SIMULATION OF 2-FLUID FLOWS BY THE LEAST-SQUARES FINITE-ELEMENT METHOD USING A CONTINUUM SURFACE-TENSION MODEL

In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols(1) and the Continuum Surface Force (CSF) model developed by Brackbill et al.(2) In the VOF method fluids of di fferent properties are identified through the use of a continuous held variable (colour function). The colour function assigns a unique cons tant (colour) to each fluid. The interfaces between different fluids a re distinct due to sharp gradients of the colour function. The evoluti on of the interfaces is captured by solving the convective equation of the colour function. The CSF model is used as a means to treat surfac e tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin,(3) is used to calculate the tension force . In the modified version, the force term is obtained by calculating t he divergence of a stress tensor defined by the gradient of the colour function. In its analytical form, this stress formulation is equivale nt to the original CSF model.(2) Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the int erfaces. The least-squares finite element method (LSFEM)(4) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present app lications. The LSFEM handles all the equations in a unified manner wit hout any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both t wo-dimensional planar and axisymmetric flows, including a dam breaking , oscillating and stationary bubbles and a conical liquid sheet in a p ressure swirl atomizer. (C) 1998 John Wiley & Sons, Ltd.