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A Maximum-Principle-Satisfying High-order Finite Volume Compact WENO Scheme for Scalar Conservation Laws

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      Abstract

      In this paper, a maximum-principle-satisfying finite volume compact scheme is proposed for solving scalar hyperbolic conservation laws. The scheme combines WENO schemes (Weighted Essentially Non-Oscillatory) with a class of compact schemes under a finite volume framework, in which the nonlinear WENO weights are coupled with lower order compact stencils. The maximum-principle-satisfying polynomial rescaling limiter in [Zhang and Shu, JCP, 2010] is adopted to construct the present schemes at each stage of an explicit Runge-Kutta method, without destroying high order accuracy and conservativity. Numerical examples for one and two dimensional problems including incompressible flows are presented to assess the good performance, maximum principle preserving, essentially non-oscillatory and highly accurate resolution of the proposed method.

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      Most cited references 27

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      Compact finite difference schemes with spectral-like resolution

       Sanjiva Lele (1992)
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        Efficient Implementation of Weighted ENO Schemes

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          Efficient implementation of essentially non-oscillatory shock-capturing schemes

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            Author and article information

            Journal
            2014-05-06
            2014-05-08
            1405.1373

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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            math.NA

            Numerical & Computational mathematics

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