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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

TVB boundary treatment for numerical solutions of conservation laws


Author: Chi-Wang Shu
Journal: Math. Comp. 49 (1987), 123-134
MSC: Primary 65N05; Secondary 35L65
MathSciNet review: 890257
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Abstract: In the computation of hyperbolic conservation laws $ {u_t} + f{(u)_x} = 0$, TVD (total-variation-diminishing) and TVB (total-variation-bounded) schemes have been very successful for initial value problems. But most of the existing boundary treatments are only proved to be linearly stable, hence the combined initial-boundary scheme may not be TVB. In this paper we describe a procedure of boundary treatment which uses the original high-order scheme up to the boundary, plus extrapolation and upwind treatment at the boundary. The resulting scheme is proved to be TVB for the scalar nonlinear case and for linear systems.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1987-0890257-7
PII: S 0025-5718(1987)0890257-7
Keywords: Conservation law, TVD, TVB, boundary condition
Article copyright: © Copyright 1987 American Mathematical Society