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Low dissipative entropy stable schemes using third order WENO and TVD reconstructions

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Abstract

A low dissipative framework is given to construct high order entropy stable flux by addition of suitable numerical diffusion operator into entropy conservative flux. The framework is robust in the sense that it allows the use of high order reconstructions which satisfy the sign property only across the discontinuities. The third order weighted essentially non-oscillatory (WENO) interpolations and high order total variation diminishing (TVD) reconstructions are shown to satisfy the sign property across discontinuities. Third order accurate entropy stable schemes are constructed by using third order WENO and high order TVD reconstructions procedures in the diffusion operator. These schemes are efficient and less diffusive since the diffusion is actuated only in the sign stability region of the used reconstruction which includes discontinuities. Numerical results with constructed schemes for various test problems are given which show the third order accuracy and less dissipative nature of the schemes.

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Acknowledgments

Authors are greatly thankful to anonymous reviewers for their technical comments and constructive suggestions which helped to improve the overall manuscript. We also acknowledge Science and Engineering Research Board, India for providing necessary funds for Mr. Biswarup through SERB Project EMR/2016/000394.

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Authors and Affiliations

  1. Research Institute and Department of Mathematics, SRM University, Tamil Nadu, 603203, India

    Biswarup Biswas & Ritesh Kumar Dubey

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  1. Biswarup Biswas
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Correspondence to Ritesh Kumar Dubey.

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Communicated by: Jean-Frédéric Gerbeau

Carried out work is supported through DST-SERB India project EMR/2016/000394.

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Biswas, B., Dubey, R.K. Low dissipative entropy stable schemes using third order WENO and TVD reconstructions. Adv Comput Math 44, 1153–1181 (2018). https://doi.org/10.1007/s10444-017-9576-2

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