Analysis of a Fourth-Order Scheme for a Three-Dimensional Convection-Diffusion Model Problem

Authors:
Ashvin Gopaul;Muddun Bhuruth
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2006

Citing 0
Cited 3

On block-circulant preconditioners for high-order compact approximations of convection-diffusion problems

Journal of Computational and Applied Mathematics
Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations

SIAM Journal on Numerical Analysis
Optimal Point-Wise Error Estimate of a Compact Difference Scheme for the Coupled Gross---Pitaevskii Equations in One Dimension

Journal of Scientific Computing

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Abstract

We derive closed form expressions for the eigenvalues and discrete solution arising from a 19-point compact discretization of a three-dimensional convection-diffusion problem. It is shown that the coefficient matrix is positive definite when the cell-Reynolds number is greater than some critical value. By analyzing the terms composing the discrete solution, we prove that an oscillation-free discrete solution is guaranteed whenever the cell-Reynolds number exceeds a value which is grid-size dependent. An interesting result is that as the mesh size is refined, this value approaches the Golden Mean.