We present an immersed interface method for solving the incompressible Navier– Stokes equations with discontinuous viscosity across the interface and singular forces. The method is based on the augmented strategy proposed by Li, Ito, and Lai [Comput. Fluids, 36 (2007), pp. 622–635] to decouple the jump conditions of the fluid variables through the introduction of two augmented variables. In the...

The jump is defined as [∇u · n] = ∇u · n +∇u ·n where u = u|Ω± and n is the unit outward pointing normal to Ω (see figure 1). Also, we denote [u] = u − u. Many numerical methods have been developed for problem (1.1). Perhaps the most notable ones are the finite difference method of Peskin [18] (i.e., immersed boundary method) and the method of LeVeque and Li [11] (i.e., the immersed interface m...

Recent progress at IIHR on the development of CFDShip-Iowa version 6 is presented. Current focus is on a sharp interface Cartesian grid method for the large-eddy simulation (LES) of turbulent two-phase incompressible flows. In this method, the level set formulation for two-phase incompressible flows is adopted. The density and pressure jump conditions across the interface (the latter due to sur...

A new sharp-interface immersed boundary method based approach for the computation of low-Mach number flow-induced sound around complex geometries is described. The underlying approach is based on a hydrodynamic/acoustic splitting technique where the incompressible flow is first computed using a second-order accurate immersed boundary solver. This is followed by the computation of sound using th...