Energy Stable High Order Finite Difference Methods for Hyperbolic Equations in Moving Coordinate Systems
2013 (English)In: AIAA Aerospace Sciences - Fluid Sciences Event, 2013, 1-14 p.Conference paper (Other academic)
A time-dependent coordinate transformation of a constant coeffcient hyperbolic equation which results in a variable coeffcient problem is considered. By using the energy method, we derive well-posed boundary conditions for the continuous problem. It is shown that the number of boundary conditions depend on the coordinate transformation. By using Summation-by-Parts (SBP) operators for the space discretization and weak boundary conditions, an energy stable finite dieffrence scheme is obtained. We also show how to construct a time-dependent penalty formulation that automatically imposes the right number of boundary conditions. Numerical calculations corroborate the stability and accuracy of the approximations.
Place, publisher, year, edition, pages
2013. 1-14 p.
IdentifiersURN: urn:nbn:se:liu:diva-96879DOI: 10.2514/6.2013-2579OAI: oai:DiVA.org:liu-96879DiVA: diva2:643630
21st AIAA Computational Fluid Dynamics Conference 24 - 27 June 2013 San Diego, California