Arc Length-Based WENO Scheme for Hamilton-Jacobi Equations

doi:10.1007/s42967-020-00091-5

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (3): 481-496.doi: 10.1007/s42967-020-00091-5

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Arc Length-Based WENO Scheme for Hamilton-Jacobi Equations

Rathan Samala¹, Biswarup Biswas²

1 Faculty of Mathematics, Department of Humanities and Sciences, Indian Institute of Petroleum and Energy-Visakhapatnam, Visakhapatnam 530003, India;
2 Department of Mathematics, Indian Institute of Technology-Delhi, New Delhi 110016, India

收稿日期:2020-03-04 修回日期:2020-06-06 出版日期:2021-09-20 发布日期:2021-09-16
通讯作者: Rathan Samala, Biswarup Biswas E-mail:rathans.math@iipe.ac.in;biswarupb7@gmail.com

Arc Length-Based WENO Scheme for Hamilton-Jacobi Equations

Rathan Samala¹, Biswarup Biswas²

1 Faculty of Mathematics, Department of Humanities and Sciences, Indian Institute of Petroleum and Energy-Visakhapatnam, Visakhapatnam 530003, India;
2 Department of Mathematics, Indian Institute of Technology-Delhi, New Delhi 110016, India

Received:2020-03-04 Revised:2020-06-06 Online:2021-09-20 Published:2021-09-16
Contact: Rathan Samala, Biswarup Biswas E-mail:rathans.math@iipe.ac.in;biswarupb7@gmail.com

摘要/Abstract

摘要： In this article, novel smoothness indicators are presented for calculating the nonlinear weights of the weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi equations. These novel smoothness indicators are constructed from the derivatives of reconstructed polynomials over each sub-stencil. The constructed smoothness indicators measure the arc-length of the reconstructed polynomials so that the new nonlinear weights could get less absolute truncation error and give a high-resolution numerical solution. Extensive numerical tests are conducted and presented to show the performance capability and the numerical accuracy of the proposed scheme with the comparison to the classical WENO scheme.

关键词: Finite difference, Hamilton-Jacobi equations, WENO scheme, Length of the curve, Smoothness indicators, Nonlinear weights

Abstract: In this article, novel smoothness indicators are presented for calculating the nonlinear weights of the weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi equations. These novel smoothness indicators are constructed from the derivatives of reconstructed polynomials over each sub-stencil. The constructed smoothness indicators measure the arc-length of the reconstructed polynomials so that the new nonlinear weights could get less absolute truncation error and give a high-resolution numerical solution. Extensive numerical tests are conducted and presented to show the performance capability and the numerical accuracy of the proposed scheme with the comparison to the classical WENO scheme.

Key words: Finite difference, Hamilton-Jacobi equations, WENO scheme, Length of the curve, Smoothness indicators, Nonlinear weights

中图分类号:

Rathan Samala, Biswarup Biswas. Arc Length-Based WENO Scheme for Hamilton-Jacobi Equations[J]. Communications on Applied Mathematics and Computation, 2021, 3(3): 481-496.

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Arc Length-Based WENO Scheme for Hamilton-Jacobi Equations

Arc Length-Based WENO Scheme for Hamilton-Jacobi Equations

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