Many-body hydrodynamics

[johnaparker]

In the current implementation, the hydrodynamics are pair-wise interactions. The mobility matrix M is constructed pair-wise, and the velocity in over-damped systems is V = M * F. To include many-body hydrodynamics, the mobility matrix must be extended to include higher stress-lets in the fluid field expansion. Then the larger mobility matrix is inverted to obtain the grand resistance matrix, R, which is then truncated to only translational and rotational stress-lets. The truncated R is then inverted to obtain the final mobility M, which now includes many-body terms.

Implementation

• Literature review to find the equations for the higher order stress-let terms
• Construct the larger mobility matrix, M (and allow an option to not include higher order stress-lets)
• Construct the final M by inverted and truncated R, and inverted again to obtain M

References

Brady and Bossis - Stokesian Dynamics.pdf
pages 123-128