Browsing by Author "LACHACHE, Mohammed"

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    Mathematical and numerical study of environmental pollution problems
    (2024) LACHACHE, Mohammed
    In this thesis, we study mathematical models that describe the motion of non-reactive pollutants using shallow water equations. We begin by studying the motion of the flow height using a shallow water model. For this purpose, we utilize the traveling wave solutions to demonstrate theoretical results through Schauder’s and Banach’s fixed point theorems. In the second model, we add a transport equation to conduct an analysis of pollutant propagation. In the third part of our work, we study the coupled system of a regularized Saint-Venant system together with the transport equation to take into account the motion of pollutants within the flow; presenting theoretical results on its well-posedness, i.e we show the necessary and sufficient conditions for the derived model to be well posed. Based on a reliable finite difference scheme, we examine the discretization of the proposed models and the implementations, to provide numerical results and show the effective behavior of the phenomena.