A symmetrical WENO-Z scheme for solving Hamilton–Jacobi equations
2020 ◽
Vol 31
(03)
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pp. 2050039
Keyword(s):
The One
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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.