Hybrid Finite Difference Fifth-Order Multi-Resolution WENO Scheme for Hamilton-Jacobi Equations (Communications in Computational Physics, 2024)
In this paper, a fifth-order hybrid multi-resolution weighted essentially non-oscillatory (WENO) scheme in the finite difference framework is proposed for solvingone- and two-dimensional Hamilton-Jacobi equations. Firstly, a new discontinuity sensor is designed based on the extreme values of the highest degree polynomial in themulti-resolution WENO procedures. This hybrid strategy does not contain any human parameters related to specific problems and can identify the troubled grid pointsaccurately and automatically. Secondly, a hybrid multi-resolution WENO scheme forHamilton-Jacobi equations is developed based on the above discontinuity sensor and asimplified multi-resolution WENO scheme, which yields uniform high-order accuracyin smooth regions and sharply resolves discontinuities. Compared with the existingmulti-resolution WENO scheme, the method developed in this paper can inherit itsmany advantages and is more efficient. Finally, some benchmark numerical experiments are performed to demonstrate the performance of the presented fifth-order hybrid multi-resolution WENO scheme for one- and two-dimensional Hamilton-Jacobiequations.