A class of non-oscillatory direct-space-time schemes for hyperbolic conservation laws. (English) Zbl 1508.65115
Summary: The main concern of this paper is to develop a class of non-oscillatory direct-space-time (DST) schemes for hyperbolic conservation laws. This class of DST schemes have optimal order of accuracy, however, similar to the standard schemes the naive implementation of these schemes produce oscillatory and unstable solutions. To study the nonlinear stability of DST schemes, a TVD flux limiter is introduced, and it is proven that the overall method is a TVD scheme. The numerical illustrations justify the non-oscillatory behaviour of the developed class of schemes in presence of shocks and discontinuities. It is worth to note that the underlying DST schemes include both of the upwind and symmetric schemes and the resulting TVD DST scheme produce comparable results with the standard non-oscillatory schemes like WENO schemes.
MSC:
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
Keywords:
high resolution schemes; non-oscillatory schemes; hyperbolic conservation laws; DST schemes; upwind and symmetric schemesReferences:
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