Mapped WENO schemes based on a new smoothness indicator for Hamilton-Jacobi equations (Q442489)

The authors propose an improved version of mapped weighted essentially nonoscillatory (WENO) schemes with a new smoothness indicator (WENO-NSM) of fifth-order convergence for the approximate solutions of the Hamilton--Jacobi equations of the form \(\phi_t+H(\nabla\phi)=0\), \(\phi(x,0)=\phi_0(x)\), \(x\in{\mathbb R}^d\), where \(H\) is the Hamiltonian. In a number of numerical experiments, the proposed schemes exhibit better performances than the known mapped WENO-M schemes and the WENO-JS schemes for hyperbolic conservation laws. Comparisons among WENO-NSM, WENO-JS and WENO-M reveal clear advantages of WENO-NSM on approximating near the discontinuities. Numerical experiments show that WENO-NSM schemes resolve discontinuities sharply while keeping an essential non-oscillatory performance. The improvement is attributed to the ability of WENO-NSM to detect the complicated solution structures.