Control of numerical effects of dispersion and dissipation in numerical schemes for efficient shock-capturing through an optimal Courant number

2008 ◽  
Vol 37 (6) ◽  
pp. 767-783 ◽  
Author(s):  
A.R. Appadu ◽  
M.Z. Dauhoo ◽  
S.D.D.V. Rughooputh
Keyword(s):  
Shock Capturing ◽  
Numerical Schemes ◽  
Courant Number

A new shock-capturing technique based on Moving Least Squares for higher-order numerical schemes on unstructured grids

2010 ◽  
Vol 199 (37-40) ◽  
pp. 2544-2558 ◽  
Author(s):  
X. Nogueira ◽  
L. Cueto-Felgueroso ◽  
I. Colominas ◽  
F. Navarrina ◽  
M. Casteleiro
Keyword(s):  
Least Squares ◽  
Unstructured Grids ◽  
Higher Order ◽  
Shock Capturing ◽  
Moving Least Squares ◽  
Numerical Schemes

scholarly journals Instability in Leapfrog and Forward–Backward Schemes

2010 ◽  
Vol 138 (5) ◽  
pp. 1497-1501 ◽  
Author(s):  
Wen-Yih Sun
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Schemes ◽  
Courant Number ◽  
Diffusion Term ◽  
Repeated Eigenvalues ◽  
Leapfrog Scheme

Abstract This paper shows that in the linearized shallow-water equations, the numerical schemes can become weakly unstable for the 2Δx wave in the C grid when the Courant number is 1 in the forward–backward scheme and 0.5 in the leapfrog scheme because of the repeated eigenvalues in the matrices. The instability can be amplified and spread to other waves and smaller Courant number if the diffusion term is included. However, Shuman smoothing can control the instability.

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