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"
-
Logically Rectangular Grids and Finite Volume Methods for
PDEs in Circular and Spherical Domains,
by Donna A. Calhoun, Christiane Helzel, and Randall J. LeVeque,
SIAM Review 50 (2008), 723-752.
-
Logically Rectangular Finite Volume Methods with
Adaptive Refinement on the Sphere,
by M. J. Berger and D. A. Calhoun, and C. Helzel, and R. J. LeVeque
Phil. Trans. R. Soc. A, to appear.
Return to Randy LeVeque's research interests