Lubricated Immersed Boundary Method: Numerical Analysis, Benchmarking, and Applications

Brandeis University, Waltham MA

Investigators

Abstract

Fluid-structure interaction is common in biological problems and engineering applications. In many cases of interest, such as red blood cell motion through the microcirculation and the opening and closing of the heart valves, small-scale fluid flows between structures in near-contact are important for the overall behavior. The presence of multiple scales in these problems poses challenges for both modeling and simulation. Whereas existing methods such as adaptive mesh refinement use algorithmic techniques to bridge these scales and incur significant computational costs, here the research develops an alternative method in which the governing equations are replaced at small scales by a much simpler asymptotic limit. The goal of this project is to develop an improved version of the immersed boundary method that uses lubrication theory to model fluid flows between structures in near contact. The immersed boundary method is a widely used approach for modeling fluid-structure interaction. A longstanding limitation of this method is that structures that are in near contact tend to stick together, so that they require unphysically large forces to separate. The lubricated immersed boundary method uses lubrication theory as a subgrid model to overcome this difficulty of the classical method. Because lubrication theory is exact in the limit that the spacing between two structures goes to zero, the accuracy of the subgrid model improves as structures come closer together. This research analyzes and benchmarks the lubricated immersed boundary method. Specific aims include performing a multiscale numerical analysis, developing efficient implementations in three dimensions, and investigating higher-order accurate extensions based on the immersed interface method. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.