In addition to an overview of the immersed boundary/continuum methods and their finite element formulations, explicit vs. implicit and incompressible vs. compressible issues are discussed. The recent finite element formulations retain the same strategies employed in the original immersed boundary method, namely, the independent Lagrangian solid mesh moves on top of a fixed or prescribed backgro...

The immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a (visco-)elastic structure. In [M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, 1998; M...

Article history: Received 4 May 2013 Received in revised form 11 March 2014 Accepted 4 April 2014 Available online 18 April 2014

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and eve...

The immersed boundary method is a practical and effective method for fluid–structure interaction problems. It has been applied to a variety of problems. Most of the timestepping schemes used in the method are explicit, which suffer a drawback in terms of stability and restriction on the time step. We propose a lattice Boltzmann based implicit immersed boundary method where the immersed boundary...

Peskin’s Immersed Boundary (IB) method is one of the most popular numerical methods for many years and has been applied to problems in mathematical biology, fluid mechanics, material sciences, and many other areas. Peskin’s IB method is associated with discrete delta functions. It is believed that the IB method is first order accurate in the L∞ norm. But almost none rigorous proof could be foun...

Abstract   The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier-Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to some other similar ...

In the present study, an immersed boundary (IB) method for the simulation of flow around a thin flexible body is presented. The present method is based on a discrete-forcing immersed boundary method proposed by Kim et al. (JCP, 2001). The dynamic equation for a thin flexible body is coupled with the incompressible Navier-Stokes equations. With the proposed method, we simulate several flow probl...

Aerodynamic sound generation at low Mach numbers around complex stationary and moving bodies is computed directly with an immersed-boundary method-based hybrid approach. The complex flow field is solved by the immersed-boundary incompressible Navier-Stokes flow solver and the sound generation and propagation are computed by the linearized perturbed compressible equations with a high-order immer...