H. Hadavinia et al., THE EVOLUTION OF RADIAL FINGERING IN A HELE-SHAW CELL USING C-1 CONTINUOUS OVERHAUSER BOUNDARY-ELEMENT METHOD, Engineering analysis with boundary elements, 16(2), 1995, pp. 183-195
An ideal porous medium can be created by a Hele-Shaw cell, a laborator
y device consisting of two parallel plates of glass separated by a thi
n gap. In this cell, in the flow of two immiscible fluids, when a flui
d of higher viscosity is displaced by a fluid of lower viscosity, the
less viscous fluid is observed to form fingers into the more viscous o
ne due to the unstable interface. The main interest in this process is
to accurately capture the evolution of the interface which may be con
tinuously deforming creating complex curvatures boundaries, hence maki
ng boundary element methods a suitable choice. The growth dynamics of
radial viscous fingering in a Hele-Shaw cell has been simulated using
boundary element method with C-1 Overhauser elements which have contin
uous representation of boundary geometry and variables. This type of s
hape function removes the instability that is encountered with CO cons
tant, linear and quadratic shape functions and allows one to simulate
unsymmetric and complicated patterns that may result due to the finger
ing phenomena. The results are compared with experimental and theoreti
cal results.