A comparative study of finite volume methods on unstructured meshes for simulation of 2D shallow water wave problems

2000 ◽  
Vol 53 (3) ◽  
pp. 171-184 ◽  
Author(s):  
Ji-Wen Wang ◽  
Ru-Xun Liu
Keyword(s):  
Comparative Study ◽  
Shallow Water ◽  
Finite Volume ◽  
Water Wave ◽  
Unstructured Meshes ◽  
Finite Volume Methods ◽  
Shallow Water Wave ◽  
Wave Problems

scholarly journals Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1439
Author(s):  
Chaudry Masood Khalique ◽  
Karabo Plaatjie
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Elliptic Integral ◽  
Momentum Conservation ◽  
Two Dimensional ◽  
Order Ordinary Differential Equation ◽  
Closed Form Solutions ◽  
Shallow Water Wave

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

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