This paper presents an efficient treatment of fluid/elastic–structure interactions that takes advantage of the Fourier representation of immersed boundaries. We assume that the fluid is incompressible with uniform density and viscosity and that the immersed boundaries have fixed topologies. These elastic bodies can have large deformations and evolve anywhere within the fluid domain. They may be...

In this paper, a hybrid computational aero/hydro-acoustic approach is proposed to deal with acoustic scattering and flow-induced noise problems based on the sharp interface immersed boundary method (IBM). For flow field, incompressible Navier–Stokes equations are solved by an in-house direct numerical simulation solver. The field predicted solving perturbation (APEs). Both solid boundaries comp...

In this paper, numerical methods are proposed for some interface problems in polar or Cartesian coordinates. The new methods are based on a formulation that transforms the interface problem with a non-smooth or discontinuous solution to a problem with a smooth solution. The new formulation leads to a simple second order finite difference scheme for the partial differential equation and a new in...

The immersed boundary method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. Immersed boundary computations typically evaluate the elastic forces explicitly in the configuration of the immersed elastic structure. In many applications this results in a severe restriction on the time step. We present a semi-implicit and a fully impli...

We prove that uniform accuracy of almost second order can be achieved with a finite difference method applied to Navier-Stokes flow at low Reynolds number with a moving boundary, or interface, creating jumps in the velocity gradient and pressure. Difference operators are corrected to O(h) near the interface using the immersed interface method, adding terms related to the jumps, on a regular gri...

In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite element methods disappears unless the discontinuity of the coefficient is resolved by partition. We show that immersed finite element solutions inherit all desir...

A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids. The interface is represented by a cubic spline along which the singularly supported elastic or surface tensio...