Clarification Needed: Time Step Calculation in MUSEN Documentation

[juwoha]

Hello everyone,

i would like to seek clarification regarding the time step calculation described in the simulator.pdf documentation for musen. The document states:

• "For the systems which are consisting only from primary particles, the recommended time step is calculated based on Rayleigh time $$T_{Rayleigh}$$."
• "If the scene consists of primary particles, as well as solid bonds, the recommended simulation time step is calculated as 10% of $$\min{(T_{Rayleigh}, T_{sim,bond})}$$."

The equations provided are as follows:

$$\Delta t_{sim,recom} = T_{Rayleigh} = \min{{ \frac{\pi R_i \sqrt{2 \rho_{i} (1 + \nu_{i}) }}{\sqrt{E_i} (0.163\nu_i + 0.8766)}}}$$

$$\Delta t_{sim,recom} = 0.1 \min{{T_{Rayleigh}, T_{sim,bond}}}$$

However, it seems that the recommended time step calculated within musen is always $$0.1 T_{Rayleigh}$$, regardless of whether bonds are being used or not.

I created a test case using the standard glass material from the materials database. For a simulation with a single sphere of diameter $D = 1 mm (R = 0.0005 m), E = 5e10Nm^{-2}, \rho =2500 kg m^{-3}$ and $\nu = 0,22$ i calculate a recommended time step of $T_{Rayleigh} = 6,01e-07 s$. However the recommended time step within musen is 6,01e-08 s.

Test Case

Here is a simple test that you can import as text to check this behavior. After deleting the bond, the recommended time step remains the same.

0 0 1 1 5 0.0005 0.0005 23 KF6843H84OPHH3017U3D 24 0 1e+300 2 0 16 0 0 0 12 0 0 0 20 0 0 0 18 0 31 0 1 0 0 42 0 0 0 36 0 0 0 0 0 0 0 0 0 37 0 15 0 0 0 
0 1 1 1 5 0.0005 0.0005 23 KF6843H84OPHH3017U3D 24 0 1e+300 2 0 16 0 0 0 12 0.001 0 0 20 0 0 0 18 0 31 0 1 0 0 42 0 0 0 36 0 0 0 0 0 0 0 0 0 37 0 15 0 0 0 
0 2 1 9 5 0 1 0.0005 0.001 23 KF6843H84OPHH3017U3D 24 0 1e+300 2 0 12 0.0005 0 0 20 0 0 0 18 0 45 0 0 0 37 0 43 0 15 0 0 0 
22 -0.0007 -0.0006 -0.0006 0.00172 0.00061 0.00061 
28 0 0 0 0 -0.005 -0.005 -0.005 0.005 0.005 0.005 
29 0 
30 0 
32 KF6843H84OPHH3017U3D Glass 0 2500 2 1e+40 7 5e+10 8 5e+07 9 5e+07 10 0.22 11 1 12 2e-05 13 0.7 14 1.7e-05 15 2e+10
33 KF6843H84OPHH3017U3D KF6843H84OPHH3017U3D 200 0.9 201 0.45 202 0.05 
40 0 2 

Am I making a mistake somewhere? I would be very happy if someone could clarify.

Environment:
Windows 10
MUSEN version 1.74.1 installed via open setup installer

Many thanks and best regards

[vasylskorych]

Hi, @juwoha, I fixed the docu, here are the currently used equations. The recommended step is calculated as
$dt_{recommended}=0.1 * min(T_{Rayleigh}, T_{bond})$
So, if you calculate $T_{Rayleigh}=6.01e-7$, then the recommended time step should indeed be 0.1 * 6.01e-7 = 6.01e-8.
Now, the bonds. Currently, $T_{bond} > T_{Rayleigh}$, so the bond does not have influence. Change the material of the bond to Steel, and you will notice the changes in the recommended time step.

[juwoha]

Dear Vasyl,

I think I was partially confused by the small error in the formula as well as my poor English. I understood the term "as well as" as "and" or "plus", not "both X or Y".

Thank you for your remarks! The uncertainty is gone, so the topic can be closed.