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solvers:strainrate [Elmer/Ice Wiki]

## Solver ComputeStrainRate

### General Informations

• Solver Fortran File: `ComputeStrainRate.f90`
• Solver Name: `ComputeStrainRate`
• Required Output Variable(s): default is `StrainRate` (else in `StrainRate Variable Name`)
• Required Input Variable(s): A `Flow Solution` (in `Flow Solution Name`)
• Optional Output Variable(s): None
• Optional Input Variable(s): None

### General Description

The aim of this solver is to compute the strain-rate tensor from the flow solution. For a 2D simulation there are 5 DOFs `(E11, E22, E33, E12, Eii)` and for a 3D simulation, 2 additional (7 DOFs) are being solved for `(E11, E22, E33, E12, E23, E31, Eii)`. This solver uses a dummy variable and solves 5 (7 in 3D) times a 1 DOF system for each strain-rate components and the trace of the strain-rate tensor `(Eii)`.

The Strain-rate tensor is computed using:

where is the velocity vector solution of the Stokes problem.

### SIF contents

The required keywords in the SIF file for this solver are:

```Solver 1
Equation = "Strain Rate"
Procedure = "ElmerIceSolvers" "ComputeStrainRate"
! this is just a dummy, hence no output is needed
!-----------------------------------------------------------------------
Variable = -nooutput "Eij"
Variable DOFs = 1

Exported Variable 1 = "StrainRate"
Exported Variable 1 DOFs = 5 !in 2D, 7 in 3D

! the name of the variable containing the flow solution (U,V,W,Pressure)
!-----------------------------------------------------------------------
Flow Solver Name = String "Flow Solution"
! the name of the strain-rate solution (default is 'StrainRate')
StrainRate Variable Name = String "StrainRate"

Linear System Solver = Direct
Linear System Direct Method = umfpack
End```

### Examples

An example using this solver can be found in `[ELMER_TRUNK]/elmerice/examples/Test_StrainRate`.