Can on-grid bounce-back scheme be made second-order accurate?

Lattice Boltzmann Method LBM: Theory
#1

Hi,

I have a question regarding on-grid bounce-back scheme. Given that it is a first-order scheme, it is not accurate enough in dealing with large Reynolds number flows. However, if one is using a complex geometry then this would be the simplest scheme to apply. And I am dealing with large Reynolds number flows in complex geometries. So, are there ways to make on-grid bounce-back scheme second-order? Any references would be helpful.

Thanks,
SK

#2

Hi,

According to Succi’s book, the very similar mid-grid bounceback is second-order accurate.

With the on-grid bounceback, particles will stream into a wall node, and then get turned around in the collision step, before streaming back in the next time step. With the mid-grid bounceback, particles that are set to stream into a wall node are simply turned around. You can consider this equivalent to the particles streaming halfway to the wall node before being reflected back by a wall halfway between the fluid node and the wall node.

Succi’s book has more details on this, though!

#3

Hi Erlend,

Thanks for the reply. I was thinking in terms of the ease with which the mid-grid bounce back can be applied. For example, if one is solving for flow in a porous medium, it would be far easier to apply on-grid bounce back because one does not have to worry about the orientation of the wall; but in case one wants to apply mid-grid bounce back then it’s more difficult owing to the orientation. So, I was wondering if on-grid bounce-back could somehow be made second-order – but I guess I am asking for too much.

I shall check Succi’s book.

Thanks and best wishes,
Srikanth