The weighted ENO scheme based on the modified smoothness indicator

2017 ◽  
Vol 150 ◽  
pp. 1-7 ◽  
Author(s):  
Fuxing Hu
Keyword(s):  
Smoothness Indicator ◽  
Weighted Eno ◽  
Eno Scheme

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Acta Numerica ◽  
2020 ◽  
Vol 29 ◽  
pp. 701-762
Author(s):  
Chi-Wang Shu
Keyword(s):  
Main Idea ◽  
High Order Accuracy ◽  
Finite Difference Schemes ◽  
Approximation Procedure ◽  
Discontinuous Solutions ◽  
Weno Schemes ◽  
Convection Diffusion ◽  
Different Types ◽  
Basic Ideas ◽  
Weighted Eno

Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

scholarly journals Implicit Weighted ENO Schemes for the Three-Dimensional Incompressible Navier–Stokes Equations

1998 ◽  
Vol 146 (1) ◽  
pp. 464-487 ◽  
Author(s):  
Jaw-Yen Yang ◽  
Shih-Chang Yang ◽  
Yih-Nan Chen ◽  
Chiang-An Hsu
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Eno Schemes ◽  
Weighted Eno

scholarly journals An efficient targeted ENO scheme with local adaptive dissipation for compressible flow simulation

2021 ◽  
Vol 425 ◽  
pp. 109902
Author(s):  
Jun Peng ◽  
Shengping Liu ◽  
Shiyao Li ◽  
Ke Zhang ◽  
Yiqing Shen
Keyword(s):  
Compressible Flow ◽  
Flow Simulation ◽  
Eno Scheme

Non-separable two-dimensional weighted ENO interpolation

2012 ◽  
Vol 62 (8) ◽  
pp. 975-987 ◽  
Author(s):  
Francesc Aràndiga ◽  
Pep Mulet ◽  
Vicent Renau
Keyword(s):  
Two Dimensional ◽  
Weighted Eno

Numerical Method with the Third-Order ENO Reconstruction Satisfying Two Conversation Laws for Linear Advection Equation

2011 ◽  
Vol 130-134 ◽  
pp. 2969-2972
Author(s):  
Rong San Chen ◽  
An Ping Liu
Keyword(s):  
Numerical Solutions ◽  
Advection Equation ◽  
Finite Volume Schemes ◽  
Third Order ◽  
The Third ◽  
Linear Advection Equation ◽  
Long Time ◽  
Super Convergence ◽  
Better Than ◽  
Eno Scheme

In recent years, Mao and his co-workers developed a class of finite-volume schemes for evolution partial differential equations, see [1-5].The schemes show a super-convergence quality and have good structure-preserving property in long-time numerical simulations. In [6], Chen and Ma developed a scheme which combine the idea of paper [5] and that of the the second-order ENO scheme [7]. In this paper, we propose a scheme which extend the result of [6] and obtain the scheme using the third-order ENO reconstruction. Numerical experiments show that our scheme is robust in long-time behaviors. Numerical solutions are far better than those of [6].

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