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

Samira Nikkar, Jan Nordström

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

A time-dependent coordinate transformation of a constant coefficient hyperbolic system of equations is considered. We use the energy method to derive well-posed boundary conditions for the continuous problem. Summationby-Parts (SBP) operators together with a weak imposition of the boundary and initial conditions using Simultaneously Approximation Terms (SATs) guarantee energy-stability of the fully discrete scheme. We construct a time-dependent SAT formulation that automatically imposes the boundary conditions, and show that the numerical Geometric Conservation Law (GCL) holds. Numerical calculations corroborate the stability and accuracy of the approximations. As an application we study the sound propagation in a deforming domain using the linearized Euler equations.

Original languageEnglish
Title of host publicationSpectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM
EditorsRobert M. Kirby, Martin Berzins, Jan S. Hesthaven
PublisherSpringer Verlag
Pages385-395
Number of pages11
ISBN (Print)9783319197999
DOIs
Publication statusPublished - 2015
Externally publishedYes
Event10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014 - Salt Lake City, United States
Duration: 23 Jun 201427 Jun 2014

Publication series

NameLecture Notes in Computational Science and Engineering
Volume106
ISSN (Print)1439-7358

Conference

Conference10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014
Country/TerritoryUnited States
CitySalt Lake City
Period23/06/1427/06/14

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Engineering
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

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