# species_bulk#

EQ = species_bulk {Galerkin_wt} Y {Interpol_fnc} <floatlist>


## Description / Usage#

This card provides information for solving a differential equation. Definitions of the input parameters are defined below. Note that <floatlist> contains five parameters to define the constant multipliers in front of each type of 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 for advection dominated problems, we can set this through a Petrov-Galerkin weight function in the material file.

 species_bulk Name of the equation to be solved. This equation type should only be listed once regardless of the number of species (the Number of bulk species card specifies the number of species_bulk equations to be solved). Differences in diffusion coefficients between species should be accounted for in the materials properties section of Goma. {Galerkin_wt} Two- to four-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 Q1_XV, Q1_GN, Q1_GP-Linear interpolation with enrichment in elements of material interfaces. This enrichment function allows discontinuity in value and gradient along interface but maintains continuity at element edges/faces. Q2_XV, Q2_GN, Q1_GP-Quadratic interpolation with enrichment in elements of material interfaces. This enrichment function allows discontinuity in value and gradient along interface but maintains continuity at element edges/faces. Y Name of the variable associated with this equation. {Interpol_fnc} Two- to four-character value that defines the interpolation function used to represent the variable Y, 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 Q1_XV, Q1_GN, Q1_GP-Linear interpolation with enrichment in elements of material interfaces. This enrichment function allows discontinuity in value and gradient along interface but maintains continuity at element edges/faces. See energy equation for more discussion. Q2_XV, Q2_GN, Q1_GP-Quadratic interpolation with enrichment in elements of material interfaces. This enrichment function allows discontinuity in value and gradient along interface but maintains continuity at element edges/faces. See energy equation for more discussion. Multiplier on mass matrix term ( d ⁄dt ). Multiplier on advective term. Multiplier on boundary term ( $$\underline{n}$$ • flux ). Multiplier on diffusion term. Multiplier on source term.

Note: These multipliers are intended to provide a means of activating or deactivating terms of an equation, and hence should be set to zero or one. If a multiplier is zero, the section of code that evaluates the corresponding term will be skipped.

## Examples#

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

EQ = species_bulk Q2 Y Q2 1. 1. 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 species equations where the interpolation is discontinuous and flux continuity is maintained by performing surface integrals. For details of the implementation of the DG method in Goma please see the viscoelastic tutorial memo. Note, the DG implementation for the species equation is only for advection dominated problems; DG methods have not yet been completely developed for diffusion operators.

Also, please see EQ=energy input for more detailed description of the Q1_GN, Q2_GN, Q1_GP, Q2_GP, Q1_XV and Q2_XV enriched basis functions.

## References#

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