Multigrid solution of monotone secondorder discretizations of hyperbolic conservation laws
Author:
Stefan Spekreijse
Journal:
Math. Comp. 49 (1987), 135155
MSC:
Primary 65N05; Secondary 35L65, 76G15
MathSciNet review:
890258
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Abstract: This paper is concerned with two subjects: the construction of secondorder accurate monotone upwind schemes for hyperbolic conservation laws and the multigrid solution of the resulting discrete steadystate equations. By the use of an appropriate definition of monotonicity, it is shown that there is no conflict between secondorder accuracy and monotonicity (neither in one nor in more dimensions). It is shown that a symmetric block GaussSeidel underrelaxation (each block is associated with 4 cells) has satisfactory smoothing rates. The success of this relaxation is due to the fact that, by coupling the unknowns in such blocks, the ninepoint stencil of a secondorder 2D upwind discretization changes into a fivepoint block stencil.
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 A. Harten, "High resolution schemes for hyperbolic conservation laws," J. Comput. Phys., v. 49, 1983, pp. 357393. MR 701178 (84g:65115)
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 S. P. Spekreijse, Second Order Accurate Upwind Solutions of the 2 D Steady Euler Equations by the Use of a Defect Correction Method, Multigrid Methods II, Proc. 2nd European Multigrid Conference (Cologne, 1985), Lecture Notes in Math., vol. 1228, SpringerVerlag, Berlin and New York, 1985, pp. 285300. MR 896067 (88f:65171)
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 [14]
 B. van Leer, "Towards the ultimate conservative difference scheme IV. A new approach to numerical convection," J. Comput. Phys., v. 23, 1977, pp. 276299.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708902589
PII:
S 00255718(1987)08902589
Keywords:
Conservation laws,
multigrid methods
Article copyright:
© Copyright 1987 American Mathematical Society
