level set#

EQ = level set {Galerkin_wt} F {Interpol_fnc} <float1> <float2> <float3>

Description / Usage#

This card provides information for solving a differential equation for the level set equation. Definitions of the input parameters are defined below. Note that <float1> through <float3> define the constant multipliers for each term in the equation. The Galerkin weight and the interpolation function must be the same for the code to work properly. If upwinding is desired, we can set this through a Petrov-Galerkin weight function in the level set section of the input file (Time Integration Specifications).

level set

Name of the equation to be solved.

{Galerkin_wt}

Two-character value that defines the type of weighting function for this equation, where:

  • P0-Constant Discontinuous

  • P1-Linear Discontinuous

  • Q1-Bilinear/Trilinear Continuous

  • Q2-Biquadratic/Triquadratic Continuous

  • Q1_D-Standard linear interpolation with special allowance for discontinuous degrees of freedom at interfaces.

  • Q2_D-Standard quadratic interpolation with special allowance for discontinuous degrees of freedom at interfaces.

  • PQ1-Q1 Discontinuous

  • PQ2-Q2 Discontinuous

F

Name of the variable associated with this equation.

{Interpol_fnc}

Two-character value that defines the interpolation function used to represent the variable F, where:

  • P0-Constant Discontinuous

  • P1-Linear Discontinuous

  • Q1-Bilinear/Trilinear Continuous

  • Q2-Biquadratic/Triquadratic Continuous

  • Q1_D-Standard linear interpolation with special allowance for discontinuous degrees of freedom at interfaces.

  • Q2_D-Standard quadratic interpolation with special allowance for discontinuous degrees of freedom at interfaces.

  • PQ1-Q1 Discontinuous

  • PQ2-Q2 Discontinuous

Examples#

The following is a sample card that uses continuous linear interpolation for the level set equation and turns on all term multipliers:

EQ = level_set Q1 F Q1 1. 1. 1.

Technical Discussion#

The interpolation/weight functions that are discontinuous, e.g. have the prefix “P”, invoke the discontinuous Galerkin (DG) method for solving the level set equations where the interpolation is discontinuous and flux continuity is maintained by evaluating surface integrals. For details of the implementation of the DG method in Goma please see the viscoelastic tutorial memo (Rao, 2000). Note that DG methods are not necessarily recommended for the level set equation since it is inherently smooth.

References#

GT-014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao