Fully Discrete Energy Stable High Order Finite Difference Methods for Hyperbolic Problems in Deforming Domains
2014 (English)Report (Other academic)
A time-dependent coordinate transformation of a constant coefficient hyperbolic system of equations which results in a variable coecient 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 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 holds automatically by using SBP-SAT in time. 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
Linköping University Electronic Press, 2014. , 31 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2014:15
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
Computational Mathematics Mathematics
IdentifiersURN: urn:nbn:se:liu:diva-111336ISRN: LiTH-MAT-R--2014/15--SEOAI: oai:DiVA.org:liu-111336DiVA: diva2:755469