Evaluation of time integration schemes for discrete particle-fluid simulations

The average or continuum level behavior of suspensions is investigated by modeling of discrete particles and time-averaging their behavior. Because of the long-range behavior of the Stokes equations, this system has to account for multi-particle interactions that are not pair-wise additive. While there are several methods to account for such interactions, the boundary element method converges to an exact representation of the multi-particle dynamics as the mesh density increases. What has not been determined is how good these simulations have to be in order to capture the relevant physics for the continuum level behavior.

To adequately benchmark the BEM model, a transient 3-D problem with an analytical solution is necessary. Such a problem for two smooth spheres has been given by DaCunha and Hinch in 1996. Using numerical approximations to this solution, the effect of time integration schemes on this system was investigated. Because most modem codes use adjustable time-step algorithms that limit the local time integration error in an attempt to control the global integration error, the dependence of the global error on the local error was determined. While this analysis is valid for two spheres and does raise possible concerns about the multi-particle dynamics, it does not give quantitative number for multi-particle BEM simulations. Possible future work will be outlined that extends the analysis presented in this thesis work from two-particle systems to many-particle systems that are more representative of real suspensions. The requirements and a suggested method will be discussed.