Transactions of Nanjing University of Aeronautics & Astronautics
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A Preconditioned Gridless Method for Solving Euler Equations at Low Mach Numbers
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Abstract:
In this paper a preconditioned gridless method is developed for solving Euler equations at low mach numbers. The preconditioned system in 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 techniques 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 have convergence for low Mach number simulations, therefore the modifications corresponding to the affect terms of preconditioning are mainly addressed in the paper. 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 nearly incompressible flow over a multi-element airfoil, which demonstrates the ability of the method presented for treating flows over complicated geometries.
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