Interface pressure calculation based on conservation of momentum for front capturing methods E. Shirani 1 , N. Ashgriz * , J. Mostaghimi Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada M5S 3G8 Received 13 March 2003; received in revised form 26 July 2004; accepted 16 August 2004 Available online 1 October 2004 Abstract A new method for the calculation of interface pressure for front capturing methods is developed. This method is based on the calculation of the pressure force at each interfacial cell face using the exact pressure due to the portion of the cell face that is occupied by each fluid. Special formulations for the pressure in the interfacial cells are derived for different orientations of an interface. This method (referred to as pressure calculation based on the interface location (PCIL)) is applied to the time evolution of a two-dimensional initially stagnant liquid drop in a gas, as well as, a gas bubble in liquid (gravity effects are not considered). A two-fluid, PLIC-VOF method is used to simulate the flow numer- ically. Both the continuum surface force (CSF) and the continuum surface stress (CSS) methods are used. A wide range of Ohnesorge numbers and density and viscosity ratios of two fluids are tested. It is shown that the new method reduces the spurious currents by up to three orders of magnitude for the cases tested. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Volume-of-fluid method; Two-phase flow; Continuum surface force; Continuum surface stress; Interface; Pressure calcu- lation based on interface location; PCIL; Free surface flows; Spurious currents; Parasitic currents 1. Introduction In simulation of interfacial flows with fixed mesh, determination of the interface pressure and surface tension has been one of the most troublesome and challenging issues. Surface tension forces appear in equa- tions by imposing a jump condition across the interface. This condition is difficult to apply numerically and has been the center of attention by many researchers. 0021-9991/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2004.08.017 * Corresponding author. Tel.: +1 416 946 3408; fax: +1 416 978 7753. E-mail address: ashgriz@mie.utoronto.ca (N. Ashgriz). 1 Permanent address: Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran. Journal of Computational Physics 203 (2005) 154–175 www.elsevier.com/locate/jcp