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On New Strategies to Control the Accuracy of WENO Algorithm Close to Discontinuities II: Cell Averages and Multiresolution

On New Strategies to Control the Accuracy of WENO Algorithm Close to Discontinuities II: Cell Averages and Multiresolution
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Year:    2020

Author:    Sergio Amat, Juan Ruiz, Chi-Wang Shu

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 4 : pp. 661–682

Abstract

This paper is the second part of the article and is devoted to the construction and analysis of new non-linear optimal weights for WENO interpolation capable of rising the order of accuracy close to discontinuities for data discretized in the cell averages. Thus, now we are interested in analyzing the capabilities of the new algorithm when working with functions belonging to the subspace $L^1\cap L^2$ and that, consequently, are piecewise smooth and can present jump discontinuities. The new non-linear optimal weights are redesigned in a way that leads to optimal theoretical accuracy close to the discontinuities and at smooth zones. We will present the new algorithm for the approximation case and we will analyze its accuracy. Then we will explain how to use the new algorithm in multiresolution applications for univariate and bivariate functions. The numerical results confirm the theoretical proofs presented.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1903-m2019-0125

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 4 : pp. 661–682

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    WENO Cell averages New optimal weights Multiresolution schemes Improved adaption to discontinuities Signal processing.

Author Details

Sergio Amat

Juan Ruiz

Chi-Wang Shu

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    Amat, Sergio | Ruiz-Álvarez, Juan | Shu, Chi-Wang | Yáñez, Dionisio F.

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    https://doi.org/10.1016/j.amc.2021.126131 [Citations: 1]

  2. Nonlinear characteristics and corrections of near-field underwater explosion shock waves

    Jia, Xiyu | Wang, Shushan | Xu, Jie | Zhang, Jingxiao | Gao, Yuan | Ma, Feng

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    https://doi.org/10.1063/5.0087939 [Citations: 14]

  3. On a new centered strategy to control the accuracy of weighted essentially non oscillatory algorithm for conservation laws close to discontinuities

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    https://doi.org/10.1002/num.22524 [Citations: 1]