Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models (1912.13314v1)

Published 31 Dec 2019 in math-ph and math.MP

Abstract: The one-dimensional shallow water equations in Eulerian and Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangian (potential) coordinates and symmetries and conservation laws in mass Lagrangian variables. For equations in Lagrangian coordinates with a flat bottom an invariant difference scheme is constructed which possesses all the difference analogues of the conservation laws: mass, momentum, energy, the law of center of mass motion. Some exact invariant solutions are constructed for the invariant scheme, while the scheme admits reduction on subgroups as well as the original system of equations. For an arbitrary shape of bottom it is possible to construct an invariant scheme with conservation of mass and momentum or energy. Invariant conservative difference scheme for the case of a flat bottom tested numerically in comparison with other known schemes.

Summary

We haven't generated a summary for this paper yet.