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Center for Nonlinear Studies |
A recent in Computational Fluid Dynamics is the study of flows involving more than one fluid. Of particular importance in this kind of flow is the correct representation of the interface among different fluids at each step of the simulation process. In this work we are using the level set method to correctly locate the interface shared by two different fluids. In the level set methodology the interface is represented as the zero level set of a smooth function that satisfies a simple advection equation. This approach allows for easy computation of geometric and physical quantities of interest, such as interface curvature and surface tension.
Our starting point in this investigation is the implementation of a 2D pressure-correction finite difference incompressible Navier-Stokes solver. As a validation study of the developed algorithm we have considered the classical driven cavity flow at Reynolds number 10, 100 and 1000. The second part of this research is devoted to the application of our numerical scheme to the case of two fluids. Several representative case studies are included to evaluate the method. Specifically, we consider the classical reversible vortex problem and motion of an air bubble in a fluid subject to a gravitational field.