Fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domains
2015 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 291, 82-98 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
Elsevier , 2015. Vol. 291, 82-98 p.
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
IdentifiersURN: urn:nbn:se:liu:diva-117360DOI: 10.1016/j.jcp.2015.02.027ISI: 000352230500006OAI: oai:DiVA.org:liu-117360DiVA: diva2:807873