Efficient Iterative Algorithms for Linear Stability Analysis of Incompressible Flows

Linear stability analysis of a dynamical system entails finding the rightmost eigenvalue for a series of eigenvalue problems. For large-scale systems, it is known that conventional iterative eigenvalue solvers are not reliable for computing this eigenvalue. A more robust method recently developed in Elman & Wu (2012) and Meerbergen & Spence (2010), Lyapunov inverse iteration, involves solving large-scale Lyapunov equations, which in turn requires the solution of large, sparse linear systems analogous to those arising from solving the underlying partial differential equations. This study explores the efficient implementation of Lyapunov inverse iteration when it is used for linear stability analysis of incompressible flows. Efficiencies are obtained from effective solution strategies for the Lyapunov equations and for the underlying partial differential equations. Existing solution strategies are tested and compared, and a modified version of a Lyapunov solver is proposed that achieves significant savings in computational cost

Optimal Design of Bacterial Carpets for Fluid Pumping

In this work, we outline a methodology for determining optimal helical flagella placement and phase shift that maximize fluid pumping through a rectangular flow meter above a simulated bacterial carpet. This method uses a Genetic Algorithm (GA) combined with a gradient-based method, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, to solve the optimization problem and the Method of Regularized Stokeslets (MRS) to simulate the fluid flow. This method is able to produce placements and phase shifts for small carpets and could be adapted for implementation in larger carpets and various fluid tasks. Our results show that given identical helices, optimal pumping configurations are influenced by the size of the flow meter. We also show that intuitive designs, such as uniform placement, do not always lead to a high-performance carpet

Optimal Design of Bacterial Carpets for Fluid Pumping

In this work, we outline a methodology for determining optimal helical flagella placement and phase shift that maximize fluid pumping through a rectangular flow meter above a simulated bacterial carpet. This method uses a Genetic Algorithm (GA) combined with a gradient-based method, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, to solve the optimization problem and the Method of Regularized Stokeslets (MRS) to simulate the fluid flow. This method is able to produce placements and phase shifts for small carpets and could be adapted for implementation in larger carpets and various fluid tasks. Our results show that given identical helices, optimal pumping configurations are influenced by the size of the flow meter. We also show that intuitive designs, such as uniform placement, do not always lead to a high-performance carpet