Volume of fluid method

Abstract: Several methods have been previously used to approximate free boundaries in finite-difference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efficient than other methods for treating complicated free boundary configurations. To illustrate the method, a description is given for an incompressible hydrodynamics code, SOLA-VOF, that uses the VOF technique to track free fluid surfaces.

Abstract: *Introduction. *Conservation Laws of Fluid Motion and Boundary Conditions. *Turbulence and its Modelling. *The Finite Volume Method for Diffusion Problems. *The Finite Volume Method for Convection-Diffusion Problems. *Solution Algorithms for Pressure-Velocity Coupling in Steady Flows. *Solution of Discretised Equations. *The Finite Volume Method for Unsteady Flows. *Implementation of Boundary Conditions. *Advanced topics and applications. Appendices. References. Index.

Abstract: A new numerical technique is presented that has many advantages for obtaining solutions to a wide variety of time-dependent multidimensional fluid dynamics problems. The method uses a finite difference mesh with vertices that may be moved with the fluid (Lagrangian), be held fixed (Eulerian), or be moved in any other prescribed manner, as in the Arbitrary Lagrangian?Eulerian (ALE) technique. In addition, it employs an implicit formulation similar to that of the Implicit Continuous-fluid Eulerian (ICE) technique, making it applicable to flows at all speeds.This paper describes the basic methodology, presents finite difference approximations, and discusses such matters as stability, accuracy, and zoning. In addition, illustrations are included from a number of representative calculations.

Abstract: Direct numerical simulations of multiphase flows, using a front-tracking method, are presented. The method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties. Interfacial terms are accounted for by adding the appropriate sources as δ functions at the boundary separating the phases. The unsteady Navier–Stokes equations are solved by a conventional finite volume method on a fixed, structured grid and the interface, or front, is tracked explicitly by connected marker points. Interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid. Advection of fluid properties such as density is done by following the motion of the front. The method has been implemented for fully three-dimensional flows, as well as for two-dimensional and axisymmetric ones. First, the method is described for the flow of two or more isothermal phases. The representation of the moving interface and its dynamic restructuring, as well as the transfer of information between the moving front and the fixed grid, are discussed. Applications and extensions of the method to homogeneous bubbly flows, atomization, flows with variable surface tension, solidification, and boiling are then presented.

Abstract: A new algorithm for the volume tracking of interfaces in two dimensions is presented. The algorithm is based upon a well-defined, second-order geometric solution of a volume evolution equation. The method utilizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology. A linearity-preserving, piecewise linear interface geometry approximation ensures that solutions generated retain second-order spatial accuracy. Second-order temporal accuracy is achieved by virtue of a multidimensional unsplit time integration scheme. We detail our geometrically based solution method, in which material volume fluxes are computed systematically with a set of simple geometric tasks. We then interrogate the method by testing its ability to track interfaces through large, controlled topology changes, whereby an initially simple interface configuration is subjected to vortical flows. Numerical results for these strenuous test problems provide evidence for the algorithm's improved solution quality and accuracy.