Modelling Water Waves on Graphs

Waves on graphs are a current subject of research interest. As opposed to flows on graphs, the reflection–transmission of waves at the graph’s vertex is a problem that needs to be further modelled mathematically. The literature on the reflection and transmission of waves at a vertex is scarce. Some...

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Bibliographic Details
Main Author: André Nachbin
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Fluids
Subjects:
Online Access:https://www.mdpi.com/2311-5521/10/6/140
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Summary:Waves on graphs are a current subject of research interest. As opposed to flows on graphs, the reflection–transmission of waves at the graph’s vertex is a problem that needs to be further modelled mathematically. The literature on the reflection and transmission of waves at a vertex is scarce. Some articles are reviewed and discussed. Water waves are a good topic for comparing different mathematical models, from hyperbolic conservation laws to weakly nonlinear, weakly dispersive systems of partial differential equations on a two-dimensional fattened (thick) graph and the respective one-dimensional graph-model reduction. In this study, we present a particular water wave model in which junction angles are systematically included in the mathematical model. Comparing the solutions with the fattened-graph model gave rise to a more general compatibility condition at the vertex. Current research topics of interest are outlined at the end.
ISSN:2311-5521