A free surface sharpening strategy using optimization method

VOF method which consists in transporting a discontinuous marker variable is widely used to capture the free surface in computational fluid dynamics. There is numerical dissipation in simulations involving the transport of the marker. Numerical dissipation makes the free surface lose its physical nature. A free surface sharpening strategy based on optimization method is presented in the paper. The strategy can keep the location of the free surface and local mass conservation at both time, and can also keep free surface in a constant width. It is independent on the types of solvers and meshes. Two famous cases were chosen for verifying the free surface sharpening strategy performance. Results show that the strategy has a very good performance on keeping local mass conservation. The efficiency of prediction of the free surface is improved by applying the strategy. Accurate modeling of flow details such as drops can also be captured by this method.

[1]  Bojan Niceno,et al.  A conservative local interface sharpening scheme for the constrained interpolation profile method , 2012 .

[2]  Berend van Wachem,et al.  Volume of fluid methods for immiscible-fluid and free-surface flows , 2008 .

[3]  Krish Thiagarajan,et al.  Simulation of the dam break problem and impact flows using a Navier-Stokes solver , 2004 .

[4]  Steven Dufour,et al.  A free surface updating methodology for marker function‐based Eulerian free surface capturing techniques on unstructured meshes , 2004 .

[5]  G. Kreiss,et al.  A conservative level set method for two phase flow II , 2005, Journal of Computational Physics.

[6]  C. K. Thornhill,et al.  Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane , 1952, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[7]  Tayfun E. Tezduyar,et al.  Stabilized-finite-element/interface-capturing technique for parallel computation of unsteady flows with interfaces , 2000 .

[8]  Shahrouz Aliabadi,et al.  Development of a hybrid finite volume/element solver for incompressible flows , 2007 .

[9]  Borut Mavko,et al.  Simulations of free surface flows with implementation of surface tension and interface sharpening in the two-fluid model , 2009 .

[10]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[11]  Krister Svanberg,et al.  A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations , 2002, SIAM J. Optim..