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Mathematics Colloquium: Two-Layer Shallow-Water Flows Along Channels: Modelling and Computational Approach

Feb 28, 2025, 3:30 - 4:30 PM

 

Speaker:  Sarswati Shah, GMU

 

Title: Two-Layer Shallow-Water Flows Along Channels: Modelling and Computational Approach

 

Abstract: One of the most important questions in the study of quasilinear partial differential equations is as follows: Is the system hyperbolic, and under what conditions will it have a unique weak solution? In general, this question is delicate and depends in a subtle way on the mathematical model and the consideration of various factors such as layers and geometry of the fluid flow. In this talk we will review some models based on hyperbolic balance laws and systems having non-conservative products.  In particular, we will see in detail a weakly compressible two-layer shallow water flow in channels with arbitrary cross sections. This model is a balance law with non-conservative products. Using the method of generalized Rankine-Hugoniot conditions, we derive the Riemann invariants for the shock and contact wave. Furthermore, a high-resolution, non-oscillatory semi-discrete path-conservative central-upwind scheme is presented. The scheme extends existing central-upwind semi-discrete numerical methods for hyperbolic balance laws. We validate the exact solution with the numerical approach. We also present numerical tests in general channels to show the merits of the scheme.

 

Time:  Friday, February 28, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

Zoom and In-person

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