Stationarity preserving schemes for multi-dimensional linear systems

• DOI: 10.1090/mcom/3394
• Publication Date: 2018-08-01T13:31:30Z
• Authors: Wasilij Barsukow
• Keywords: Divergence (linguistics); Regular grid

There is a qualitative difference between one-dimensional and multi-dimensional solutions to the Euler equations: new features that arise are vorticity nontrivial incompressible (low Mach number) limit. They present challenges finite volume methods. It seems an important step in this direction first study for acoustic equations. exists analogue of low number limit system its stationary. shown scheme possesses stationary discrete (vorticity preserving) also has states discretizations all analytic states. This property termed stationarity preserving. Both these not generically fulfilled by schemes; paper condition derived determines whether preserving (or, equivalently, on Cartesian grid. Additionally, uncovers previously unknown connection schemes comply with Truly found naturally it divergence discussed literature only possible one (in certain class).