High resolution upwind-mixed finite element methods for advection-diffusion equations with variable time-stepping

✍ Scribed by Clint Dawson

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 630 KB
• Volume: 11
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.1690110508

✦ Synopsis

Numerical methods for advection-diffusion equations are discussed based on approximating advection using a high-resolution upwind finite difference method, and incorporating diffusion using a mixed finite element method. In this approach, advection is approximated explicitly and diffusion implicitly. We first describe the basic procedure where each advection timestep is followed by a diffusion step. Because the explicit nature of the advective scheme requires a CFL time-step constraint, the basic procedure may be expensive, especially if the CFL constraint is severe. Two alternative time-stepping approaches are presented for improving computational efficiency while preserving accuracy. In the first approach, several advective time-steps are computed before taking a diffusion step. In the second approach, the advective time-steps are also allowed to vary spatially. Numerical results for these three procedures for a model problem arising in flow through porous media are given. 0 1995 John Wiley & Sons, Inc.