybrid Algorithm for Euler Equations

Abstract

A fast hybrid algorithm based on gridless method coupled with finite volume method (FVM) is developed for the solution to Euler equations. Compared with pure gridless method, the efficiency of the hybrid algorithm is improved to the level of finite volume method for most parts of the flow filed are covered with grid cells. Moreover, the hybrid method is flexible to deal with the configurations as clouds of points are used to cover the region adjacent to the bodies. Mirror satellites and mirror grid cells are introduced to the interface to accomplish data communication between the different parts of the flow field. The Euler Equations are spatially discretized with finite volume method and gridless method in mesh and clouds of points respectively, and an explicit four-stage Runge-Kutta scheme is utilized to reach the steady-state solution. Internal flows in channels and external flows over airfoils are investigated with hybrid method, and the solutions are compared to those using pure finite volume method and pure gridless method. Numerical examples show that the hybrid algorithm captures the shock waves accurately, and it is as efficient as finite volume method.