or perhaps with a forcing term g(u, x, t) on the right-hand side. Here u 5 (u1 , ..., um), f 5 (f1 , ..., fd), x 5 (x1 , ..., xd) In this paper, we further analyze, test, modify, and improve the high order WENO (weighted essentially non-oscillatory) finite differand t . 0. ence schemes of Liu, Osher, and Chan. It was shown by Liu et al. WENO schemes are based on ENO (essentially nonthat WENO sc...

Abstract. We develop a locally conservative Eulerian-Lagrangian finite volume scheme with the weighted essentially non-oscillatory property (EL-WENO) in one-space dimension. This method has the advantages of both WENO and Eulerian-Lagrangian schemes. It is formally high-order accurate in space (we present the fifth order version) and essentially non-oscillatory. Moreover, it is free of a CFL ti...

The aim of this study is to develop a novel sixth-order weighted essentially non-oscillatory (WENO) finite difference scheme. To design new WENO weights, we present two important measurements: a discontinuity detector (at the cell boundary) and a smoothness indicator. The interpolation method is implemented by using exponential polynomials with tension parameters such that they can be tuned to ...

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...

Abstract A new class of high order weighted essentially non-oscillatory (WENO) schemes [J. Comput. Phys., 318 (2016), 110-121] is applied to solve Euler equations with steady state solutions. It is known that the classical WENO schemes [J. Comput. Phys., 126 (1996), 202-228] might suffer from slight post-shock oscillations. Even though such post-shock oscillations are small enough in magnitude ...

Weighted essentially non-oscillatory (WENO) schemes have proved useful in a variety of physical applications. They capture sharp gradients without smearing, and feature high order of accuracy along with nonlinear stability. The high order of accuracy, robustness, and smooth numerical uxes of the WENO schemes make them ideal for use with Jacobian based iterative solvers, to directly simulate the...

We present a novel mapping approach for WENO schemes through the use of an approximate constant function which is constructed by employing approximation classic signum function. The new designed to meet overall criteria proper required in design WENO-PM6 scheme. scheme was proposed overcome potential loss accuracy WENO-M developed recover optimal convergence order WENO-JS at critical points. Ou...

In this paper, we adapt a simple weighted essentially non-oscillatory (WENO) limiter, originally designed for discontinuous Galerkin (DG) schemes [42], to the correction procedure via reconstruction (CPR) framework for solving conservation laws. The objective of this simple WENO limiter is to simultaneously maintain uniform high order accuracy of the CPR framework in smooth regions and control ...

In our previous studies (Li and Zhong, 2021a; Li 2021b), the commonly reported issue that most of existing mapped WENO schemes suffer from either losing high resolutions or generating spurious oscillations in long-run simulations hyperbolic problems has been successfully addressed, by devising improved schemes, namely MOP-WENO-X, where “X” stands for version scheme. However, all MOP-WENO-X brin...