In this paper we proposed the kinetic framework based fifth-order adaptive finite difference WENO schemes abbreviated as WENO-AO-K schemes to solve the compressible Euler equations, which are quasi-linear hyperbolic equations that can admit discontinuous solutions like shock and contact waves. International Journal of Computer Mathematics: Vol.

The first WENO scheme is constructed in 1994 by Liu,Osher and Chan for a third order finite volume version. 3, pp. Finite difference methods are easily Chapter 5: Finite differences.

Polyharmonic splines are utilized in the WENO recon-struction of finite volume discretizations, yielding a numerical method for scalar conservation laws of arbitrary high order. An explicit finite volume method followed shortly afterwards in 2012, due to Bessemoulin-Chatard and Filbet.

Introduction to Partial Differential Equations. China. An alternative formulation of conservative weighted essentially non-oscillatory (WENO) finite difference scheme with the classical WENO-JS weights (Jiang et al. 568-584. This WENO-ZQ scheme is based on a combination of a large stencil and two small stencils. The fifth-order finite difference WENO scheme in Jiang and Shu (1996) has been used in most applications. Smith, G. D. (1985), Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd ed., Oxford University Press; Peter Olver (2013). The first WENO scheme was introduced in 1994 by Liu, Osher and Chan in their pioneering paper, in which a third order accurate finite volume WENO scheme was designed.

A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of the weighted essentially nonoscillatory scheme. The scheme … in their pioneering … As a service The first WENO scheme is developed by Liu, Chan and Osher in 1994. Here we propose to use the new simple finite difference WENO-ZQ scheme recently developed by Zhu and Qiu [35]. The formulation of the proposed schemes is based on the kinetic theory where one can recover the … In 1996, Jiang and Shu proposed a general framework of arbitrary high order finite difference WENO (WENO-JS) schemes, which are more efficient in the multi-dimensional problems (for details and history of the WENO scheme, see and references therein). The method can also be used for high order finite difference ENO schemes and an example is given to demonstrate a similar result as that for the WENO schemes. The finite difference weighted essentially non-oscillatory (WENO) schemes play an important role in solving the hyperbolic conservation laws and other convection dominated partial differential equations. al. It computes a high-order numerical flux by a Taylor expansion in space, with the lowest-order term solved from a Riemann solver and the higher-order terms constructed from physical fluxes by limited central differences. High Order Arbitrary Lagrangian-Eulerian Finite Difference WENO Scheme for Hamilton-Jacobi Equations† Yue Li1, Juan Cheng2,3,∗, Yinhua Xia4 and Chi-Wang Shu5 1 Graduate School, China Academy of Engineering Physics, Beijing 100088, P.R. Finite Difference Schemes and Partial Differential Equations (2nd ed.). The key component of the WENO scheme is a polynomial reconstruction procedure that can adaptively switch from a high order polynomial to a … The fifth-order finite difference WENO-SW scheme is a characteristic variable reconstruction based method which uses the Steger-Warming flux splitting for inviscid terms, the sixth-order central difference for viscous terms, and three stages Runge-Kutta time stepping for the time integration. The original WENO scheme was proposed by Liu et al. For the WENO scheme will I need to use a higher-order scheme (5th order?) High order multi-resolution analysis is used to detect the high gradients regions of the numerical solution in order to capture the shocks with the WENO scheme while the smooth regions are computed with the more efficient and accurate central finite difference scheme… 23 However, the global smoothness indicator has a little different from WENO‐ZQ scheme. High order finite volume and finite difference WENO schemes have been Email address: [email protected] (Shengtai Li and J. Mac Hyman). Finite Difference WENO Schemes with Lax-Wendroff-Type Time Discretizations @article{Qiu2002FiniteDW, title={Finite Difference WENO Schemes with Lax-Wendroff-Type Time Discretizations}, author={Jianxian Qiu and Chi-Wang Shu}, journal={SIAM J. It requires uniform computational meshes. The fifth-order finite difference WENO scheme in Jiang and Shu (1996) has been used in most applications.