# stress#

EQ = {eqname} {Galerkin_wt} {varname} {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 constants for the Stress equation defining the constant multipliers for 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.

 {eqname} The name of the component of the stress equation to be solved, one of the following: stress11, stress12, stress13, stress22, stress23, stress33. {Galerkin_wt} Two-character or three-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 PQ-Q1 Discontinuous PQ-Q2 Discontinuous {varname} The name of the variable associated with the respective components (11, 12, 13, 22, 23, and 33) of the symmetric Stress tensor, which are S11, S12, S13, S22, S23, S33. {Interpol_fnc} Two-character or three-character value that defines the interpolation function used to represent the variable S11, S12, S13, S22, S23 or S33, where: P0-Constant Discontinuous P1-Linear Discontinuous Q1-Bilinear/Trilinear Continuous Q2-Biquadratic/Triquadratic Continuous PQ-Q1 Discontinuous PQ2-Q2 Discontinuous 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 a linear continuous interpolation for stress and turns on all the term multipliers:

EQ = stress11 Q1 S11 Q1 1. 1. 1. 1. 1.


## Technical Discussion#

The interpolation/weight functions that are discontinuous, e.g. have the prefix “P”, invoke the discontinuous Galerkin method for solving the stress equations where the interpolation is discontinuous and flux continuity is maintained by performing surface integrals. For details of the implementation of the discontinuous Galerkin method in Goma please see the viscoelastic tutorial memo (Rao, 2000).

## References#

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