Title

An Ellam Scheme for Advection-Diffusion Equations in Two Dimensions

Author(s)

Hong Wang, University of South Carolina - ColumbiaFollow
Helge K. Dahle
Richard E. Ewing
Magne S. Espedal
Robert Sharpley, University of South Carolina - ColumbiaFollow
Shushuang Man

Document Type

Article

Subject Area(s)

Mathematics

Abstract

We develop an Eulerian{Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to demonstrate the strength of the ELLAM scheme.

Publication Info

Published in Siam Journal on Scientific Computing, Volume 20, Issue 6, 1999, pages 2160-2194.

© Siam Journal on Scientific Computing 1999, Society for Industrial and Applied Mathematics

Wang, H., Dahle, H., Ewing, R., Espedal, M., Sharpley, R., & Man, S. (1999). An ELLAM Scheme for Advection-Diffusion Equations in Two Dimensions. SIAM Journal On Scientific Computing, 20(6), 2160-2194. doi: 10.1137/s1064827596309396