Historically, boundary fitted grids have been used to model complex geometries. The authors are investigating a novel grid generation concept, Immersed Boundary Method, as an improved methodology to boundary fitted grids. There are two significant disadvantages to using a boundary fitted grid. First, whether structured or unstructured, fitting a grid to a complex geometry prevents the use of si...

The immersed boundary method has been extensively used to simulate the motion of elastic structures immersed in a viscous fluid. For some applications, such as modeling biological materials, capturing internal boundary viscosity is important. We present numerical methods for simulating Kelvin-Voigt and standard linear viscoelastic structures immersed in zero Reynolds number flow. We find that t...

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...

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...

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...

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the p...

Peskin’s Immersed Boundary Method has been widely used for simulating many fluid mechanics and biology problems. One of the essential components of the method is the usage of certain discrete delta functions to deal with singular forces along one or several interfaces in the fluid domain. However, the Immersed Boundary Method is known to be first-order accurate and usually smears out the soluti...

A strongly coupled algorithm is presented for the incompressible fluid–rigid body interaction using moving immersed boundary method. The pressure and force are treated as Lagrange multipliers to enforce incompressibility no-slip wall constraints. To compute two unknowns from velocity field, we adopt fractional step successively apply Poisson equation a derived force, respectively. As both coeff...