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A symmetrical WENO-Z scheme for solving Hamilton–Jacobi equations

Author

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  • Rooholah Abedian

    (School of Engineering Science, College of Engineering, University of Tehran, Iran)

Abstract

In this paper, a new WENO procedure is proposed to approximate the viscosity solution of the Hamilton–Jacobi (HJ) equations. In the one-dimensional (1D) case, an optimum polynomial on a six-point stencil is obtained. This optimum polynomial is fifth-order accurate in regions of smoothness. Then, this optimum polynomial is considered as a symmetric and convex combination of four polynomials with ideal weights. Following the methodology of the classic WENO-Z procedure [Borges et al., J. Comput. Phys. 227, 3191 (2008)], the new nonoscillatory weights are calculated with the ideal weights. Several numerical experiments in 1D, 2D and 3D are performed to illustrate the capability of the scheme.

Suggested Citation

  • Rooholah Abedian, 2020. "A symmetrical WENO-Z scheme for solving Hamilton–Jacobi equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-24, February.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:03:n:s0129183120500394
    DOI: 10.1142/S0129183120500394
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