Stability of the standard Crank-Nicolson-Galerkin scheme applied to the diffusion-convection equation: Some new insights

Journal Article · Wed Sep 01 00:00:00 EDT 1993 · Water Resources Research; (United States)

DOI:https://doi.org/10.1029/93WR01413· OSTI ID:5254843

Perrochet, P; Berod, D ^[1]

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1. Ecole Polytechnique Federale de Lausanne (Switzerland)

A stability analysis of the classical Crank-Nicolson-Galerkin (CNG) scheme applied to the one-dimensional solute transport equation is proposed on the basis of two fairly different approaches. Using a space-time eigenvalue analysis, it is shown, at least for subsurface hydrology applications, that the CNG scheme is theoretically stable under the condition PeCr [le] 2, where Pe and Cr are the mesh Peclet and Courant numbers. Then, to assess the computational stability of the scheme, the amplification matrix is constructed, and its norm is displayed in the (Pe, Cr) space. The results indicate that the norm of the amplification matrix is never smaller than unity and exhibits a hyperbolic nature analogous to the above theoretical condition. 21 refs., 2 figs.

• OSTI ID: 5254843
• Journal Information: Water Resources Research; (United States), Vol. 29:9; ISSN 0043-1397
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
CONVECTION
FLUID MECHANICS
DIFFUSION
FLUID FLOW
FINITE DIFFERENCE METHOD
NUMERICAL SOLUTION
GALERKIN-PETROV METHOD
HYDROLOGY
CALCULATION METHODS
ENERGY TRANSFER
HEAT TRANSFER
ITERATIVE METHODS
MASS TRANSFER
MECHANICS
420400* - Engineering- Heat Transfer & Fluid Flow
990200 - Mathematics & Computers