| The Immersed Boundary method has long been used to study fluid-structure interaction problems, particularly in biological applications but increasingly with an engineering focus as well. Despite this success, the IB method has presented a number of challenges to practitioners. Due to the large stiffness of the elastic forces involved, the timestep has been severely restricted in explicit discretizations (and even in many implicit discretizations) in order to maintain stability. Because the computed velocity field in which the immersed boundary moves is not continuously divergence-free, fluid can leak across pressurized membranes and this can result in a lack of volume conservation for closed pressurized objects. In addition to the constraint of incompressibility that makes the Navier-Stokes equations difficult to solve, coupling the immersed boundary positions and forces to the fluid velocity increases the difficulty of solving the equations. Solving the fully coupled system of equations can be computationally expensive, but using an explicit discretization to decouple the system can result in a severe timestep restriction that also results in high computational cost.; For some of these challenges, methods have been introduced to fix the problem, but these methods have not been widely adopted due to various drawbacks. For other challenges, solutions have proved elusive. This dissertation explores each of these challenges and presents new solutions for each of them. |
