For a nonlinear scalar conservation law in one-space dimension, we develop a locally conservative semi-Lagrangian finite difference scheme based on weighted essentially non-oscillatory reconstructions (SL-WENO). This scheme has the advantages of both WENO and semi-Lagrangian schemes. It is a locally mass conservative finite difference scheme, it is formally high-order accurate in space, it has ...

The weighted-essentially non-oscillatory (WENO) schemes have been used to calculate the shock-embedded compressible fluid flow ([9]). The potential high-fidelity qualities of this approach make it attractive for jet noise simulation. However, in its present form, the WENO procedure has many drawbacks that prevent direct applications to jet noise simulations. In this paper, various WENO procedur...

Accuracy-preserving and non-oscillatory shock-capturing technique is the bottle neck in the development of discontinuous Galerkin method. Inspired by the success of the k-exact WENO limiters for high order finite volume methods, this paper generalize the k-exact WENO limiter to discontinuous Galerkin methods. Also several improvements are put forward to keep the compactness and high-order accur...

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...

ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For u...

We introduce a multi-domain Fourier-Continuation/WENO hybrid method (FCWENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-ca...