English
Related papers

Related papers: Towards optimal high-order compact schemes for sim…

200 papers

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

Improved five-point low dissipation nonlinear schemes are proposed in this paper within the framework of weighted compact nonlinear schemes (WCNSs) \cite{Deng2000}. Particularly we follow the work of Li and Du \cite{Li2016} on the two-stage…

Numerical Analysis · Mathematics 2022-08-15 Huaibao Zhang , GX Wang

In this paper we develop a new sixth-order finite difference central weighted essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for nonlinear degenerate parabolic equations. The centered polynomial is introduced for…

Numerical Analysis · Mathematics 2024-05-13 Samala Rathan , Jiaxi Gu

This paper extends the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulations on a rotating coordinate frame. The kinetic equation with the inclusion of centrifugal and Coriolis acceleration is used in the…

Computational Physics · Physics 2022-11-01 Yue Zhang , Xing Ji , Kun Xu

A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…

Fluid Dynamics · Physics 2025-08-05 Jianhua Pan , Luxin Li , Ji Yin , Wei-Gang Zeng

Although there are many improvements to WENO3-Z that target the achievement of optimal order in the occurrence of the first-order critical point (CP1), they mainly address resolution performance, while the robustness of schemes is of less…

Computational Engineering, Finance, and Science · Computer Science 2022-08-05 Qin Li , Xiao Huang , Pan Yan , Guozhuo Tan , Yi Duan , Yancheng You

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…

Numerical Analysis · Mathematics 2024-03-04 Yaqing Yang , Liang Pan , Kun Xu

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

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

We propose a class of essentially non-oscillatory schemes with adaptive order (ENO-AO) for solving hyperbolic conservation laws. The new schemes select candidate stencils by novel smoothness indicators which are the measurements of the…

Numerical Analysis · Mathematics 2021-08-31 Hua Shen

This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data…

Numerical Analysis · Mathematics 2021-10-22 Sabana Parvin , Ritesh Kumar Dubey

An incremental-stencil WENO reconstruction method, which uses low-order candidate stencils with incrementally increasing width, is proposed for finite-volume simulation of compressible two-phase flow with the quasi-conservative interface…

Computational Physics · Physics 2019-05-30 Bing Wang , Gaoming Xiang , Xiangyu Y. Hu

A general framework for the development of high-order compact schemes has been proposed recently. The core steps of the schemes are composed of the following. 1). Based on a kinetic model equation, from a generalized initial distribution of…

Fluid Dynamics · Physics 2022-08-25 Fengxiang Zhao , Xing Ji , Wei Shyy , Kun Xu

In this work, we present the feedforward neural network based on the conservative approximation to the derivative from point values, for the weighted essentially non-oscillatory (WENO) schemes in solving hyperbolic conservation laws. The…

Numerical Analysis · Mathematics 2025-07-09 Kwanghyuk Park , Jiaxi Gu , Jae-Hun Jung

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

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

We consider implementations of high-order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for the Euler equations in cylindrical and spherical coordinate systems with radial dependence only. The main concern of this…

Numerical Analysis · Mathematics 2017-01-19 Sheng Wang , Eric Johnsen

The weighted essentially non-oscillatory {technique} using a stencil of $2r$ points (WENO-$2r$) is an interpolatory method that consists in obtaining a higher approximation order from the non-linear combination of interpolants of $r+1$…

Numerical Analysis · Mathematics 2024-04-26 Pep Mulet , Juan Ruiz-Alvarez , Chi-Wang Shu , Dionisio F. Yáñez

The approximation of data is a fundamental challenge encountered in various fields, including computer-aided geometric design, the numerical solution of partial differential equations, or the design of curves and surfaces. Numerous methods…

Numerical Analysis · Mathematics 2025-01-27 Inmaculada Garcés , José M. Ramón , Juan Ruiz-Álvarez , Dionisio F. Yáñez

Shepard method is a fast algorithm that has been classically used to interpolate scattered data in several dimensions. This is an important and well-known technique in numerical analysis founded in the main idea that data that is far away…

Numerical Analysis · Mathematics 2024-12-04 David Levin , José M. Ramón , Juan Ruiz-Alvarez , Dionisio F. Yáñez