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Comparison of two cell‐centered multigrid schemes for problems with discontinuous coefficients
Author(s) -
Ersland Brit Gunn,
Teigland Rune
Publication year - 1993
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.1690090306
Subject(s) - multigrid method , mathematics , simple (philosophy) , grid , constant coefficients , mathematical optimization , mathematical analysis , partial differential equation , geometry , philosophy , epistemology
Two different schemes for constructing coarse‐grid operators are implemented in a linear multigrid code. In the first scheme, the construction of the coarse‐grid operators is done using a variational approach. Certain conservation properties of the fine‐grid matrices are shown to be preserved on the coarser grids by the variational construction. In the second scheme, the diffusion coefficients for the coarse grids are calculated by a simple restriction of the coefficient from the fine grid, using a flux conservation principle. The multigrid codes are then applied to solve the linear equations from an IMPES formulation of a two‐phase porous‐media flow model. A standard elliptic model problem with jump discontinuous coefficients is also solved using the two multigrid schemes. In simple cases of particular elliptic equations these two schemes are identical. However, in more general cases, such as in reservoir problems, these schemes differ. It is shown that multigrid efficiency typical of the constant coefficient cases is obtained for these problems involving discontinuous coefficients. © 1993 John Wiley & Sons, Inc.