ASecond-Order Finite-Difference Method for Compressible Fluids in Domains with Moving Boundaries  

作　　者：Alina Chertock Armando Coco Alexander Kurganov Giovanni Russo 

机构地区：[1]Department of Mathematics,North Carolina State University,Raleigh,NC 27695,USA [2]Department of Mechanical Engineering and Mathematical Sciences,Oxford Brookes University,Oxford OX331HX,UK [3]Department of Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong 518055,China and Mathematics Department,Tulane University,New Orleans,LA 70118,USA [4]Dipartimento diMatematica ed Informatica,Universit`a di Catania,95125,Catania,Italy.

出　　处：《Communications in Computational Physics》2018年第1期230-263,共34页计算物理通讯（英文）

基　　金：The work of A.Chertock was supported in part by the NSF Grants DMS-1216974 and DMS-1521051;The work of A.Kurganov was supported in part by the NSF Grants DMS-1216957 and DMS-1521009;The work of G.Russo was supported partially by the University of Catania,Project F.I.R.Charge Transport in Graphene and Low Dimensional Systems,and partially by ITN-ETN Horizon 2020 Project Mod Comp Shock,Modeling and Computation on Shocks and Interfaces,Project Reference 642768.

摘　　要：In this paper,we describe how to construct a finite-difference shockcapturing method for the numerical solution of the Euler equation of gas dynamics on arbitrary two-dimensional domainΩ,possibly with moving boundary.The boundaries of the domain are assumed to be changing due to the movement of solid objects/obstacles/walls.Although the motion of the boundary could be coupled with the fluid,all of the numerical tests are performed assuming that such a motion is prescribed and independent of the fluid flow.The method is based on discretizing the equation on a regular Cartesian grid in a rectangular domainΩ_(R)⊃Ω.Ωe identify inner and ghost points.The inner points are the grid points located insideΩ,while the ghost points are the grid points that are outsideΩbut have at least one neighbor insideΩ.The evolution equations for inner points data are obtained from the discretization of the governing equation,while the data at the ghost points are obtained by a suitable extrapolation of the primitive variables(density,velocities and pressure).Particular care is devoted to a proper description of the boundary conditions for both fixed and time dependent domains.Several numerical experiments are conducted to illustrate the validity of themethod.Ωe demonstrate that the second order of accuracy is numerically assessed on genuinely two-dimensional problems.

关 键 词：Compressible fluids Euler equations of gas dynamics ghost-cell extrapolation moving boundaries finite-difference shock-capturing methods 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]