An explicit fourth-order compact finite difference scheme for three-dimensional convection-diffusion equation

✍ Scribed by Zhang, Jun

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 141 KB
• Volume: 14
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/(sici)1099-0887(199803)14:3<209::aid-cnm139>3.0.co;2-p

✦ Synopsis

We present an explicit fourth-order compact ®nite dierence scheme for approximating the threedimensional convection±diusion equation with variable coecients. This 19-point formula is de®ned on a uniform cubic grid. We compare the advantages and implementation costs of the new scheme with the standard 7-point scheme in the context of basic iterative methods. Numerical examples are used to verify the fourth-order convergence rate of the scheme and to show that the Gauss±Seidel iterative method converges for large values of the convection coecients. Some algebraic properties of the coecient matrices arising from dierent discretization schemes are compared. We also comment on the potential use of the fourthorder compact scheme with multilevel iterative methods.