RBF methods for solving laterally averaged Saint Venant equations: application to eutrophication prevention through aeration

A vertical 2D(xz) laterally averaged hydrodynamic model is presented in this paper to study the aeration process in lakes. The system exhibits highly nonlinear behaviour due to the phenomena involved such as stratification, air concentration, and convective terms. The suggested model is used to simulate mechanical aeration to overcome and prevent the eutrophication in lakes. The multiquadric radial basis functions are used to solve numerically the governing partial differential equations. Because of the difficulty and the complexity when choosing a suitable shape parameter in radial basis functions, an alternative way is introduced in this work to overcome these difficulties. A validation study is carried out using several test examples, including Poisson, Navier-Stokes and transport equations. Finally, the proposed model is first applied to simulate a squared domain aeration problem and then a real test case has been considered. The obtained results are in good agreement with the results reported in the literature.