Karato and Wu, 1990 rheology implementation UWGeodynamics.

[Prasanna2989]

Hi,

Will you be able to provide the implementation of the non linear rheology of Karato and Wu, 1990 which is in UWGeodynamic module (Please see the attachment for details). I am trying to implement this non linear rheology in UW2 for one of my mantle convection models. I think Romain has done it somewhere. I want to implement this directly in UW2.

This. is how I did it for diffusion creep

    E_N = 300000
    E = E_N/R/delta_T_N;
    V_N = 3.e-6;
    V = V_N*3300.*g_N*height_N/R/delta_T_N ;
    eta = viscosity_M * uw.function.math.exp(((E+(V*depth))/(temperatureField +1.))-(E/(delta_T_M +1.)));

Could you please give me some help?

Thanks Pras

[julesghub]

Hi Pras, Your eta doesn't appear to depend on values directly related to the solution unknowns i.e. velocity or pressure. As such no non linearity exists. For this Karato and Wu dislocation mechanism the effective eta should be equal to some function of the strain rate 2nd invariant.

For a demo on implementing a model with an effective eta that is strain rate 2nd inv. dependent see, cell 10 of this https://github.com/julesghub/uw_models/blob/master/SlabDetachment/SlabDetachment_B.ipynb.

Also you can run the above model directly on binder hitting this button

[lmoresi]

Perhaps it would be helpful to add the strain-rate dependence to the diffusion creep mechanism - which should result in the same solution because the dependency does nothing but which, formally, would trigger the non-linear solver to light up. On 11 May 2020, 3:14 PM +1000, Julian Giordani notifications@github.com, wrote:

Hi Pras, Your eta doesn't appear to depend on values directly related to the solution unknowns i.e. velocity or pressure. As such no non linearity exists. For this Karato and Wu dislocation mechanism the effective eta should be equal to some function of the strain rate 2nd invariant.

For a demo on implementing a model with an effective eta that is strain rate 2nd inv. dependent see, cell 10 of this https://github.com/julesghub/uw_models/blob/master/SlabDetachment/SlabDetachment_B.ipynb.

Also you can run the above model directly on binder hitting this button

[Binder]https://mybinder.org/v2/gh/julesghub/uw_models/master?filepath=SlabDetachment%2FSlabDetachment_B.ipynb

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[Prasanna2989]

So, What would be the implication of applying non linearity? Will that eventually reach the lower limit of the viscosity? Also, I was thinking whether I should constraint the depth for the non linear rheology?

[lmoresi]

I’m suggesting that you try implementing the non-linear dependency for a case that is actually linear (stress exponent 1.0) so that you can see which parts of the solver light up in response to the new dependency but the results should be unchanged.

I am not sure what you mean by lower-limit in this case. Whether you apply a depth limit depends on the science problem you are trying to solve. I am only speaking about the numerics for the moment. On 11 May 2020, 3:28 PM +1000, Prasanna2989 notifications@github.com, wrote:

So, What would be the implication by applying non linearity? Will that eventually reach the lower limit of the viscosity? Also, I was thinking whether I should constraint the depth for the non linear rheology?

— You are receiving this because you commented. Reply to this email directly, view it on GitHubhttps://github.com/underworldcode/underworld2/issues/478#issuecomment-626477626, or unsubscribehttps://github.com/notifications/unsubscribe-auth/ADABPI4F3OYPJ4ZRYXQ635LRQ6EF3ANCNFSM4MWZAHXQ.

[Prasanna2989]

Thank you Louis, I got the idea. Here the lower limit means, the upper and lower limit values that I included to keep the model within a prescribed range. I should have mentioned it. Basically I am limiting the model viscosity between 1.e18 and 1.e25 for mantle convection model.

On Mon, May 11, 2020 at 3:32 PM Louis Moresi notifications@github.com wrote:

I’m suggesting that you try implementing the non-linear dependency for a case that is actually linear (stress exponent 1.0) so that you can see which parts of the solver light up in response to the new dependency but the results should be unchanged.

I am not sure what you mean by lower-limit in this case. Whether you apply a depth limit depends on the science problem you are trying to solve. I am only speaking about the numerics for the moment. On 11 May 2020, 3:28 PM +1000, Prasanna2989 notifications@github.com, wrote:

So, What would be the implication by applying non linearity? Will that eventually reach the lower limit of the viscosity? Also, I was thinking whether I should constraint the depth for the non linear rheology?

— You are receiving this because you commented. Reply to this email directly, view it on GitHub< https://github.com/underworldcode/underworld2/issues/478#issuecomment-626477626>, or unsubscribe< https://github.com/notifications/unsubscribe-auth/ADABPI4F3OYPJ4ZRYXQ635LRQ6EF3ANCNFSM4MWZAHXQ>.

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-- Prasanna M. Gunawardana

PhD candidate Earth, Atmosphere and Environment Science Monash University, Melbourne Australia

[julesghub]

Closing this issue for now. Feel free to reopen if you still have issues @Prasanna2989.