Fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domains

JOURNAL OF COMPUTATIONAL PHYSICS

卷:291

Article

Nikkar, Samira¹  Nordstrom, Jan¹ 

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

关键词: Deforming domain;    Initial boundary value problems;    High order accuracy;    Well-posed boundary conditions;    Summation-by-parts operators;    Stability;    Convergence;    Conservation;    Numerical geometric conservation law;    Euler equation;    Sound propagation;   

DOI  :  10.1016/j.jcp.2015.02.027

来源: Elsevier

【 摘 要 】

A time-dependent coordinate transformation of a constant coefficient hyperbolic system of equations which results in a variable coefficient system of equations is considered. By applying the energy method, well-posed boundary conditions for the continuous problem are derived. Summation-by-Parts (SBP) operators for the space and time discretization, together with a weak imposition of boundary and initial conditions using Simultaneously Approximation Terms (SATs) lead to a provable fully-discrete energy-stable conservative finite difference scheme. We show how to construct a time-dependent SAT formulation that automatically imposes boundary conditions, when and where they are required. We also prove that a uniform flow field is preserved, i.e. the Numerical Geometric Conservation Law (NGCL) holds automatically by using SBP-SAT in time and space. The developed technique is illustrated by considering an application using the linearized Euler equations: the sound generated by moving boundaries. Numerical calculations corroborate the stability and accuracy of the new fully discrete approximations. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free