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Numerical inaccuracies across the interface of a nested grid
Author(s) -
Peggion Germana
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100405
Subject(s) - advection , grid , interface (matter) , scale (ratio) , computational science , diffusion , wavelength , computer science , function (biology) , resolution (logic) , length scale , mathematics , mathematical optimization , mechanics , geometry , physics , parallel computing , thermodynamics , artificial intelligence , optoelectronics , bubble , quantum mechanics , maximum bubble pressure method , evolutionary biology , biology
This article addresses and discusses the inaccuracies in finite differencing across the interface of a nested grid. Explicit schemes for the advection and diffusion equations are analyzed on the fine and coarse grids and reformulated at the interface to guarantee that the evolving solution is unaffected by the abrupt change of the spatial grid resolution. The associated errors are expressed as a function of the wavelength of the initial field distribution and the ratio between the coarse and fine grid resolution. It is found that large‐scale features of the coarse grid must supply energy to sustain the small‐scale features of the fine grid. To not deplete the large‐scale motion, a source of energy must be given at the interface in the form of a computational diffusive term with negative viscosity coefficient. On the other hand, not all the energy of the small‐scale features of the fine grid has to be transferred to the large‐scale motion, but some of it needs to be computationally dissipated at the interface. © 1994 John Wiley & Sons, Inc.