IJPAM: Volume 49, No. 3 (2008)

ON THE IMPLICIT DOWNWIND SCHEME
FOR SCALAR CONVECTION

Tore Flåtten$^1$, Olaf Huseby$^2$, Jan Sagen$^3$
$^{1,2,3}$Institute for Energy Technology
Kjeller, NO-2007, NORWAY
$^1$e-mail: toref@student.matnat.uio.no
$^2$e-mail: olaf.huseby@ife.no
$^3$e-mail: Jan.Sagen@ife.no
$^{1,2,3}$url: https://www.ife.no


Abstract.Standard explicit numerical methods for transport equations and conservation laws are restricted by the condition that the CFL number $C$ must be less than unity. Conversely, the implicit downwind scheme is stable for all $C>1$ and possesses some desirable accuracy properties. However, it hinges strongly on the boundary conditions being periodic. We here present an ongoing research effort to extend the implicit downwind scheme to general boundary conditions. Furthermore, we construct a hybrid explicit upwind/implicit downwind-based method that is stable for all CFL numbers. Some analytical results are presented, as well as an application to simulation of tracer flow in a 2D petroleum reservoir. Improved accuracy over standard implicit-based methods is demonstrated.

Received: August 14, 2008

AMS Subject Classification: 35L60, 35L65, 65C20

Key Words and Phrases: downwind, implicit, conservation laws

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 3