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Two classes of third-order weighted compact nonlinear schemes for Hamilton-Jacobi equations

Author

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  • Huang, Xiaoqian
  • Jiang, Yanqun
  • Yang, Huanhuan

Abstract

The solutions of Hamilton-Jacobi (HJ) equations may contain discontinuous derivatives, which brings numerical difficulties in capturing sharply these derivatives. This paper presents a third-order weighted compact nonlinear scheme (WCNS) and a third-order perturbed WCNS (WCNS-P) for solving HJ equations. A linear combination of hybrid cell-edge and cell-node values of the function is applied to approximate the spatial derivatives of the function. For the WCNS, the upwind-biased nonlinear weighted interpolation is used for the unknown cell-edge values, while for the WCNS-P perturbations with a free parameter is introduced to the upwind-biased linear interpolation. The free parameter can be optimized to reduce numerical errors in smooth regions. To enhance the numerical stability, a monotone polynomial interpolation method is designed to switch the WCNS-P to the WCNS. Several numerical experiments are performed to test the order of accuracy and the discontinuity-capturing ability of the two schemes.

Suggested Citation

  • Huang, Xiaoqian & Jiang, Yanqun & Yang, Huanhuan, 2024. "Two classes of third-order weighted compact nonlinear schemes for Hamilton-Jacobi equations," Applied Mathematics and Computation, Elsevier, vol. 469(C).
    • Handle: RePEc:eee:apmaco:v:469:y:2024:i:c:s0096300324000262
    DOI: 10.1016/j.amc.2024.128554
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