A novel multidimensional solution reconstruction and edge-based limiting procedure for unstructured cell-centered finite volumes with application to shallow water dynamics

2012 ◽  
Vol 71 (5) ◽  
pp. 584-633 ◽  
Author(s):  
A. I. Delis ◽  
I. K. Nikolos
Keyword(s):  
Shallow Water ◽  
Water Dynamics ◽  
Finite Volumes ◽  
Shallow Water Dynamics ◽  
Edge Based

Stability of blow-up solution for the two component Camassa–Holm equations

2020 ◽  
Vol 120 (3-4) ◽  
pp. 319-336
Author(s):  
Xintao Li ◽  
Shoujun Huang ◽  
Weiping Yan
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Water Regime ◽  
Blow Up ◽  
Dynamical Behavior ◽  
Water Dynamics ◽  
Two Component ◽  
Breaking Mechanism ◽  
Self Similar ◽  
Shallow Water Dynamics

This paper studies the wave-breaking mechanism and dynamical behavior of solutions near the explicit self-similar singularity for the two component Camassa–Holm equations, which can be regarded as a model for shallow water dynamics and arising from the approximation of the Hamiltonian for Euler’s equation in the shallow water regime.

A simple justification of the singular limit for equatorial shallow-water dynamics

2009 ◽  
Vol 62 (3) ◽  
pp. 322-333 ◽  
Author(s):  
Alexandre Dutrifoy ◽  
Steven Schochet ◽  
Andrew J. Majda
Keyword(s):  
Shallow Water ◽  
Singular Limit ◽  
Water Dynamics ◽  
Shallow Water Dynamics
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