Ll. Stell et Sf. Shen, A FIXED DOMAIN METHOD FOR INJECTION GOVERNED BY THE STOKES EQUATIONS, SIAM journal on scientific computing, 16(4), 1995, pp. 798-818
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.