Add P3 Sink Terms

[anastasia-popova]

Purpose

This PR aims to add the necessary collision sink terms to the P3 Scheme

To-do

Content

---

• I have read and checked the items on the review checklist.

[codecov]

Codecov Report

Attention: Patch coverage is 99.00000% with 1 line in your changes missing coverage. Please review.

Project coverage is 97.09%. Comparing base (f30e789) to head (63b479b).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #381      +/-   ##
==========================================
+ Coverage   96.96%   97.09%   +0.12%     
==========================================
  Files          37       37              
  Lines        1452     1550      +98     
==========================================
+ Hits         1408     1505      +97     
- Misses         44       45       +1     

Components	Coverage Δ
src	98.89% <99.00%> (+<0.01%)	⬆️
ext	69.79% <ø> (ø)

[trontrytel]

I think we need to make the integrals more complicated. This is because we want to use the 2M Seifert and Beheng scheme for the cloud and rain part. That means we should integrate overt the assumed 2M distributions for cloud and rain (instead of assuming continuous q). And for precipitation we need to consider the fact that rain has a terminal velocity of its own (see for example eq 25 in 1M docs.

I wrote down some notes, trying to keep the notation the same as in SB and P3 scheme docs pages:

[trontrytel]

In the 1M scheme we take the velocity difference out of the integral by approximating it by the mass weighted velocity difference. Thats one way of making this simpler. The alternative is to swicth to numerical integrals, and keep the velocities in the integral

[trontrytel]

Also, in the writeup, I'm not sure how the a(x, D) term would actually look for the different cross section regimes in P3. Do you have any ideas?

[trontrytel]

Do we have any ideas what to assume for the other particle regimes?

[anastasia-popova]

I do not have anything concrete. I was thinking finding some D' value for the regimes where the area is not in the form of D^2 such that D'^2 = D^sigma and then using D' in this calculation but I am not convinced that this would give us anything helpful.

[trontrytel]

I think it should be

Suggested change

	\frac{dq}{dt} = \frac{1}{2 \rho_a} \int_{0}^{\infty} \! \frac{dm(D)}{dt} N'(D) \mathrm{d}D
	\frac{dq}{dt} = \int_{0}^{\infty} \! \frac{dm(D)}{dt} N'(D) \mathrm{d}D

because in the P3 scheme q is in kg/m3 we don't need to divide by air density. Maybe it would be good to write the P3 variables as rho_air q. I think this way the notation bewteen P3 and the 1M and 2M schemes would actually be consistent and we could remove one of the todos

[trontrytel]

I can help revive this branch after #403 is merged. Lets see if we can make this work with limiters, or if we have to do without