Simple ball drop, huge impact of time step

[Yves ROBERT]

Hello,

I wanted to verify that my time step was right in my "ball drop" simulations. in DEM-Engine.

One minimal example I created is attached. I just drop one ball in a 5 meter-high box from z=2m with a null velocity. Then, I record and plot the velocity and elevation of the ball over time. 

Here are some examples attached, with dt=1e-4, 1e-5, 2e-5, 3e-5, and 5e-5 seconds.

What I found is that the behavior of the ball is completely different between different time steps: the bounces can make the ball go higher than its initial position, which breaks the energy conservation. Even stranger, setting a very small time step also leads to that issue. 

Here, I do not know which one should be taken as true, dt=1e-5s seems good, but if I double the time step there are still bounces, just lower. Here this is for a very simple example, but that tells me that there is too much variability in the results based on the time step. 

Therefore, I was wondering: is there an issue with my test? If not, how do we know the time step we are setting is hitting the sweet spot: not too low, not too large? Is there a criterion we can use? And finally, can DEM-Engine adapt its time step automatically to prevent the user to play with that value when it might produce unrealistic behaviors?

Thanks!

[Ruochun Zhang]

Hi Yves,

This is expected. The step sizes 1e-4, 5e-5, and 3e-5 you used gave unphysical responses since they were not fine enough to capture the collision. Past those, it becomes better. I'd like to note that the test scenario is challenging to begin with, since the ball impacts with a high velocity and the wall stiffness is very high (2.5e11 Pa), making the contact difficult to resolve. I am not surprised at all that it requires a step size as small as 1e-5s. You should try smaller step sizes too, and they should converge to a specific bouncing pattern, and this is perhaps the way to find an appropriate step size to use (the largest one that gives this "converged" bouncing).

In reality, the vast majority of DEM simulations use artificially reduced stiffness to relax the physics, with empirically decided step sizes. The rule is trying to ensure that the contact events are resolved with no less than 4 time steps (but more is even better), but it's not always necessary to do separate tests to find that out. Reasonable bulk metrics like total energy or max velocity are sometimes enough of an indicator of good simulations, plus many simulations have main physics driven by prolonged contacts like grinding rather than "hard" collisions, making resolving "worst" contacts like the collisions that happen only in parts of the simulation not a big concern. 

You probably know that DEM-Engine has the method UpdateStepSize to allow for on-fly step size change, should the physics change significantly at different parts of your simulation which mandates an update on the step size. However, that is manual and requires that you have an idea of the appropriate step size. As for automatic step size adaption, it is a bigger engineering problem, and the way I plan to implement that involves a complex prerequisite subsystem too (I won't spoil it). It will not be there too soon, because the testing needed to show it is a meaningful mechanism sounds like a full paper to me.

Thank you,

Ruochun

[Yves ROBERT]

Thank you, Ruochun, for your answer.

That makes sense. Is there a common criterion (equation) for determining the max velocity/Young's modulus vs. the time step?

In addition, what are common wall properties that people would use? In my field, the ball properties are extensively discussed, but the wall properties are never.

Thank you!

[Ruochun Zhang]

Hi Yves,

The particle size and the physics model come into play in determining the step size, too. There might also be other factors. So using velocity and stiffness alone is not enough to decide. However, if you already know the proper step size for a set of properties, then you can perhaps empirically decide how the step size should change if you change the properties. For example, an increase in the max velocity should linearly decrease the required step size. That's how I typically do it.

For the wall properties, I don't see it being governed by different rules other than the particles', should you need to relax the physics. The underlying contact model is the same.

Thank you,

Ruochun

[Yves ROBERT]

Ruochun,

That is much clearer, thank you!

I will relax the Young's modulus,  and try to run some tests to have a correct range of time steps for my application.

Thanks!