Symmetrical weighted essentially non-oscillatory-flux limiter schemes for Hamilton-Jacobi equations

In this paper, we propose a new scheme that combines weighted essentially non-oscillatory (WENO) procedures together with monotone upwind schemes to approximate the viscosity solution of the Hamilton-Jacobi equations. In one-dimensional (1D) case, first, we obtain an optimum polynomial on a four-point stencil. This optimum polynomial is third-order accurate in regions of smoothness. Next, we modify a second-order ENO polynomial by choosing an additional point inside the stencil in order to obtain the highest accuracy when combined with the Harten-Osher reconstruction-evolution method limiter. Finally, the optimum polynomial is considered as a symmetric and convex combination of three polynomials with ideal weights. Following the methodology of the classic WENO procedure, then, we calculate the non-oscillatory weights with the ideal weights. Numerical experiments in 1D and 2D are performed to compare the capability of the hybrid scheme to WENO schemes. Copyright (C) 2015 John Wiley & Sons, Ltd.