64th IUVSTA workshop - arrata and comments

Introduction

Dear participants of the 64th IUVSTA workshop,

at the workshop I presented DSMC results for the benchmark problems. Some of these resutls were significantly different (+17%) compared to the results presented by Prof. Sharipov. Prof. Sharipov is using his own implementaiotn of the DSMC method. There is a simple explanation for this deviation: different model parameters. The purpose if this communication is to demonstrate that PI-DSMC can produce the same results as Prof. Sharipov if the same model parameters are used.

The readers who are not familiar with the benchmark problems can find the definition of the problems here, here and here.
The presentation given at the workshop can be downloaded here.

Channel - 2D planar

Let me discuss the channel cases first. The molecular species for all benchmark problems is helium. The gas temperature is 300K.

Prof. Sharipov used the hard sphere model while I used the variable hard sphere model (VHS) as a model for the helium molecules. The hard sphere model is the most simple model that is not valid for real gases. The VHS model, developed by Dr. Bird, is more sophisticated as the collision cross section depends on the relative velocity. This diference in the model parameters exlains the deviation in the calculated mas flow rate for benchmark cases 1-15.

The VHS model was also used for the benchmark cases 16-20. After checking the configuration file, I realized that I did not define the geometry correctly. The ratio between channel width and channel diameter was 0.5 instead of 1. The obtained results for a ratio of 1 and molecules modeled as hard spheres is shown in the table below. The computation time is given for the most demanding cases (16-20). The remaning cases can be solved in less time, e.g. all cases with delta=100 can be solved in less time than case 20.

case W CPU time [min]
16 0.342 24
17 0.349 87
18 0.406 121
19 0.812 114
20 1.337 1409








Conlusions

First of all I want to make clear that PI-DSMC produces results that are in very good agreement with the results obtained by Prof. Sharipov. The results of Prof. Sharipov in turn agree very well with the results presented by Prof. Titarev who used numerical methods to solve the kinetic equation.

Sincerely yours,
Martin Rose