CONVERGENCE OF THE SMOOTHED PARTICLE HYDRODYNAMICS METHOD FOR A SPECIFIC BAROTROPIC FLUID FLOW: CONSTRUCTIVE KERNEL THEORY

作     者：Franz, Tino Wendland, Holger 

作者机构：Univ Bayreuth Appl & Numer Anal Dept Math D-95440 Bayreuth Germany 

出 版 物：《SIAM JOURNAL ON MATHEMATICAL ANALYSIS》 (工业与应用数学会数学分析杂志)

年 卷 期：2018年第50卷第5期

页      面：4752-4784页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Deutsche Forschungsgemeinschaft (DFG) [WE 2333/9-1] 

主　　题：Euler equations smoothed particle hydrodynamics convergence analysis kernel-based approximation 

摘      要：Smoothed particle hydrodynamics (SPH) is a popular particle- and kernel-based method for numerically computing solutions to fluid-flow problems. In this paper, we study the convergence of SPH for the Euler equations of a specific barotropic fluid. In contrast to previous works, we distinguish carefully between the smoothing and the discretization parameters and give explicit relations between both of them to guarantee convergence. This convergence heavily depends on certain properties of the underlying kernel. Hence, a large part of this paper is devoted to constructing compactly supported, radial kernels which possess the required properties.