Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N05, 35L65

Retrieve articles in all journals with MSC: 65N05, 35L65

Additional Information

Keywords: Conservation law, TVD, TVB, boundary condition
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society