How Does Particle Spacing Affect SPH Simulations of Seismic Behavior?

[CarlFaberge]

Hello Everyone,

I'm trying to solve the following Problem:

(taken from "SPH simulation for seismic behavior of Earth structures" - Y.Ono et. al)

To this end, I wrote a small MATLAB skript, to be found here. The paper presents results at t=10s and t=20s:

which my solution reproduces quite accurately if i set kh (the ratio from particle spacing to smoothing length) to 1:

(snapshot taken at t=20)

However, as soon as I increase kh the solution quickly deteriorates:

(kh=2, snapshot taken at t=5).

Currently, I think that this is due to the boundary deficiency of SPH. That is, increasing h will lead to larger deficient boundary regions like so:

reconstruction of the derivative of a sine function, top with kh = 2, bottom with kh=8. Code.

I already tried to:
- assign densities according to

- adapt h according to h_p = h_init*(rho_init/rho_p), using the densities computed with the formula above
- introduce CSPM corrections (even though the paper clearly states that the problem should be solvable employing "vanilla" sph only).

I would be very grateful for any input.

PS: I hope this is the right subforum

EDIT: In case anybody was wondering about the kernel

 

[KataKoniK]

used, it is the Gaussian kernel with compact support.

Hi there,

First of all, great job on writing the MATLAB script and reproducing the results from the paper! It's always exciting to see someone actively working on solving scientific problems.

Now, onto your question. It seems like you have already tried a few different approaches to improve the accuracy of your solution, such as adjusting the particle spacing and introducing CSPM corrections. This is definitely a good start, and it shows that you are thinking critically about the problem.

One potential solution could be to use a different kernel function that has better boundary properties, such as the cubic spline kernel or the quintic spline kernel. These kernels have a smoother transition at the boundary and may help to reduce the boundary deficiency that you are observing.

Another approach could be to increase the number of particles in your simulation. This would result in a higher resolution and potentially improve the accuracy of your solution.

I would also recommend checking your boundary conditions and making sure they are properly incorporated into your simulation. Sometimes, boundary conditions can be a source of error in simulations.

Lastly, I would suggest reaching out to the authors of the paper and asking for their input. They may have some insights or suggestions based on their experience with the problem.

Best of luck and keep up the good work!