refactor: mixture density computation in multiphase poromechanics solvers

[castelletto1]

This PR modifies the computation of the mixture (solid + fluid) density favoring use of primary variables over secondary variables.

[castelletto1]

We should decide whether we want to refer to the expression:

$$\rho=(1-\phi)\rho_{\text{solid}}+\phi\sum_{c}\rho_c=(1-\phi)\rho_{\text{solid}}+\phi\sum_{c}\sum_{\ell=1}^{np}x_{c\ell}\rho_{\ell}s_{\ell}=(1-\phi)\rho_{\text{solid}}+\phi\sum_{\ell=1}^{np}\rho_{\ell}s_{\ell}$$

as mixture density or bulk density, and be consistent everywhere.

[paveltomin]

❤️

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 19 lines in your changes missing coverage. Please review.

Project coverage is 56.32%. Comparing base (7130462) to head (122ab3f).
Report is 85 commits behind head on develop.

Files with missing lines	Patch %	Lines
...s/poromechanicsKernels/MultiphasePoromechanics.hpp	0.00%	10 Missing ⚠️
...omechanicsKernels/MultiphasePoromechanics_impl.hpp	0.00%	7 Missing ⚠️
...csSolvers/multiphysics/MultiphasePoromechanics.cpp	0.00%	1 Missing ⚠️
...icsKernels/ThermalMultiphasePoromechanics_impl.hpp	0.00%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #3342      +/-   ##
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+ Coverage    56.30%   56.32%   +0.01%     
===========================================
  Files         1065     1065              
  Lines        90227    90210      -17     
===========================================
+ Hits         50805    50807       +2     
+ Misses       39422    39403      -19     

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[dkachuma]

I suppose this means that these terms cancel out and we should end up with a value that is numerically close to zero?

[castelletto1]

If we highlight in the body force term the dependencies on the primary variables we have:

$$\rho \mathbf{g}=(1-\phi(\epsilon_v(\mathbf{u}),p,T))\rho_{\text{solid}}(p,T)\mathbf{g}+\phi(\epsilon_v(\mathbf{u}),p,T)\sum_{c}\rho_c\mathbf{g}$$

We have a direct dependency on temperature exclusively on porosity at the moment -- eventually on the solid phase density $\rho_s$ (not considered at the moment in the code). I agree that one can probably show that looping over phases produces dTotalMassDensity_dTemperature = 0.

[CusiniM]

We should decide whether we want to refer to the expression:

ρ = ( 1 − ϕ ) ρ solid + ϕ ∑ c ρ c = ( 1 − ϕ ) ρ solid + ϕ ∑ c ∑ ℓ = 1 n p x c ℓ ρ ℓ s ℓ = ( 1 − ϕ ) ρ solid + ϕ ∑ ℓ = 1 n p ρ ℓ s ℓ

as mixture density or bulk density, and be consistent everywhere.

can we call this totalDensity instead of bulk density ? ? It's certainly not the mixture density.

[CusiniM]

We should decide whether we want to refer to the expression:
ρ = ( 1 − ϕ ) ρ solid + ϕ ∑ c ρ c = ( 1 − ϕ ) ρ solid + ϕ ∑ c ∑ ℓ = 1 n p x c ℓ ρ ℓ s ℓ = ( 1 − ϕ ) ρ solid + ϕ ∑ ℓ = 1 n p ρ ℓ s ℓ
as mixture density or bulk density, and be consistent everywhere.

can we call this totalDensity instead of bulk density ? ? It's certainly not the mixture density.

Looking at the code, IMO, what we call totalMassDensity should be called mixtureDensity and the totalDensity should include the solid part.

[castelletto1]

We should decide whether we want to refer to the expression:
ρ = ( 1 − ϕ ) ρ solid + ϕ ∑ c ρ c = ( 1 − ϕ ) ρ solid + ϕ ∑ c ∑ ℓ = 1 n p x c ℓ ρ ℓ s ℓ = ( 1 − ϕ ) ρ solid + ϕ ∑ ℓ = 1 n p ρ ℓ s ℓ
as mixture density or bulk density, and be consistent everywhere.

can we call this totalDensity instead of bulk density ? ? It's certainly not the mixture density.

Looking at the code, IMO, what we call totalMassDensity should be called mixtureDensity and the totalDensity should include the solid part.

I agree it is confusing. Often, in the poromechanics literature authors refer to mixture including the solid phase, for example: "... a three-phase mixture composed of a solid matrix whose voids are continuous and filled
with water and air ..." [Borja, CMAME (2004)].

In my opinion, we should agree on consistent naming for:

• solid phase(s)
• fluid phases and their mixture
• solid/fluid combined

Also the notation used in the documentation should be updated accordingly.

[CusiniM]

We should decide whether we want to refer to the expression:
ρ = ( 1 − ϕ ) ρ solid + ϕ ∑ c ρ c = ( 1 − ϕ ) ρ solid + ϕ ∑ c ∑ ℓ = 1 n p x c ℓ ρ ℓ s ℓ = ( 1 − ϕ ) ρ solid + ϕ ∑ ℓ = 1 n p ρ ℓ s ℓ
as mixture density or bulk density, and be consistent everywhere.

can we call this totalDensity instead of bulk density ? ? It's certainly not the mixture density.

Looking at the code, IMO, what we call totalMassDensity should be called mixtureDensity and the totalDensity should include the solid part.

I agree it is confusing. Often, in the poromechanics literature authors refer to mixture including the solid phase, for example: "... a three-phase mixture composed of a solid matrix whose voids are continuous and filled with water and air ..." [Borja, CMAME (2004)].

In my opinion, we should agree on consistent naming for:

* solid phase(s)

* fluid phases and their mixture

* solid/fluid combined

Also the notation used in the documentation should be updated accordingly.

I mean, I think the definition of mixture is quite broad so technically one could see the solid + fluids as a mixture. However, since we are often interested in the properties of just the fluid mixture I think that it is more straightforward to call:

• mixture or fluidMixture the mixture of the fluid phases and so refer to the mixtureDensity or the fluidMixtureDensity for that one.
• totalDensity the density of the fluidMixture plus the solid. And I d do the same thing with energy, enthalpy etc.
  Mainly coz it's weird to have something called totalDensity that does not include all phases present.

[paveltomin]

• totalDensity the density of the fluidMixture plus the solid. And I d do the same thing with energy, enthalpy etc.
  Mainly coz it's weird to have something called totalDensity that does not include all phases present.

i would say totalDensity is kind of reserved for fluid total density

[CusiniM]

• totalDensity the density of the fluidMixture plus the solid. And I d do the same thing with energy, enthalpy etc.
  Mainly coz it's weird to have something called totalDensity that does not include all phases present.

i would say totalDensity is kind of reserved for fluid total density

yeah, I actually don't like the name totalDensity for the fluid mixture one. But at the end of the day as long as we are consistent, it's fine.