A key idea in finite difference weighted essentially non-oscillatory (WENO) schemes is a combination of lower order fluxes to obtain a higher order approximation. The choice of the weight to each candidate stencil, which is a nonlinear function of the grid values, is crucial to the success of WENO. For the system case, WENO schemes are based on local characteristic decompositions and flux split...

In order to simulate accurately the interaction of shock wave/complex flows, hybrid schemes combining the compact scheme and weighted essentially non-oscillatory(WENO) scheme are beneficial, especially the high order low diffusion schemes used in smooth regions. There are two key issues, one is how to detect the discontinuity, the other is how to choose the high order low diffusion scheme to en...

To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws in [14] to convection diffusion equations, we propose a non-conventional high order finite volume weighted essentially non-oscillatory (WENO) scheme which can be proven maximum-principle-satisfying. Two-dimensional extensions are straightforward. We also show that the same idea can be used to construct hi...

In our latest studies, by introducing the novel order-preserving (OP) criterion, we have successfully addressed widely concerned issue of previously published mapped weighted essentially non-oscillatory (WENO) schemes that it is rather difficult to achieve high resolutions on premise removing spurious oscillations for long-run simulations hyperbolic systems. present study, extend OP criterion W...

In ([10], JCP 227 No. 6, 2008, pp. 3101–3211), the authors have designed a new fifth order WENO finite-difference scheme by adding a higher order smoothness indicator which is obtained as a simple and inexpensive linear combination of the already existing low order smoothness indicators. Moreover, this new scheme, dubbed as WENO-Z, has a CPU cost which is equivalent to the one of the classical ...

This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for shallow water equations under arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The WENO reconstruction is adopted on moving meshes, which distinguishes smooth, non-smooth, and transition stencils by a simple smoothness detector. To maintain positivi...

In this short note we address the issue of numerical resolution and efficiency of high order weighted essentially nonoscillatory (WENO) schemes for computing solutions containing both discontinuities and complex solution features, through two representative numerical examples: the double Mach reflection problem and the Rayleigh–Taylor instability problem. We conclude that for such solutions wit...

In this paper we propose new Z-type nonlinear weights of the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme for hyperbolic conservation laws. Instead employing classical smoothness indicators weights, take pth root and follow form leading to fifth order accuracy in smooth regions, even at critical points, sharper approximations around discontinuities. We also p...

The simulation of turbulent compressible flows requires an algorithm with high accuracy and spectral resolution to capture different length scales, as well as nonoscillatory behavior across discontinuities like shock waves. Compact schemes have the desired resolution properties and thus, coupled with a nonoscillatory limiter, are ideal candidates for the numerical solution of such flows. A clas...

Weighted essentially non-oscillatory (WENO) methods have been developed to simultaneously provide robust shockcapturing in compressible fluid flow and avoid excessive damping of fine-scale flow features such as turbulence. Under certain conditions in compressible turbulence, however, numerical dissipation remains unacceptably high even after optimization of the linear component that dominates i...