ADAPTIVE FINITE-ELEMENT SIMULATION OF STOKES-FLOW IN POROUS-MEDIA

The Stokes problem describes how of an incompressible constant-viscosi ty fluid when the Reynolds number is small so that inertial and transi ent-time effects are negligible. The numerical solution of the Stokes problem requires special care, since classical finite element discreti zation schemes, such as piecewise linear interpolation for both the ve locity and the pressure, fail to perform. Even when an appropriate sch eme is adopted, the grid must be selected so that the error is as smal l as possible. Much of the challenge in solving Stokes problems is how to account for complex geometry and to capture important features suc h as flow separation. This paper applies adaptive mesh techniques, usi ng a posteriori error estimates, in the finite element solution of the Stokes equations that model flow at pore scales. Different selected n umerical test cases associated with various porous geometrics are pres ented and discussed to demonstrate the accuracy and efficiency of our methodology. (C) 1998 Elsevier Science Limited.