Choosing a material model and formulation

ASPECT
1

Hi all,

I am working on a model for plate-mantle interaction (small-scale convection) and associated melt production. I’d like to do 3D regional upper mantle models over ~100 Myr time span, so tracking melt in a 2-phase flow model is probably too slow, and also not really needed, as I am mostly interested in where melt forms, and roughly how much. The approach to tracking melt and associated latent heat effects as described in Gassmoeller et al., 2016, https://doi.org/10.1002/2015GC006177, seems to me just the kind of complexity that seems right for this model. I have a few questions related to this:

  1. Which is the best material model to set this up? I have mainly been using the ‘Visco plastic’ material model for different geodynamic models, and already built a model for this project using this material model as well: I would like to explore the effects of composite rheology, and perhaps other rheological features, and would also like to use multiple compositions with their own material properties, so this material model is quite suitable in that respect. But at the moment, the melting part is really too simple: I only calculate melting using the available parameterised melting postprocessor, so cannot incorporate any feedback of this melting (e.g. latent heating). I could adapt the material model to incorporate the melt calculation inside it, include the latent heat effect as a heat source, and track the depletion to affect the solidus temperature (as done in Gassmoeller et al. (2016)), but I wonder if this is the best way forward. Should I switch to another material model, and if so, is there one that has (some of) these features already incorporated?

  2. This material model choice relates to another question: the ‘Visco plastic’ model is incompressible. Given the sensitivity of melting to the ambient mantle temperature, incorporating latent heat of melting would be essential, and including adiabatic heating and viscous heating should then probably also be included. But how internally consistent would that be if the model is incompressible? Such model would probably amount to the ‘Extended Boussinesq Approximation’. But given that ASPECT has several compressible material options, would it be more appropriate to use one of those instead? I think I would prefer to stick to an incompressible model, but only if that is still ‘acceptable’ in combination with the different heating terms.

  3. Are any examples available to look at for any of the above?

Many thanks for any support, advice or thoughts.
Jeroen

2

Hi Jeroen,

Thanks for posting this question to the forum!

First, to summarize the approach taken in Gassmoeller et al., 2016 after a quick read:

  • At each point in the model the amount of melt is calculated following Katz et al. 2003
  • The effect of melting and freezing is included into the energy equation.
  • The amount of melt is tracked and advected with a compositional field.
  • Crustal thickness maps are generated in post processing steps.

Some initial thoughts:

  1. Given you would like to use a multi-component composite rheology, the visco-plastic material model is likely the best choice here. Certainly the case if you want to use plasticity and/or elasticity.

  2. Calculating the amount of melt present at each point and adding these terms to a compositional field through reaction terms could be accomplished through a material model plugin that uses the visco plastic material model as the base model. This open PR would allow specifying that the compositional field tracking melt should not be used in the material property calculation. See the finite_strain cookbook for an example of how a material plugin works.

  3. The effects of melting/freezing can likely be incorporated into the energy equation through a new heating model. The existing heating model latent_heat_melt likely incorporates similar terms, but does not appear to include the effects of freezing at first glance (I may be wrong about this).

Others will likely have input and opinions about this as well, and if possible I think this would be a good topic to discuss at one of the bi-weekly ASPECT user meetings.

Cheers,
John

3

Hi Jeroen,

I would like to add that you can find the most recent version of the code used in the Gassmoeller et al. 2016 paper here: GitHub - ebredow/aspect at reunion_plume_model (it was used and extended by Eva Bredow for several follow-up publications). The models use a new material model (plume.cc) that has components from the steinberger model (for the viscosity) and the latent heat melt model (for the latent heat). Of course this is still from 2016 and some things may not work with the current ASPECT master any more.

But I am happy to discuss this in more detail at a user meeting.

I also want to add that if you only model the upper mantle, where compressibility is not that important, I think it is totally fine to use an incompressible formulation with shear heating, adiabatic heating, and latent heat (I think many people do that).

Cheers,
Juliane