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Related papers: High-order Unified Gas-kinetic Scheme

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This paper focuses on the numerical approximation of the solutions of non-local conservation laws in one space dimension. These equations are motivated by two distinct applications, namely a traffic flow model in which the mean velocity…

Analysis of PDEs · Mathematics 2016-12-20 Christophe Chalons , Paola Goatin , Luis Villada

Benefitting from the direct modeling of physical laws in a discretized space and the automatic decomposition of hydrodynamic waves and particles, the unified gas-kinetic wave-particle (UGKWP) method offers notable advantages in various…

Computational Physics · Physics 2025-06-17 Junzhe Cao , Yufeng Wei , Wenpei Long , Chengwen Zhong , Kun Xu

In this paper, the unified gas-kinetic wave-particle (UGKWP) method has been constructed on three-dimensional unstructured mesh with parallel computing for multiscale flow simulation. Following the direct modeling methodology of the unified…

Computational Physics · Physics 2020-10-28 Yipei Chen , Yajun Zhu , Kun Xu

In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient…

Numerical Analysis · Mathematics 2015-06-17 Andrew J. Christlieb , James A. Rossmanith , Qi Tang

In this paper, we develop a high order residual distribution (RD) method for solving steady state conservation laws in a novel Hermite weighted essentially non-oscillatory (HWENO) framework recently developed in [24]. In particular, we…

Numerical Analysis · Mathematics 2022-03-14 Jianfang Lin , Yupeng Ren , Rémi Abgrall , Jianxian Qiu

Shallow water moment equations are reduced-order models for free-surface flows that allow to represent vertical variations of the velocity profile at the expense of additional evolution equations for a number of additional variables, so…

Numerical Analysis · Mathematics 2025-07-02 Mirco Ciallella , Julian Koellermeier

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

A modified Weighted Essentially Non-Oscillatory (WENO) reconstruction technique preventing accuracy loss near critical points (regardless of their order) of the underlying data is presented. This approach only uses local data from the…

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

In this work we construct a high-order, single-stage, single-step positivity-preserving method for the compressible Euler equations. Space is discretized with the finite difference weighted essentially non-oscillatory (WENO) method. Time is…

Numerical Analysis · Mathematics 2015-11-03 David C. Seal , Qi Tang , Zhengfu Xu , Andrew J. Christlieb

In this paper, we present a multi-dimensional, arbitrary-order hybrid reconstruction framework for compressible flows on unstructured meshes. The method combines the efficiency of linear reconstruction with the robustness of high-order…

Numerical Analysis · Mathematics 2026-01-22 Yiren Tong , Panagiotis Tsoutsanis

In this paper, we propose a new high order semi-implicit scheme for the all Mach full Euler equations of gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL restrictions…

Numerical Analysis · Mathematics 2021-10-28 Sebastiano Boscarino , Jing-Mei Qiu , Giovanni Russo , Tao Xiong

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

A third-order weighted essentially non-oscillatory compact least-squares scheme is developed for the finite volume method on structured curvilinear non-uniform grids. The proposed scheme features compact least-squares reconstruction with…

Fluid Dynamics · Physics 2025-08-05 Jianhua Pana , Luxin Li , Wei-Gang Zeng

We propose a simple modification of standard WENO finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of the one-dimensional discretization when applied to nonlinear multidimensional systems of…

Numerical Analysis · Mathematics 2016-08-30 Pawel Buchmüller , Christiane Helzel

We propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation…

Numerical Analysis · Mathematics 2022-07-20 Hua Shen , Matteo Parsani

In this paper, we develop two finite difference weighted essentially non-oscillatory (WENO) schemes with unequal-sized sub-stencils for solving the Degasperis-Procesi (DP) and $\mu$-Degasperis-Procesi ($\mu$DP) equations, which contain…

Numerical Analysis · Mathematics 2022-03-14 Jianfang Lin , Yan Yu , Huiwen Xue , Xinghui Zhong

Recently, successes have been achieved for the high-order gas-kinetic schemes (HGKS) on unstructured meshes for compressible flows. In this paper, to accelerate the computation, HGKS is implemented with the graphical processing unit (GPU)…

Numerical Analysis · Mathematics 2024-07-02 Yuhang Wang , Waixiang Cao , Liang Pan

The gas dynamics under external force field is essentially associated with multiple scale nature due to the large variations of density and local Knudsen number. Single scale fluid dynamic equations, such as the Boltzmann and Navier-Stokes…

Fluid Dynamics · Physics 2017-10-31 Tianbai Xiao , Kun Xu , Qingdong Cai , Tiezheng Qian

This study presents a high-order finite volume scheme capable of large time-step integration for three-temperature radiation diffusion (3TRD) equations, where conservation is naturally achieved through energy update. To handle local large…

Numerical Analysis · Mathematics 2026-03-26 Fengxiang Zhao , Yaqing Yang , Yibing Chen , Kun Xu

A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin…

Instrumentation and Methods for Astrophysics · Physics 2014-01-27 Olindo Zanotti , Michael Dumbser , Arturo Hidalgo , Dinshaw Balsara