ISSN:
1069-8299
Keywords:
three-dimensional convection-diffusion equation
;
fourth-order compact scheme
;
iterative methods
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
We present an explicit fourth-order compact finite difference scheme for approximating the three-dimensional convection-diffusion equation with variable coefficients. This 19-point formula is defined 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 coefficients. Some algebraic properties of the coefficient matrices arising from different discretization schemes are compared. We also comment on the potential use of the fourth-order compact scheme with multilevel iterative methods. © 1998 John Wiley & Sons, Ltd.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
