Hydrodynamic design optimization using non stationary porous media model

Abstract In this paper, we focus on the penalty finite element method for non stationary porous media model. We begin by showing existence and uniqueness of solution initial problem. Error estimates velocity pressure are obtained via energy method. introduce a time discretization use backward Euler scheme combined with fully discrete to approximate penalized problem establish an error estimate which will be used show convergence The shape optimization is find optimal in that it minimizes cost functional related comfort fish population. derive adjoint system associated compute gradient terms state variables. procedure implemented using continuous Numerical simulations presented efficiency robustness proposed