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...

In an attempt to investigate the structures of ultra-relativistic jets injected into intracluster medium (ICM) and associated flow dynamics, such as shocks, velocity shear, turbulence, we have developed a new special relativistic hydrodynamic (RHD) code in Cartesian coordinates, based on weighted essentially non-oscillatory (WENO) scheme. It is finite difference scheme high spatial accuracy, wh...

This article describes the development of a high order finite volume method for the solution of transonic flows. The high order of accuracy is achieved by a reconstruction procedure similar to the weighted essentially non-oscillatory schemes (WENO). On the contrary to the WENO schemes, the weighted least square (WLSQR) scheme is easily extensible to the case of complex geometry.

In this article we introduce the multi-domain hybrid Spectral-WENO method aimed at the discontinuous solutions of hyperbolic conservation laws. The main idea is to conjugate the non-oscillatory properties of the high order weighted essentially non-oscillatory (WENO) finite difference schemes with the high computational efficiency and accuracy of spectral methods. Built in a multi-domain framewo...

In this paper, a general high-order multi-domain hybrid DG/WENO-FDmethod, which couples a p-order (p ≥ 3) DG method and a q-order (q ≥ 3) WENO-FD scheme, is developed. There are two possible coupling approaches at the domain interface, one is non-conservative, the other is conservative. The non-conservative coupling approach can preserve optimal order of accuracy and the local conservative erro...

A hierarchical Hermite WENO reconstruction-based discontinuous Galerkin method, designed not only to enhance the accuracy of discontinuous Galerkin method but also to avoid spurious oscillation in the vicinity of discontinuities, is developed for compressible flows on tetrahedral grids. In this method, a quadratic polynomial solution is first reconstructed from the underlying linear polynomial ...

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 ...

In this paper, we investigate a simple limiter using weighted essentially non-oscillatory (WENO) methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving conservation laws, with the goal of obtaining a robust and high order limiting procedure to simultaneously achieve uniform high order accuracy and sharp, non-oscillatory shock transitions. The idea of this limiter is to re...

As a new attempt to solve hyperbolic conservation laws with spatially varying fluxes, the weighted essentially non-oscillatory (WENO) method is applied to solve a multi-class traffic flow model for an inhomogeneous highway. The numerical scheme is based upon a modified equivalent system that is written in a “standard” hyperbolic conservation form. Numerical examples, which include the difficult...

Jing-Mei Qiu and Andrew Christlieb 3 Abstract In this paper, we propose a novel Vlasov solver based on a semi-Lagrangian method which combines Strang splitting in time with high order WENO (weighted essentially nonoscillatory) reconstruction in space. A key insight in this work is that the spatial interpolation matrices, used in the reconstruction process of a semi-Lagrangian approach to linear...