We show that, for solutions of a model of two-dimensional, viscous, compressible fluid flow, curves which are initially transverse to the spatial boundary and across which the fluid density is discontinuous become tangent to the boundary instantaneously in time. We also show by similar techniques that, for the Euler equations of two-dimensional, inviscid, incompressible flow and for a large cla...

We study the flow of an incompressible viscous fluid through a long tube with compliant walls. The flow is governed by a given time-dependent pressure drop between the inlet and the outlet boundary. The pressure drop is assumed to be small, thereby introducing creeping flow in the tube. Stokes equations for incompressible viscous fluid are used to model the flow, and the equations of a curved, ...

The transient motion and the heat transfer of a viscous incompressible flow contained between two vertically eccentric spheres maintained at different temperatures and rotating about a common axis with different angular velocities is numerically considered when the angular velocities are an arbitrary functions of time. The resulting flow pattern, temperature distribution, and heat transfer char...

Unsteady Couette flow of a viscous incompressible fluid between two horizontal porous flat plates is considered. The stationary plate is subjected to a periodic suction and the plate in uniform motion is subjected to uniform injection. Approximate solutions have been obtained for the velocity and the temperature fields, skin friction by using perturbation technique. The heat transfer characteri...

In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity ω0 and the circulation γ of the initial flow around the obstacle. We prove that, if γ is sufficiently small, the limit flow satisfies the full-plane Navier-Stokes system, with initial vorticity ω0 + γδ, where δ is the standard Dirac measure. ...

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. ”. In this study, we revisit the problem of reversed stagnation-point flow over a flat plate. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. This is no true in neglecting the vi...

The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic viscous magnetohydrodynamic equations to the weak solutions of the incompressible viscous magnetohydrodynamic equations is proved as the density becomes constant...

Capillary forces determine the shape of a liquid interface. Although often not considered, elastic solids with a free surface are also subjected to surface forces and these become important for materials of low Young's modulus. Here we consider two equivalent problems where a capillary free surface deforms due to vortices: (i) in a steady viscous flow [solved by Jeong and Moffatt, J. Fluid Mech...

This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier–Stokes equations with mixed boundary conditions containing the pressure. The minimization problem of total dissipated energy was established in the fluid domain. We derive the structures of shape gradient of the cost functional by using the differentiabil...

A Projection Method for Incompressible Viscous Flow on a Deformable Domain by David Paul Trebotich Doctor of Philosophy in Mechanical Engineering University of California, Berkeley Professor Phillip Colella, Chair 1 A second-order accurate finite difference method is presented for numerical solution of the incompressible Navier-Stokes equations on a deformable domain. The target problem is flow...