A local radial basis function projection method for incompressible flows in water eutrophication

We present a meshless local radial basis function projection method for solving incompressible flows in water eutrophication. The model consists of the incompressible Navier-Stokes equations for the flow variables coupled to a transport equation for the void fraction. A state equation for the mixture density is used to close the system and the Boussinesq approximation is accounted for in the flow equations. The meshless method solves the primitive equations for the velocity and pressure solutions using projection techniques and a semi-implicit time stepping. A local collocation is used in our radial basis function method to avoid the ill-conditioning issues associated with the global collocations. In this case only sparse matrices are needed to be inverted for the solutions and the computational cost allocated for this step is far lower than in its global collocation counterpart. The performance of the proposed method is examined for a test example of incompressible Navier-Stokes equations with known analytical solution and for the benchmark of lid-driven cavity flow. We also present numerical results for a problem of water eutrophication for the Bouregreg lake in Morocco. The computed results support our expectations for a stable and highly accurate meshless method for incompressible flows in water eutrophication.