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Stability and accuracy of a semi‐implicit Godunov scheme for mass transport
Author(s) -
Bradford Scott F.
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.702
Subject(s) - discretization , advection , stability (learning theory) , temporal discretization , courant–friedrichs–lewy condition , mathematics , diffusion , convection–diffusion equation , von neumann stability analysis , numerical stability , numerical analysis , mathematical analysis , computer science , physics , machine learning , thermodynamics
Abstract Semi‐implicit, Godunov‐type models are adapted for solving the two‐dimensional, time‐dependent, mass transport equation on a geophysical scale. The method uses Van Leer's MUSCL reconstruction in conjunction with an explicit, predictor–corrector method to discretize and integrate the advection and lateral diffusion portions of the governing equation to second‐order spatial and temporal accuracy. Three classical schemes are investigated for computing advection: Lax‐Wendroff, Warming‐Beam, and Fromm. The proposed method uses second order, centred finite differences to spatially discretize the diffusion terms. In order to improve model stability and efficiency, vertical diffusion is implicitly integrated with the Crank–Nicolson method and implicit treatment of vertical diffusion in the predictor is also examined. Semi‐discrete and Von Neumann analyses are utilized to compare the stability as well as the amplitude and phase accuracy of the proposed method with other explicit and semi‐implicit schemes. Some linear, two‐dimensional examples are solved and predictions are compared with the analytical solutions. Computational effort is also examined to illustrate the improved efficiency of the proposed model. Copyright © 2004 John Wiley & Sons, Ltd.