A FIXED DOMAIN METHOD FOR INJECTION GOVERNED BY THE STOKES EQUATIONS

In this paper, the authors describe a fixed domain method to simulate the injection of a fluid governed by the Stokes equations into a parti ally filled cell. The Baiocchi transformation of the pressure and velo city results in equations which hold in the entire cell and which impl icitly enforce the conditions on the moving boundary. A finite element discretization is applied to this transformed problem, and the result ing discrete system is solved by a successive approximation iteration on the fractional volume content of fluid in each element. For a two-d imensional channel, transient and steadily advancing fluid fronts (kno wn as the ''fountain-flow'' problem) computed by this method are compa red with those computed by some front-tracking algorithms. New example s, not found in the literature, that involve turning and internal obst acles are also presented.