THE EVOLUTION OF RADIAL FINGERING IN A HELE-SHAW CELL USING C-1 CONTINUOUS OVERHAUSER BOUNDARY-ELEMENT METHOD

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.