Numerical simulation of incompressible flows through granular porous media Original Research Article

The primitive equations of incompressible flows through isotropic granular porous media have been deduced by DuPlessis and Masliyah in the form of generalized Navier–Stokes equations. We first derive some analytical solutions of these equations in the form of generalized Hagen–Poiseuille, Couette–Poiseuille and Beltrami type flows. The respective classic flows are the limit cases of generalized solutions as porosity approaches zero. Then we develop a finite difference semi-implicit scheme, which is applied to numerical simulation of 3D flows in granular porous medium. The theoretical properties of accuracy and stability of this scheme are investigated and a method of specifying boundary conditions is suggested. The constructed scheme is applied to simulation of the obtained analytical solutions as well as to test problems of the lid-driven cavity flow.