Conservative and Non-Conservative Formulations

Because the velocity field is divergence free, use either the conservative or the non-conservative formulation of the level set or phase field equation. The conservative form perfectly conserves the mass of each fluid, but the computational time is in general longer.

Phase Initialization

If the study type Transient with Initialization is selected, the level set variable or the phase field variables are automatically first initialized. For that study, two study steps are created, Phase Initialization and Time Dependent. The Phase Initialization step solves for the distance to the initial interface, Dwi. The Time Dependent study then uses the initial condition for the level set function according to the following expression:

in domains initially filled with Fluid 1 and

in domains initially filled with Fluid 2.

Correspondingly, for the phase field method the following expressions are used:

D

0 = –tanh ------wi---

2

in Fluid 1 and

D

0 = tanh ------wi---

2

214 | C H A P T E R 6 : M U L T I P H A S E F L O W B R A N C H

in Fluid 2. The initial condition for the help variable is 0 = 0. These expressions are based on the analytical solution of the steady state solution of Equation 6-6, Equation 6-7, and Equation 6-8 for a straight, non-moving interface.

For the initialization to work it is crucial that there are two Initial Value features and one Initial Interface feature. One of the Initial Value feature should use Fluid initially in domain: Fluid 1and the other Fluid initially in

domain: Fluid 2. The Initial Interface feature should have all interior

Important

boundaries where the interface is initially present as selection. If the selection of the Initial interface feature is empty, the initialization fails.

Numerical Stabilization

Four types of stabilization methods are available for the, flow (Navier-Stokes), turbulence, and the interface (level set or phase field) equations. Two of these are consistent stabilization methods—streamline diffusion and crosswind diffusion, and two are inconsistent—isotropic diffusion and anisotropic diffusion.

To display this section, click the Show button () and select Stabilization.

• Show Stabilization in the COMSOL Multiphysics User’s Guide

References for the Level Set and Phase Field Interfaces

1. E. Olsson and G. Kreiss, “A Conservative Level Set Method for Two Phase Flow,”

J. Comput. Phys., vol. 210, pp. 225–246, 2005.

2.P. Yue, J. J. Feng, C. Liu, and J. Shen, “A Diffuse-interface Method for Simulating Two-phase Flows of Complex Fluids”, J. Fluid Mech., vol. 515, pp. 293–317, 2004.

3.B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, and G. Zanetti “Modelling Merging and Fragmentation in Multiphase Flows with SURFER.” J. Comput. Phys., vol. 113, no. 1, pp. 134–147, 1994.

T H E O R Y F O R T H E TW O - P H A S E F L O W I N T E R F A C E S | 215

7

M a t h e m a t i c s , M o v i n g I n t e r f a c e B r a n c h

The fluid-flow interfaces are grouped by type under the Fluid Flow main branch in the Model Wizard. In addition, the Level Set and Phase Field Moving Interfaces are available under the Mathematics>Moving Interface branch (). See also The Mechanisms for Modeling Multiphase Flow to help you choose the best one to start with.

In this chapter:

•The Level Set Interface

•The Phase Field Interface

•Theory for the Level Set Interface

•Theory for the Phase Field Interface

217