Solving hyperbolic problems on curved manifolds
Conservation laws on curved manifolds arise in various contexts, for example
in solving geophysical problems on the surface of a sphere, or solving
astrophysical problems in curved space. Our work has focused on extending
high-resolution finite volume methods to two-dimensional manifolds described
by an arbitrary metric.
Some references:
-
A wave propagation algorithm for hyperbolic systems on curved
manifolds,
by J. A. Rossmanith, D. S. Bale, and R. J. LeVeque,
J. Comput. Phys. 199 (2004), pp. 631-662.
Info/Download
- Derek Bale's
thesis, "Wave propagation algorithms on curved manifolds with
applications to relativistic hydrodynamics"
- James
Rossmanith's thesis, "A Wave Propagation Method with
Constrained Transport for Ideal and Shallow Water Magnetohydrodynamics"
Return to Randy LeVeque's research interests