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...

The purpose of this paper is twofold. Firstly we carry out an extension of the finite-volume WENO approach to three space dimensions and higher orders of spatial accuracy (up to eleventh order). Secondly, we propose to use three new fluxes as a building block in WENO schemes. These are the one-stage HLLC [29] and FORCE [24] fluxes and a recent multistage MUSTA flux [26]. The numerical results i...

We present two versions of third order accurate jet schemes, which achieve high order accuracy by tracking derivative information of the solution along characteristic curves. For a benchmark linear advection problem, the efficiency of jet schemes is compared with WENO and Discontinuous Galerkin methods of the same order. It is demonstrated that jet schemes possess the simplicity and speed of WE...

In this paper we continue our research on the numerical study of convergence to steady state solutions for a new class of finite volume weighted essentially non-oscillatory (WENO) schemes in [38], from tensor product meshes to triangular meshes. For the case of triangular meshes, this new class of finite volume WENO schemes was designed for time-dependent conservation laws in [37] for the third...

We present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions. The proposed WENO scheme provides at least the same or improved behavior over the classical fifth-order WENO scheme [9] and other fifth-order ...

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...

Keywords: Adaptive mesh refinement (AMR) WENO High order finite difference Multiscale simulations a b s t r a c t In this paper, we propose a finite difference AMR-WENO method for hyperbolic conservation laws. The proposed method combines the adaptive mesh refinement (AMR) framework [4,5] with the high order finite difference weighted essentially non-oscillatory (WENO) method in space and the t...

Polyharmonic splines are utilized in the WENO reconstruction of finite volume discretizations, yielding a numerical method for scalar conservation laws of arbitrary high order. The resulting WENO reconstruction method is, unlike previous WENO schemes using polynomial reconstructions, numerically stable and very flexible. Moreover, due to the theory of polyharmonic splines, optimal reconstructio...

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 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...