Abstract

Five-point finite-difference approximations are considered for a model (linear, constant-coefficient) convection-diffusion equation in two dimensions. Standard difference schemes for such problems behave badly when the convective terms are dominant. A new discretization is derived from a local integral representation of the true solution. This derivation is analogous to the way that the discrete Laplacian can be derived from the mean-value property of harmonic functions, and it generalizes an approach due to Allen and Southwell [Quart. J. Mech. Appl. Math., 8 (1955), pp. 129–45]. Also discussed is how the strong upwind bias of this and other discretizations serves to make more stable some methods of the two-sweep or marching type for the direct solution of the resulting linear algebraic equations.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.