Methods for suspensions of passive and active filaments

Flexible filaments and fibres are essential components of important complex fluids that appear in many biological industrial settings. Direct simulations these systems capture the motion deformation immersed suspension remain a formidable computational challenge due to complex, coupled fluid--structure interactions all filaments, numerical stiffness associated with filament bending, various constraints must be maintained as deform. In this paper, we address challenges by describing kinematics using quaternions resolve both bending twisting, applying implicit time-integration alleviate stiffness, quasi-Newton methods obtain solutions resulting system nonlinear equations. particular, employ geometric time integration ensure unit move. We also show our framework can used variety models methods, including matrix-free fast low Reynolds number hydrodynamic interactions. provide series tests example demonstrate performance possible applications method. Finally, link MATLAB/Octave implementation learn more about approach tool for simulation.