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Steady state simulations} of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially…

Computational Physics · Physics 2019-03-14 Amareshwara Sainadh Chamarthi , Kimiya Komurasaki , Rei Kawashima

The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock…

Numerical Analysis · Mathematics 2020-09-29 David Frenzel , Jens Lang

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

Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…

Numerical Analysis · Mathematics 2007-05-23 Fausto Cavalli , Giovanni Naldi , Gabriella Puppo , Matteo Semplice

The high-order gas-kinetic scheme(HGKS) with WENO spatial reconstruction method has been extensively validated through many numerical experiments, demonstrating its superior accuracy efficiency, and robustness. Compared with WENO class…

Fluid Dynamics · Physics 2023-09-20 Junlei Mu , Congshan Zhuo , Qingdian Zhang , Sha Liu , Chengwen Zhong

We develop a simple, high-order, conservative and robust positivity-preserving sweeping procedure for the density and the nonlinear pressure function in the compressible Euler equations. Using the scaling limiter in Zhang and Shu (2010), we…

Numerical Analysis · Mathematics 2025-11-03 D. Chloe Griffin , Chi-Wang Shu

Simulating discontinuities is a long standing problem especially for shock waves with strong nonlinear feather. Despite being a promising method, the recently developed physics-informed neural network (PINN) is still weak for calculating…

Fluid Dynamics · Physics 2025-06-24 Li Liu , Shengping Liu , Hui Xie , Fansheng Xiong , Tengchao Yu , Mengjuan Xiao , Lufeng Liu , Heng Yong

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

The advantage of WENO-JS5 scheme [ J. Comput. Phys. 1996] over the WENO-LOC scheme [J. Comput. Phys.1994] is that the WENO-LOC nonlinear weights do not achieve the desired order of convergence in smooth monotone regions and at critical…

Numerical Analysis · Mathematics 2023-02-21 Samala Rathan , G. Naga Raju , Ashlesha A. Bhise

We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is…

Computational Physics · Physics 2019-02-20 Adam Reyes , Dongwook Lee , Carlo Graziani , Petros Tzeferacos

In this article we present a modification of the algorithm for data discretized in the point values introduced in [S. Amat, J. Ruiz, C.-W. Shu, On a new WENO algorithm of order 2r with improved accuracy close to discontinuities, App. Math.…

Numerical Analysis · Mathematics 2020-05-15 Sergio Amat , Juan Ruiz , Chi-Wang Shu , Dionisio F. Yanez

We study a conservative data-driven discretization for one-dimensional hyperbolic conservation laws based on the classical fifth-order WENO finite-volume scheme and a hypernetwork architecture. In the proposed Hyper--WENO5 Conservative-Form…

Numerical Analysis · Mathematics 2026-05-14 Yongsheng Chen , Wei Guo , Xinghui Zhong

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

A new approach to prevent spurious behavior caused by conventional shock-capturing schemes when solving stiff detonation waves problems is introduced in the present work. Due to smearing of discontinuous solution by the excessive numerical…

Computational Physics · Physics 2017-08-04 Xi Deng , Honghui Teng , Bin Xie , Feng Xiao

The recently proposed high-order TENO scheme [Fu et al., Journal of Computational Physics, 305, pp.333-359] has shown great potential in predicting complex fluids owing to the novel weighting strategy, which ensures the high-order accuracy,…

Numerical Analysis · Mathematics 2022-05-23 Zhe Ji , Tian Liang , Lin Fu

Current Deep Learning methods for environment segmentation and velocity estimation rely on Convolutional Recurrent Neural Networks to exploit spatio-temporal relationships within obtained sensor data. These approaches derive scene dynamics…

Computer Vision and Pattern Recognition · Computer Science 2023-06-21 Marco Braun , Moritz Luszek , Mirko Meuter , Dominic Spata , Kevin Kollek , Anton Kummert

In our latest studies, by introducing the novel order-preserving (OP) criterion, we have successfully addressed the widely concerned issue of the previously published mapped weighted essentially non-oscillatory (WENO) schemes that it is…

Numerical Analysis · Mathematics 2022-08-03 Ruo Li , Wei Zhong

We introduce a new methodology for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities, which we call the $C$-method. We…

Computational Physics · Physics 2015-06-04 Jon Reisner , Jonathan Serencsa , Steve Shkoller

A new type of finite volume WENO schemes for hyperbolic problems was devised in [36] by introducing the order-preserving (OP) criterion. In this continuing work, we extend the OP criterion to the WENO-Z-type schemes. We firstly rewrite the…

Numerical Analysis · Mathematics 2022-08-03 Ruo Li , Wei Zhong

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