Skip to Main content Skip to Navigation
Reports

Extensions to Higher-Dimensions of an Unconditionally Stable ADE Scheme for the Convection-Diffusion Equation

Martin Guay 1, * Fabrice Colin 1 Richard Egli 1
* Corresponding author
Abstract : An unconditionally stable alternating direction explicit scheme (ADE) to solve the one-dimensional unsteady convection-diffusion equation was developed by J. Xie, Z. Lin and J. Zhou in [6]. Aside from being explicit and unconditionally stable, the method is straightforward to implement. In this paper we show extensions of this scheme to higher-dimensions of the convection-diffusion equation subject to Dirichlet boundary conditions. By expressing the equation with a local series expansion over a rectangular grid, a linear system of symbolic equations is obtained which is tedious to solve for manually and we addressed this challenge using symbolic computation. The solutions obtained are explicit closed-form formulas which are then used to iteratively solve the unsteady convectiondiffusion equation by traversing the discrete grid in an alternating direction fashion. Finally, extensions to higher dimensions can be easily deduced from the 2D formulas. We conclude the paper with numerical simulation results for diffusion and convection-diffusion problems compared to analytical solutions showing the performance of the method and its numerical stability.
Document type :
Reports
Complete list of metadata


https://hal.inria.fr/hal-00750389
Contributor : Martin Guay Connect in order to contact the contributor
Submitted on : Friday, November 9, 2012 - 4:57:43 PM
Last modification on : Wednesday, February 10, 2021 - 10:10:02 AM
Long-term archiving on: : Sunday, February 10, 2013 - 4:25:11 AM

Files

GuayColinEgli_ADE_TechRep.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00750389, version 1

Citation

Martin Guay, Fabrice Colin, Richard Egli. Extensions to Higher-Dimensions of an Unconditionally Stable ADE Scheme for the Convection-Diffusion Equation. [Research Report] 2011, pp.21. ⟨hal-00750389v1⟩

Share

Metrics

Record views

66

Files downloads

368