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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 propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used…

Numerical Analysis · Mathematics 2018-10-17 Jianfang Lin , Rémi Abgrall , Jianxian Qiu

Existing mapped WENO schemes can hardly prevent spurious oscillations while preserving high resolutions at long output times. We reveal in this paper the essential reason for such phenomena. It is actually caused by that the mapping…

Numerical Analysis · Mathematics 2022-02-04 Ruo Li , Wei Zhong

Weighted essentially non-oscillatory (WENO) reconstruction schemes are presented that preserve cylindrical symmetry for radial flows on an equal-angle polar mesh. These new WENO schemes are used with a Lagrangian discontinuous Galerkin (DG)…

Computational Physics · Physics 2019-08-22 Xiaodong Liu , Nathaniel R. Morgan , Donald E. Burton

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, 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

Entropy conditions play a crucial role in the extraction of a physically relevant solution for systems of conservation laws, thus motivating the construction of entropy stable schemes that satisfy a discrete analogue of such conditions.…

Numerical Analysis · Mathematics 2025-06-04 Philip Charles , Deep Ray

We develop new more efficient A-WENO schemes for both hyperbolic systems of conservation laws and nonconservative hyperbolic systems. The new schemes are a very simple modification of the existing A-WENO schemes: They are obtained by a more…

Numerical Analysis · Mathematics 2025-05-26 Shaoshuai Chu , Alexander Kurganov , Ruixiao Xin

We propose a simple yet effective local smoothness indicator for the downwind stencil in central-upwind weighted essentially non-oscillatory (WENO) schemes of even order for hyperbolic conservation laws. Starting from an odd-order upwind…

Numerical Analysis · Mathematics 2026-03-30 Jiaxi Gu , Bao-Shan Wang , Wai Sun Don , Jae-Hun Jung

We propose an alternative reconstruction for weighted essentially non-oscillatory schemes with adaptive order (WENO-AO) for solving hyperbolic conservation laws. The alternative reconstruction has a more concise form than the original…

Numerical Analysis · Mathematics 2021-03-24 Hua Shen

Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and…

Computational Physics · Physics 2017-10-10 Prabal Singh Verma , Wolf-Christian Müller

We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…

Numerical Analysis · Mathematics 2025-10-20 Alexander Kurganov , Doron Levy

We propose a new kind of localized shock capturing for continuous (CG) and discontinuous Galerkin (DG) discretizations of hyperbolic conservation laws. The underlying framework of dissipation-based weighted essentially nonoscillatory (WENO)…

Numerical Analysis · Mathematics 2026-01-26 Joshua Vedral , Dmitri Kuzmin

The blood flow model maintains the steady state solutions, in which the flux gradients are non-zero but exactly balanced by the source term. In this paper, we design high order finite difference weighted non-oscillatory (WENO) schemes to…

Numerical Analysis · Mathematics 2016-07-01 Zhenzhen Wang , Gang Li , Olivier Delestre

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

In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…

Numerical Analysis · Mathematics 2025-05-09 Lorenzo Micalizzi , Eleuterio F. Toro

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

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

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws represent a technology that has been reasonably consolidated. They are extremely popular because, when applied to multidimensional…

Numerical Analysis · Mathematics 2024-03-05 Dinshaw S. Balsara , Deepak Bhoriya , Chi-Wang Shu , Harish Kumar

Applying high-order finite-difference schemes, like the extensively used linear-upwind or WENO schemes, to curvilinear grids can be problematic. The geometrically induced error from grid Jacobian and metrics evaluation can pollute the flow…

Computational Physics · Physics 2019-10-23 Yujie Zhu , Xiangyu Hu