A fully discrete, stable and conservative summation-by-parts formulation for deforming interfaces

JOURNAL OF COMPUTATIONAL PHYSICS

卷:339

Article

Nikkar, Samira¹  Nordstrom, Jan¹ 

[1] Linkoping Univ, Dept Math, Computat Math, SE-58183 Linkoping, Sweden

关键词: Finite difference;    High order accuracy;    Deforming domains;    Time-dependent interface;    Well-posedness;    Conservation;    Summation-by-parts;    Stability;    Hyperbolic problems;   

DOI  :  10.1016/j.jcp.2017.02.047

来源: Elsevier

【 摘 要 】

We introduce an interface/coupling procedure for hyperbolic problems posed on time dependent curved multi-domains. First, we transform the problem from Cartesian to boundary-conforming curvilinear coordinates and apply the energy method to derive well posed and conservative interface conditions. Next, we discretize the problem in space and time by employing finite difference operators that satisfy a summation-by-parts rule. The interface condition is imposed weakly using a penalty formulation. We show how to formulate the penalty operators such that the coupling procedure is automatically adjusted to the movements and deformations of the interface, while both stability and conservation conditions are respected. The developed techniques are illustrated by performing numerical experiments on the linearized Euler equations and the Maxwell equations. The results corroborate the stability and accuracy of the fully discrete approximations. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free