Abstract
The present paper deals with the numerical simulation of the growth of viscous fingers in a thin liquid layer. A new type of computational model for that problem is proposed. The govering flow equations are derived from the three-dimensional Navier-Stokes equations and the equation of continuity by averaging them in the direction of thickness of the layer. They are expressed in terms of velocity and pressure. To avoid the handling of a deformable solution domain with a moving free surface, we solve two-phase flows composed of liquid and its adjacent fluid (gas in the present paper) on the solution domain with only fixed boundaries. The liquid free surface is recognized as a line of density discontinuity. The flow equations are discritized by the finite element method in space and by the finite difference method in time. Three characteristic phenomena of spreading, splitting and shielding and their combined phenomena have been calculated. The present results agreed well with other numerical results.
