IJPAM: Volume 53, No. 2 (2009)

A NOVEL FLUX APPROXIMATION SCHEME FOR
SPHERICALLY SYMMETRIC CONSERVATION LAWS

J.H.M. ten Thije Boonkkamp$^1$, M.J.H. Anthonissen$^2$
$^{1,2}$Department of Mathematics and Computer Science
Eindhoven University of Technology
P.O. Box 513, MB Eindhoven, 5600, THE NETHERLANDS
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.We apply the finite volume method to a spherically symmetric conservation law of advection-diffusion-reaction type. For the numerical flux we use the so-called complete flux scheme. In this scheme the flux is computed from a local boundary value problem for the complete equation, including the source term. As a result, the numerical flux is the sum of a homogeneous flux and an inhomogeneous flux. The resulting scheme has only a three-point stencil and is second order accurate, uniformly in the local Peclet numbers.

Received: April 9, 2009

AMS Subject Classification: 34B05, 34B99, 65L10

Key Words and Phrases: advection-diffusion-reaction equation, spherical symmetry, flux, finite volume method, integral representation flux, numerical flux

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 2