@inproceedings{3d0c7bca41e342d68d3e31a2874c6a4a,
title = "Fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domains",
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.",
author = "Samira Nikkar and Jan Nordstr{\"o}m",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014 ; Conference date: 23-06-2014 Through 27-06-2014",
year = "2015",
doi = "10.1007/978-3-319-19800-2_35",
language = "English",
isbn = "9783319197999",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer Verlag",
pages = "385--395",
editor = "Kirby, {Robert M.} and Martin Berzins and Hesthaven, {Jan S.}",
booktitle = "Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM",
address = "Germany",
}