Abstract Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities are well-known
pathways towards turbulent mixing layers, in many cases characterized by significant mass …

In these lecture notes we describe the construction, analysis, and application of ENO
(Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for …

Instability of flows and their transition to turbulence are widespread phenomena in
engineering and the natural environment, and are important in applied mathematics …

A level set formulation is derived for incompressible, immiscible Navier–Stokes equations
separated by a free surface. The interface is identified as the zero level set of a smooth …

A numerical method for computing Stokes flows in the presence of immersed boundaries
and obstacles is presented. The method is based on the smoothing of the forces, leading to …

The flapping or bending of a flexible planar structure in a surrounding fluid flow, which
includes the flapping of flags and the self-streamlining of flexible bodies, constitutes a …

We present experimental force and power measurements demonstrating that the power
required to propel an actively swimming, streamlined, fish-like body is significantly smaller …

The authors introduce a new concept of measure-valued solution for the 3-D incompressible
Euler equations in order to incorporate the complex phenomena present in limits of …

The initial-value problem for perturbations of a flat, constant-strength vortex sheet is linearly
ill posed in the sense of Hadamard, owing to Kelvin-Helmholtz instability. Previous …

A “Hamilton-Jacobi” level set formulation of the equations of motion for propagating
interfaces has been introduced recently by Osher and Sethian. This formulation allows fronts …