Re: [sparta-users] [EXTERNAL] 2d axi with global weight cell radius/only + adapt_grid

[<pi...@rt...>]

Thank you Michael for your feedback,

I first answer your questions, then iterate on your suggestions with a 
few questions. I added some notations at the end if some figures are not 
self explanatory.

The figures not attached with this email are available here: 
https://drive.proton.me/urls/QF4YQJ25B8#dWlg2z6lhC2B

1) Answer to questions:

a) Time step

In the simulation I presented the results in my previous email, I took a 
time step of 0.008 times the mean collision time of the free-stream 
conditions, so: 9.96e-06 sec. For all the 2D/3D simulations at these 
conditions, this is small enough in my experience.

Here are the conditions:

rho                    : 9.64e-08 kg/m3
n                      : 2.13271410878877e+18
Tov                    : 247  K
vx                     : 7500  m/s
vy                     : -0  m/s
vz                     : 0   m/s
fnum                   : 929853604014801
lambda free-stream     : 0.592513992703437 m
timeStep               : 9.96344920141672e-06 sec

With the setup described in my last email, including the grid adaption 
described below (1c), I have tried some large variations in time step 
but there are not much differences as 
ML110_grid_adaptation_mfp__time_step_convergence.png shows

b) Number of particles

With the setup described in my last email, including the grid adaption 
described below (1c), I have tried some large variations in the number 
of particles but there are not much differences as 
ML110_grid_adaptation_mfp__particles_convergence.png shows.

c) Grid adaptation

I have adapted the grid between 0.5 and 0.25 the local mean free path 
using:

_ compute             cLambdaS lambda/grid f_nrho[*] f_ftemp[*] N2 kall_
_ adapt_grid          all refine coarsen value c_cLambdaS[2] 2 4 combine 
min thresh less more maxlevel 12 cells 2 2 1_

 From what I have tested, that kind of adaptation is working well in 2D 
and 3D even though some cells/cut-cell end up having only a few 
particles - or less than 1 - on average. Here it does not.

2) Discretization error

Based on your remark regarding the discretization error, I assume that 
grid adaptation strategy 1c) is not possible for 2D axi computation. So 
I changed the adaptation strategy to only refine/coarsen the grid based 
on the number of particles using:

_ adapt_grid          all refine coarsen particle 60 15 combine min 
thresh less more maxlevel ${maxlevel} cells 2 2 1_

Then I did carry out a convergence study both for the number of 
particles and time step. The results are illustrated in 
ML110_grid_adaptation_particles__particles_convergence.png and 
ML110_grid_adaptation_particles__time_step_convergence.png

a) Convergence in number of particles

Sparta converged toward what looks like a good enough solution. But the 
convergence is especially difficult near the stagnation area. That area 
shows a large dependency with the number of particles. The 2D axi case 
that models a sphere requires much more particles to converge (SP2048) 
than the identical geometry but in 2D (not 2D axi) that models a 
cylinder : SP128 or less is enough. I have not much experience in 
axisymmetric DSMC computation, so that is a surprising result to me ! Do 
you have any comments on this ? For exemple a strategy to avoid that 
extra need for a large number of particles for 2D axi simulation ?

b) Difference between the 2D axi case and the 3D case

There are some differences between the 3D simulations and the 2D axi 
one, both simulated with sparta as illustrated in 
ML110_grid_adaptation_particles.png for clarity. This is especially true 
for the friction and the heat rate. I used a 2 deg discretization for 
the meshes of both setup (2D axi and 3D) and full accommodation as wall 
BC. The 3D results from sparta matches also well with the other code (3D 
run). Any thoughts on how to improve further the 2D axi results with 
respect to the 3D ones ?

3) Figure notation:

- Cf: friction coefficient

- Cp: pressure coefficient

- Cq: heat coefficient

- SP1024 : FNUM such that 1024 simulation particles are in a cubic cell 
of length the mean free path (mfp) of the free-stream conditions

- dt0.008: time step

- "Sparta 3D" : results carried out with the same script but adapted 
from 3D using dt0.008 and SP128

- ref : solution from another DSMC code

Thank you in advance for you answer and best regards,

Pierre