A preconditioned gridless method for solving Euler equations at low Mach numbers

作者：Cao Cheng; Chen Hongquan^*

来源：Transactions of Nanjing University of Aeronautics & Astronautics, 2015, 32(4): 399-407.

• Cloud of point
• Complicated geometry
• Conservation forms
• Gridless methods
• Multi element airfoils
• Nearly incompressible
• Numerical results
• Preconditioning

A preconditioned gridless method is developed for solving the Euler equations at low Mach numbers. The preconditioned system in a conservation form is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the Euler equations, which are discretized using a gridless technique wherein the physical domain is distributed by clouds of points. The implementation of the preconditioned gridless method is mainly based on the frame of the traditional gridless method without preconditioning, which may fail to converge for low Mach number simulations. Therefore, the modifications corresponding to the affected terms of preconditioning are mainly addressed. The numerical results show that the preconditioned gridless method still functions for compressible transonic flow simulations and additionally, for nearly incompressible flow simulations at low Mach numbers as well. The paper ends with the nearly incompressible flow over a multi-element airfoil, which demonstrates the ability of the method presented for treating flows over complicated geometries.

• 出版日期2015
• 单位南京航空航天大学