High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Capturing shock reflections: an improved flux formula
Journal of Computational Physics
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
A wave propagation method for three-dimensional hyperbolic conservation laws
Journal of Computational Physics
A class of approximate Riemann solvers and their relation to relaxation schemes
Journal of Computational Physics
A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Wave propagation algorithms on curved manifolds with applications to relativistic hydrodynamics
Wave propagation algorithms on curved manifolds with applications to relativistic hydrodynamics
Journal of Computational Physics
A wave propagation method for hyperbolic systems on the sphere
Journal of Computational Physics
A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Journal of Computational Physics
Journal of Computational Physics
Imaging brain activation streams from optical flow computation on 2-riemannian manifolds
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Analytic solutions and conserved quantities of wave equation on torus
Computers & Mathematics with Applications
Method of Moving Frames to Solve Conservation Laws on Curved Surfaces
Journal of Scientific Computing
Hi-index | 31.47 |
An extension of the wave propagation algorithm first introduced by LeVeque [J. Comput. Phys. 131 (1997) 327] is developed for hyperbolic systems on a general curved manifold. This extension is important in a variety of applications, including the propagation of sound waves on a curved surface, shallow water flow on the surface of the Earth, shallow water magnetohydrodynamics in the solar tachocline, and relativistic hydrodynamics in the presence of compact objects such as neutron stars and black holes. As is the case for the Cartesian wave propagation algorithm, this new approach is second order accurate for smooth flows and high-resolution shock-capturing. The algorithm is formulated such that scalar variables are numerically conserved and vector variables have a geometric source term that is naturally incorporated into a modified Riemann solver. Furthermore, all necessary one-dimensional Riemann problems are solved in a locally valid orthonormal basis. This orthonormalization allows one to solve Cartesian Riemann problems that are devoid of geometric terms. The new method is tested via application to the linear wave equation on a curved manifold as well as the shallow water equations on part of a sphere. The proposed algorithm has been implemented in the software package CLAWPACK and is freely available on the web.