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Well-Balanced Kinetic Schemes For The Shallow Water Equation With Bulk Recharge And Discharge

The department of Mathematics and Statistics at the University of Limerick invites you to a seminar by Dr Omar Lakkis (University of Sussex)

Title:  Well-Balanced Kinetic Schemes For The Shallow Water Equation With Bulk Recharge And Discharge

Abstract: In flood risk assessment modelling, Saint-Venant's shallow water equations (SWEs) must be coupled with other systems describing the interacting meteorological and hydrological phenomena such as rain and groundwater flows. The SWEs must therefore be appropriately modified to accommodate source and sink terms; while modifications of the SWEs in this direction have been recently proposed, we depart from existing literature by proposing a model that is, to the best of our knowledge, novel as a natural extension of the SWEs that is “entropy-consistent” and respects its kinetic formulations connections. Kinetic schemes were developed in the late 1990s and throughout the 2000s, and have proved crucial in modelling river flows over long (physical) times.


We call our model a "natural extension'' of the standard system as it is approached via matched asymptotic expansions from the Navier--Stokes model. The infiltration-recharge mechanism is treated through boundary conditions similar to the Beavers--Joseph--Saffman conditions appearing in fluid-solid interaction problems, where porous media models for underground flows are coupled with surface flows. This approach also provides the appearance of novel "friction'' terms (accounting for the inertial effects of recharge) to ensure moment-conservation consistency. We provide extensive numerical testing to illustrate our findings.

This talk is based on joint work with Mehmet Ersoy (Université de Toulon, France) and Philip J.A. Townsend (University of Sussex, England UK).

This seminar will take place on Friday , 5th May, at 3pm, in  Room A2-002.

If you have any questions regarding this seminar, please direct them to Iain Moyles (061 233726,

A full list of upcoming seminars can be found at


Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (, centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.----------------------------------------------------------------------------