Abstract: RIPPLE: A Computer Program for Incompressible Flows with Free Surfaces is a computer program for modeling transient, two-dimensional, incompressible fluid flows with surface tension on free surfaces of general topology. Incompressible free surface fluid flows form an integral part of natural and industrial processes. The fluid behavior can be especially difficult to understand and quantify when ... the free surfaces have appreciable surface tension and are arbitrarily complex in topology. Examples of such flows can be found in nuclear reactor thermal hydraulics, internalcombustion-engine fuel sprayers, ink-jet printers, the application of industrial surfactants, raindrop formation, casting and mold filling processes, drop/bubble dynamics, and in cryogenic liquids in a micro-gravity environment. Modeling these types of flows poses a significant challenge because a required boundary condition must be applied to a transient, irregular surface (the free surface) that is ideally a discontinuity. Surface tension frequently constrains the accuracy with which the resulting boundary condition is applied in numerical models.

In RIPPLE, surface tension at free surfaces is replaced by a volume force derived from the continuum surface force model. A two-step projection method is used to solve for incompressible flow, with the pressure Poisson equation solved via a robust incomplete Cholesky conjugate gradient technique. Momentum advection is estimated with a technique very similar to the weakly monotonic upwind method of van Leer. Flow obstacles and curved boundaries interior to the mesh are representable with a partial cell treatment that borrows from two-phase flow physics. The numerical scheme of RIPPLE is based on a finite difference solution of a coupled set of partial differential equations governing incompressible fluid flow. Finite difference solutions to the incompressible Navier-Stokes equations are obtained on an Eularian, rectilinear mesh in Cartesian or cylindrical geometries. Free surfaces are represented with volume-of-fluid data on the mesh. Surface tension is modeled as a volume force derived from the continuum surface force model. The continuum surface force model for surface tension gives RIPPLE both robustness and accuracy in modeling surface tension effects at the free surface. RIPPLE can also model wall adhesion effects.