Fill Weight Function

Fill Weight Function = {Galerkin | Taylor-Galerkin | SUPG}

Description / Usage

Sets the weight function used for the FILL equation for either the VOF or Level Set methods. The options for this card are as follows:

Galerkin

Name of the weight function formulation. This option requests a standard Galerkin finite element weighted residual treatment. A floating point parameter is not used for this option.

Taylor-Galerkin

Name of the weight function formulation

SUPG

Name of the weight function formulation. This option requests a Streamwise Upwinding Petrov Galerkin formulation. No floating point parameter is required.

The default value for the Fill Weight Function is Taylor-Galerkin.

Examples

This is a sample card:

Fill Weight Function = Galerkin

Technical Discussion

This card selects the integration/weight function used in solving for the VOF color function or the level set distance function (i.e., the FILL unknown). The user should refer to the tutorial on Level Set Computations for a detailed description of level set interface tracking. (See References.)

References

GT-020.1: Tutorial on Level Set Interface Tracking in GOMA, February 27, 2001, T.A. Baer

A. N. Brooks and T. J. R. Hughes, “Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations,” Comp. Math. In Appl. Mechanics and Eng., 32, 199 - 259 (1992).

A. J. A. Unger, P. A. Forsyth and E. A. Sudicky, “Variable spatial and temporal weighting schemes for use in multi-phase compositional problems,” Advances in Water Resources, 19, 1 - 27 (1996).

R. Helmig and R. Huber, “Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media,” Advances in Water Resources, 21, 697-711 (1998).

E. Gundersen and H. P. Langtangen, “Finite Element Methods for Two-Phase Flow in Heterogeneous Porous Media,” in Numerical Methods and Software Tools in Industrial Mathematics, Morten Daehlen, Aslak Tveito, Eds., Birkhauser, Boston, 1997.

S. F. Bradford and N. D. Katopodes, “The anti-dissipative, non-monotone behavior of Petrov-Galerkin Upwinding,” International J. for Numerical Methods in Fluids, v. 33, 583-608 (2000).