An Indirect-Forcing Immersed Boundary Method for Incompressible Viscous Flows with Interfaces on Irregular Domains (Communications in Computational Physics, 2020)
An indirect-forcing immersed boundary method for solving the incompressibleNavier-Stokes equations involving the interfaces and irregular domains is developed.The rigid boundaries and interfaces are represented by a number of Lagrangiancontrol points. Stationary rigid boundaries are embedded in the Cartesian grid andsingular forces at the rigid boundaries are applied to impose the prescribed velocityconditions. The singular forces at the interfaces and the rigid boundaries are then distributedto the nearby Cartesian grid points using the immersed boundary method. Inthe present work, the singular forces at the rigid boundaries are computed implicitlyby solving a small system of equations at each time step to ensure that the prescribedvelocity condition at the rigid boundary is satisfied exactly. For deformable interfaces,the forces that the interface exerts on the fluid are computed from the configurationof the elastic interface and are applied to the fluid. The Navier-Stokes equations arediscretized using finite difference method on a staggered uniform Cartesian grid by asecond order accurate projection method. The ability of the method to simulate viscousflows with interfaces on irregular domains is demonstrated by applying to therotational flow problem, the relaxation of an elastic membrane and flow in a constrictionwith an immersed elastic membrane.