High-Resolution Conservative Algorithms for Advection in Incompressible Flow
by Randall LeVeque, SIAM J. Numer. Anal., 33 (1996), 627-665

Abstract. A class of high-resolution algorithms is developed for advection of a scalar quantity in a given incompressible flow field in one, two, or three space dimensions. Multidimensional transport is modeled using a wave-propagation approach in which the flux at each cell interface is built up on the basis of information propagating in the direction of this interface from neighboring cells. A high-resolution second-order method using slope limiters is quite easy to implement. For constant flow, a minor modification gives a third-order accurate method. These methods are stable for Courant numbers up to 1. Fortran implementations are available by anonymous ftp.

Keywords. multidimensional advection, incompressible flow, high-resolution methods, finite volume methods, flux-limiters, wave-propagation methods

AMS(MOS) Subject Classifications. 65M06, 76M20

SINUM webpage for this paper

0733033.pdf, 4.3MB

bibtex entry:

@Article{rjl:advect,
  author =       "R. J. LeVeque",
  title =        "High-resolution conservative algorithms for advection
                 in incompressible flow",
  journal =      "SIAM J. Numer. Anal.",
  volume =       "33",
  year =         "1996",
  pages =        "627--665",
}

Note: The algorithms described in this paper formed the based for later work on wave-propagation algorithms for more general systems and the CLAWPACK software. Implementations of some of the examples in this paper in CLAWPACK may be found in the applications/advection subdirectory.