An efficient method for capturing free boundaries in multi‐fluid simulations

An easy-to-use front capturing method is devised by directly solving the transport equation for a volume of fluid (VOF) function. The key to this method is a semi-Lagrangian conservative scheme, namely CIP_CSL3, recently proposed by the author. In the CIP_CSL3 scheme, the first-order derivative of the interpolation polynomial at each cell centre is used to control the shape of the reconstructed profile. We show in the present paper that the first-order derivative, which plays a crucial role in reconstructing the interpolation profile, can also be used to eliminate numerical diffusion. The resulting algorithm can be directly used to compute the VOF-like function and retain the compact thickness of the moving interface in multi-fluid simulations. No surface reconstruction based on the value of VOF function is required in the method, which makes it quite economical and easy to use. The presented method has been tested with various interfacial flows including pure rotation, vortex shearing, multi-vortex deformation and the moving boundaries in real fluid as well. The method gives promising results to all computed problems. Copyright © 2003 John Wiley & Sons, Ltd.