Multigrid solution of monotone second-order discretizations of hyperbolic conservation laws

Author:
Stefan Spekreijse

Journal:
Math. Comp. **49** (1987), 135-155

MSC:
Primary 65N05; Secondary 35L65, 76G15

DOI:
https://doi.org/10.1090/S0025-5718-1987-0890258-9

MathSciNet review:
890258

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Abstract: This paper is concerned with two subjects: the construction of second-order accurate monotone upwind schemes for hyperbolic conservation laws and the multigrid solution of the resulting discrete steady-state equations. By the use of an appropriate definition of monotonicity, it is shown that there is no conflict between second-order accuracy and monotonicity (neither in one nor in more dimensions).

It is shown that a symmetric block Gauss-Seidel 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 nine-point stencil of a second-order 2D upwind discretization changes into a five-point block stencil.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1987-0890258-9

Keywords:
Conservation laws,
multigrid methods

Article copyright:
© Copyright 1987
American Mathematical Society