摘要
In this work, we explore various relevant aspects of the Smoothed Particle Hydrodynamics regarding Burger's equation. The stability, precision, and efficiency of the algorithm are investigated in terms of different implementations.In particular, we argue that the boundary condition plays an essential role in the stability of numerical implementation.Besides, the issue is shown to be closely associated with the initial particle distribution and the interpolation scheme.Among others, we introduce an interpolation scheme termed symmetrized finite particle method. The main advantage of the scheme is that its implementation does not involve any derivative of the kernel function. Concerning the equation of motion, the calculations are carried out using two distinct scenarios, where the particles are chosen to be either stationary or dynamically evolved. The obtained results are compared with those obtained by using the standard finite difference method for spatial derivatives. Our numerical results indicate subtle differences between different schemes regarding the choice of boundary condition. In particular, a novel type of instability is observed where the regular distribution is compromised as the particles start to traverse each other. Implications and further discussions of the present study are also addressed.
作者
Chong Ye
Philipe Mota
Jin Li
Kai Lin
Wei-Liang Qian
叶翀;Philipe Mota;李瑾;林恺;钱卫良(College of Physics,Chongqing University,Chongqing 401331,China;Centro Brasileiro de Pesquisas Fisicas,22290-180,Rio de Janeiro,RJ,Brazil;Institute of Geophysics and Geoinforma tics,China University of Geosciences,Wuhan 430074,China;Escola de Engenharia de Lorena,Universidade de Sao Paulo,12602-810,Lorena,SP,Brazil;Faculdade de Engenharia de Guaratinguetá,Universidade Estadual Paulista,12516-410,Guaratingueta,SP,Brazil;School of Physical Science and Technology,Yangzhou University,Yangzhou 225002,China)
基金
financial support from Brazilian funding agencies Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)
Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq)
Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)
National Natural Science Foundation of China (NNSFC) under Grant Nos.11805166 and 11873001
Nature Science Fund of Chongqing under Grant No.cstc2018jcyjAX0767
作者简介
李瑾,E-mail: cqstarv@hotmail.com。
