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The weighted essentially non-oscillatory (WENO) schemes are widely used for hyperbolic conservation laws due to the ability to resolve discontinuities and maintain high-order accuracy in smooth regions at the same time. For hyperbolic…

Numerical Analysis · Mathematics 2025-10-09 Yue Wu , Chi-Wang Shu

In this paper, a third-order weighted essentially non-oscillatory (WENO) scheme is developed for hyperbolic conservation laws on unstructured quadrilateral and triangular meshes. As a starting point, a general stencil is selected for the…

Numerical Analysis · Mathematics 2018-11-14 Fengxiang Zhao , Liang Pan , Shuanghu Wang

The essentially non-oscillatory (ENO) method is an efficient high order numerical method for solving hyperbolic conservation laws designed to reduce the Gibbs oscillations, if existent, by adaptively choosing the local stencil for the…

Numerical Analysis · Mathematics 2017-05-23 Jingyang Guo , Jae-Hun Jung

This paper proposes high-order accurate, oscillation-eliminating Hermite weighted essentially non-oscillatory (OE-HWENO) finite volume schemes for hyperbolic conservation laws. The OE-HWENO schemes apply an OE procedure after each…

Numerical Analysis · Mathematics 2024-09-17 Chuan Fan , Kailiang Wu

In this paper, a fifth-order Hermite weighted essentially non-oscillatory (HWENO) scheme with artificial linear weights is proposed for one and two dimensional hyperbolic conservation laws, where the zeroth-order and the first-order moments…

Numerical Analysis · Mathematics 2020-07-15 Zhuang Zhao , Jianxian Qiu

In this article we present the first better than second order accurate unstructured Lagrangian-type one-step WENO finite volume scheme for the solution of hyperbolic partial differential equations with non-conservative products. The method…

Numerical Analysis · Mathematics 2013-04-18 Michael Dumbser , Walter Boscheri

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

We present a newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. WENO is a higher order accurate finite difference scheme designed for problems with…

Astrophysics · Physics 2009-11-10 Long-Long Feng , Chi-Wang Shu , Meng-Ping Zhang

This paper presents a novel and straightforward compact reconstruction procedure for the high-order finite volume method on unstructured grids. In this procedure, we constructed a linear approximation relationship between the mean values…

Fluid Dynamics · Physics 2026-03-27 Ling Wen , Yan-Tao Yang , Qing-Dong Cai

In this paper, a simple fifth-order finite difference Hermite WENO (HWENO) scheme combined with limiter is proposed for one- and two- dimensional hyperbolic conservation laws. The fluxes in the governing equation are approximated by the…

Numerical Analysis · Mathematics 2023-06-08 Min Zhang , Zhuang Zhao

We illustrate that numerical solutions of high order finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for some nonconvex conservation laws perform poorly or converge to the entropy solution in a slow speed. The…

Numerical Analysis · Mathematics 2017-09-18 Xiaofeng Cai , Jianxian Qiu , Jing-Mei Qiu

The modified dimension-by-dimension finite volume (FV) WENO method on Cartesian grids proposed by Buchm\"{u}ller and Helzel can retain the full order of accuracy of the one-dimensional WENO reconstruction and requires only one flux…

Numerical Analysis · Mathematics 2019-01-08 Yulong Du , Li Yuan* , Yahui Wang

Third order WENO and CWENO reconstruction are widespread high order reconstruction techniques for numerical schemes for hyperbolic conservation and balance laws. In their definition, there appears a small positive parameter, usually called…

Numerical Analysis · Mathematics 2016-06-13 I. Cravero , M. Semplice

High order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the…

Numerical Analysis · Mathematics 2020-01-30 Manuel J. Castro-Dìaz , Matteo Semplice

This paper presents a generalized ENO (GENO)-type nonlinear reconstruction scheme for compressible flow simulations. The proposed reconstruction preserves the accuracy of the linear scheme while maintaining essentially non-oscillatory…

Numerical Analysis · Mathematics 2025-08-12 Fengxiang Zhao , Kun Xu

In this paper, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes for convection-diffusion equations. The proposed…

Numerical Analysis · Mathematics 2024-06-04 Nanyi Zheng , Xiaofeng Cai , Jing-Mei Qiu , Jianxian Qiu

We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving…

Numerical Analysis · Mathematics 2013-07-16 David I. Ketcheson , Matteo Parsani , Randall J. LeVeque

We develop a high-order kinetic scheme for entropy-based moment models of a one-dimensional linear kinetic equation in slab geometry. High-order spatial reconstructions are achieved using the weighted essentially non-oscillatory (WENO)…

Numerical Analysis · Mathematics 2019-08-27 Florian Schneider , Graham Alldredge , Jochen Kall

The high-order gas-kinetic scheme (HGKS) features good robustness, high efficiency and satisfactory accuracy,the performaence of which can be further improved combined with WENO-AO (WENO with adaptive order) scheme for reconstruction. To…

Fluid Dynamics · Physics 2023-04-13 Junlei Mu , Congshan Zhuo , Qingdian Zhang , Sha Liu , Chengwen Zhong

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