In the viscoelastic_stress_build-up benchmark are simga_ij, edot_ii, eta, and mu stored so that we can easily access them?

ASPECT
1

Mack and I are testing the quadratic particle interpolation on problems in solid mechanics / plate tectonics that John Naliboff has added to the benchmarks directory in the ASPECT repository. In particular, we are computing the following benchmark from

$ASPECT_DIR/benchmarks/viscoelastic_stress_build-up

The analytical solution is given in a comment at the top of the parameter file

viscoelastic_stress_build-up.prm:

The analytical solution for viscoelastic stress build-up in an incompressible medium with a constant
strain-rate is: simga_ij = 2 * edot_ii * eta * (1 - e^(-mu*t/eta)), where sigma_ij is the elastic deviatoric stress tensor, edot_ij is the deviatoric strain-rate, eta is the background viscosity, mu is the shear modulus and t is time.

My thought is to essentially copy the structure of the computational version of the exact solution for SolCx, which is actually in SolCx.h not SolCx.cc, a portion of which I quote here (sorry for the length):

/*
* @name Reference quantities
* @{
/
virtual double reference_viscosity () const
{
return 1;
}
/*
* @}
/
/*
* Returns the viscosity value on the right half of the domain,
* typically 1 or 1e6
/
double get_eta_B() const
{
return eta_B;
}
/*
* Returns the background density of this model. See the
* corresponding member variable of this class for more information.
/
double get_background_density() const
{
return background_density;
}
private:
/*
* Viscosity value on the right half of the domain, typically 1 or
* 1e6
/
double eta_B;
/*
* A constant background density over which the density variations
* are overlaid. This constant density has no effect on the dynamic
* pressure and consequently on the flow field, but it contributes
* to the total pressure via the adiabatic pressure. We use this
* field to support our claim in the first ASPECT paper that the
* accuracy of the solutions is guaranteed even if we don’t subtract
* the adiabatic pressure in our computations.
*/
double background_density;

My question is this: "Are all of the quantities in the exact (analytical) solution: simga_ij, edot_ii, eta, and mu stored somewhere where we can easily access them, or will we have to compute some them ourselves in our solution.cc file?

2

John can probably give a more detailed answer, but it looks like there is no source code and as such no code that implements the exact solution at this point.

3

Timo is correct that their is no existing source code that computes the exact solution at this point. However, with that said all of the variables you mentioned should be readily accessible:

  • sigma_ij is the viscoelastic stress tensor, which is stored on compositional fields or particles
  • edot_ii is the second invariant of the deviatoric strain rate. The strain rate tensor is a material model input and examples of how to calculate the second invariant are in the viscoelastic and visco_plastic material models.
  • eta is the background viscosity (user defined value)
  • mu is the shear modulus (user-defined valued)

Here is a general question - is it necessary to write a plugin to do the comparison between the computed and analytical solution? One could load the output data (VTU, ascii, HDF5) into python and do the comparison there?