A genuinely high order total variation diminishing scheme for one-dimensional scalar conservation laws. (English) Zbl 1226.65083

The authors develop a high order accuracy total variation diminishing (TVD) scheme in the \(L^1\)-norm for one-dimensional scalar conservation laws. Numerical results for five test problems including a traffic flow model are discussed using a fifth order scheme. The advantage of the proposed high order scheme is that it satisfies strictly a maximum principle; therefore, it has better resolution than the usual TVD scheme, when the solution contains many waves, and it does not generate any unphysical solution.


65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35B50 Maximum principles in context of PDEs
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