Vesicle suspensions appear in many biological and industrial applications. These suspensions are characterized by rich and complex dynamics of vesicles due to their interaction with the bulk fluid, and their large deformations and nonlinear elastic properties. Many existing state-of-the-art numerical schemes can resolve such complex vesicle flows. However, even when using provably optimal algorithms, these simulations can be computationally expensive, especially for suspensions with a large number of vesicles. These high computational costs can limit the use of simulations for parameter exploration, optimization, or uncertainty quantification. One way to reduce the cost is to use low-resolution discretizations in space and time. However, it is well-known that simply reducing the resolution results in vesicle collisions, numerical instabilities, and often in erroneous results. In this paper, we investigate the effect of a number of algorithmic empirical fixes (which are commonly used by many groups) in an attempt to make low-resolution simulations more stable and more predictive. Based on our empirical studies for a number of flow configurations, we propose a scheme that attempts to integrate these fixes in a systematic way. This low-resolution scheme is an extension of our previous work [51,53. Our low-resolution correction algorithms (LRCA) include anti-aliasing and membrane reparametrization for avoiding spurious oscillations in vesicles’ membranes, adaptive time stepping and a repulsion force for handling vesicle collisions and, correction of vesicles’ area and arc-length for maintaining physical vesicle shapes. We perform a systematic error analysis by comparing the low-resolution simulations of dilute and dense suspensions with their high-fidelity, fully resolved, counterparts. We observe that the LRCA enables both efficient and statistically accurate low-resolution simulations of vesicle suspensions, while it can be 10× to 100× faster.
Kabacaoğlu, G., Quaife, B., & Biros, G. (2018). Low-resolution simulations of vesicle suspensions in 2D. Journal of Computational Physics, 357, 43–77. https://doi.org/10.1016/j.jcp.2017.12.023