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We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind…

Numerical Analysis · Mathematics 2022-11-15 Alina Chertock , Shaoshuai Chu , Alexander Kurganov

In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques. The established WENO algorithm is improved by training a…

Numerical Analysis · Mathematics 2023-09-20 Tatiana Kossaczká , Ameya D. Jagtap , Matthias Ehrhardt

Classical high-order weighted essentially non-oscillatory (WENO) schemes are designed to achieve optimal convergence order for smooth solutions and to maintain non-oscillatory behaviors for discontinuities. However, their spectral…

Numerical Analysis · Mathematics 2025-08-20 Jinrui Zhou , Yiqi Gu , Song Jiang , Hua Shen , Liwei Xu , Guanyu Zhou

In this paper, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme on unstructured meshes…

Numerical Analysis · Mathematics 2019-09-05 Liang Pan , Kun Xu

A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to…

Numerical Analysis · Mathematics 2024-05-16 M. C. Martí , P. Mulet , D. F. Yáñez , D. Zorío

In situations where a wide range of flow scales are involved, the nonlinear scheme used should be capable of both shock capturing and low-dissipation.Most of the existing WCNS schemes are too dissipative because the weights deviate from…

Computational Physics · Physics 2023-06-19 Xuan Liu , Yaobing Min , Jinsheng Cai , Yankai Ma , Zhenguo Yan

In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and decrease numerical dissipation. Based on the characteristic-wise approach, the scheme switches the numerical flux of each characteristic…

Fluid Dynamics · Physics 2018-02-13 X. Y. Hu , B. Wang , N. A. Adams

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…

Numerical Analysis · Mathematics 2016-03-30 Hongxu Liu , Xiangmin Jiao

This paper presents an extension of the hybrid scheme proposed by Wang et al. (J. Comput. Phys. 229 (2010) 169-180) for numerical simulation of compressible isotropic turbulence to flows with higher turbulent Mach numbers. The scheme still…

Computational Physics · Physics 2021-03-11 L. Q. Liu , J. C. Wang , Y. P. Shi , S. Y. Chen , X. T. He

In this paper we introduce a general framework for defining and studying essentially non-oscillatory reconstruction procedures of arbitrarily high order accuracy, interpolating data in a central stencil around a given computational cell…

Numerical Analysis · Mathematics 2018-07-09 I. Cravero , G. Puppo , M. Semplice , G. Visconti

We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes,our method is based on reconstructing a piecewise-polynomial…

Numerical Analysis · Mathematics 2025-10-20 D. Levy , G. Puppo , G. Russo

We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids, the proposed scheme is designed to be arbitrarily…

Numerical Analysis · Mathematics 2020-10-16 Siddhartha Mishra , Carlos Parés-Pulido , Kyle G. Pressel

In this paper, a new family of very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control (TENO-AA) is proposed. The new framework allows for constructing arbitrarily high-order TENO schemes in a unified…

Fluid Dynamics · Physics 2021-09-30 Lin Fu

In this paper, a robustness-enhanced reconstruction for the high-order finite volume scheme is constructed on the 2-D structured mesh, and both the high-order gas-kinetic scheme(GKS) and the Lax-Friedrichs(L-F) flux solver are considered to…

Numerical Analysis · Mathematics 2024-02-20 Hong Zhang , Xing Ji , Kun Xu

In this article, we propose a modified convex combination of the polynomial reconstructions of odd-order WENO schemes to maintain the central substencil prevalence over the lateral ones in all parts of the solution. New "centered" versions…

Numerical Analysis · Mathematics 2023-11-17 Daniel Barreto , Rafael B. de R. Borges , Bruno Costa , Silvaneo dos Santos

A novel scheme, based on third-order Weighted Essentially Non-Oscillatory (WENO) reconstructions, is presented. It attains unconditionally optimal accuracy when the data is smooth enough, even in presence of critical points, and…

Numerical Analysis · Mathematics 2024-02-06 Antonio Baeza , Raimund Bürger , Pep Mulet , David Zorío

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high order accuracy at a fraction of the cost of a finite volume WENO…

Numerical Analysis · Mathematics 2023-04-19 Dinshaw S. Balsara , Deepak Bhoriya , Chi-Wang Shu , Harish Kumar

We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus of this work is on nonlinear stabilization of continuous…

Numerical Analysis · Mathematics 2023-05-31 Dmitri Kuzmin , Joshua Vedral

Based on the understandings regarding linear upwind schemes with flux splitting to achieve free-stream preservation (Q. Li, etc. Commun. Comput. Phys., 22 (2017) 64-94), a series of WENO interpolation-based and upwind-biased nonlinear…

Computational Physics · Physics 2019-02-26 Qin Li , Dong Sun

Cases have shown that WENO schemes usually behave robustly on problems containing shocks with high pressure ratios when uniformed or smooth grids are present, while nonlinear schemes based on WENO interpolations might relatively be liable…

Computational Physics · Physics 2019-03-26 Qin Li , Dong Sun