Mathematics – Numerical Analysis
Scientific paper
2008-08-14
Mathematics
Numerical Analysis
22 pages, 10 figures. This is the third part of a series; see also arXiv:math/0612846 and arXiv:math/0612847
Scientific paper
We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments of longitude and latitude lines. The structure of the mesh allows for a discrete version of a natural geometric compatibility condition, which arose earlier in the well-posedness theory established by Ben-Artzi and LeFloch. We study here several classes of flux vectors which define the conservation law under consideration. They are based on prescribing a suitable vector field in the Euclidean three-dimensional space and then suitably projecting it on the sphere's tangent plane; even when the flux vector in the ambient space is constant, the corresponding flux vector is a non-trivial vector field on the sphere. In particular, we construct here "equatorial periodic solutions", analogous to one-dimensional periodic solutions to one-dimensional conservation laws, as well as a wide variety of stationary (steady state) solutions. We also construct "confined solutions", which are time-dependent solutions supported in an arbitrarily specified subdomain of the sphere. Finally, representative numerical examples and test-cases are presented.
Ben-Artzi Matania
Falcovitz Joseph
LeFloch Philippe G.
No associations
LandOfFree
Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-650233