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

Chertock, Alina1; Coco, Armando2; Kurganov, Alexander3,4; Russo, Giovanni5

2018-01

10.4208/cicp.OA-2016-0133

Communications in Computational Physics   Impact Factor & Quartile

1815-2406

1991-7120

In this paper, we describe how to construct a finite-difference shock-capturing method for the numerical solution of the Euler equation of gas dynamics on arbitrary two-dimensional domain Omega, 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 domain Omega(R) superset of Omega. We identify inner and ghost points. The inner points are the grid points located inside Omega, while the ghost points are the grid points that are outside W but have at least one neighbor inside Omega. 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 the method. We demonstrate that the second order of accuracy is numerically assessed on genuinely two-dimensional problems.

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

SCI

English

Corresponding

ITN-ETN Horizon Project ModCompShock, Modeling and Computation on Shocks and Interfaces[642768]

Physics

Physics, Mathematical

WOS:000426269200008

GLOBAL SCIENCE PRESS

Web of Science

1.North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
2.Oxford Brookes Univ, Dept Mech Engn & Math Sci, Oxford OX33 1HX, England
3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
4.Tulane Univ, Dept Math, New Orleans, LA 70118 USA
5.Univ Catania, Dipartimento Matemat & Informat, I-95125 Catania, Italy

Chertock, Alina,Coco, Armando,Kurganov, Alexander,et al. A Second-Order Finite-Difference Method for Compressible Fluids in Domains with Moving Boundaries[J]. Communications in Computational Physics,2018,23(1):230-263.

Chertock, Alina,Coco, Armando,Kurganov, Alexander,&Russo, Giovanni.(2018).A Second-Order Finite-Difference Method for Compressible Fluids in Domains with Moving Boundaries.Communications in Computational Physics,23(1),230-263.

Chertock, Alina,et al."A Second-Order Finite-Difference Method for Compressible Fluids in Domains with Moving Boundaries".Communications in Computational Physics 23.1(2018):230-263.