High-Order Central WENO Schemes for Multidimensional Hamilton-Jacobi Equations

Central WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes

We derive Godunov-type semidiscrete central schemes for Hamilton–Jacobi equations on triangular meshes. High-order schemes are then obtained by combining our new numerical fluxes with high-order WENO reconstructions on triangular meshes. The numerical fluxes are shown to be monotone in certain cases. The accuracy and high-resolution properties of our scheme are demonstrated in a variety of nume...

High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations

Mapped WENO and weighted power ENO reconstructions in semi-discrete central schemes for Hamilton–Jacobi equations

We incorporate new high-order WENO-type reconstructions into Godunov-type central schemes for Hamilton–Jacobi equations. We study schemes that are obtained by combining the Kurganov–Noelle–Petrova flux with the weighted power ENO and the mapped WENO reconstructions. We also derive new variants of these reconstructions by composing the weighted power ENO and the mapped WENO reconstructions with ...

A Weighted Essentially Nonoscillatory, Large Time-Step Scheme for Hamilton-Jacobi Equations

We investigate the application of weighted essentially nonoscillatory (WENO) reconstructions to a class of semi-Lagrangian schemes for first order time-dependent Hamilton–Jacobi equations. In particular, we derive a general form of the scheme, study sufficient conditions for its convergence with high-order reconstructions, and perform numerical tests to study its efficiency. In addition, we pro...

Hermite WENO schemes for Hamilton–Jacobi equations

In this paper, a class of weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving Hamilton–Jacobi equations is presented. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and used in the reconstruction, ...