This paper discusses boundary conditions appropriate to a theory of single-crystal plasticity (Gurtin, 2002) that includes an accounting for the Burgers vector through energetic and dissipative dependences on the tensor G = curlH, with H the plastic part in the additive decomposition of the displacement gradient into elastic and plastic parts. This theory results in a flow rule in the form of N...

The general form of Maxwell’s velocity slip boundary condition for rarefied gas flows depends on both the geometry of the surface and the constitutive relations used to relate the viscous stress to rate of strain. The dependence on geometry is often overlooked in current rarefied flow calculations, and the generality of the constitutive dependence means the condition can also be usefully applie...

The Navier-Stokes equations for the motion of compressible, viscous fluids in the half-space R+ with the no-slip boundary condition are studied. Given a constant equilibrium state (ρ̄, 0), we construct a global in time, regular weak solution, provided that the initial data ρ0,u0 are close to the equilibrium state when measured by the norm |ρ0 − ρ̄|L∞ + |u0|H1 and discontinuities of ρ0 decay near ...

The Navier-Stokes equations for the motion of compressible, viscous flows with the no-slip boundary condition are considered. We study the problem of determining the evolution of the interface of discontinuity of a piece-wise smooth density when the interface is in transversal contact with the boundary of the domain. A unique global solution near a static constant equilibrium is constructed. Th...

We design an artificial boundary condition for the steady incompressible Navier-Stokes equations in streamfhction-vorticity formulation in a flat channel with slip boundary conditions on the wall. The new boundary condition is derived fiom the Oseen equations and the method of lines. A numerical experiment for the non-linear Navier-Stokes equations is presented. The artificial boundary conditio...

A new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion. Like previous methods, a boundary force is applied at the immersed surface to satisfy the no-slip constraint. This extra constraint can be added to the incompressible Navier–Stokes eq...

The development of rotor flow associated with mountain lee waves is investigated through a series of highresolution simulations with the nonhydrostatic Coupled Ocean–Atmospheric Mesoscale Prediction System (COAMPS) model using free-slip and no-slip lower boundary conditions. Kinematic considerations suggest that boundary layer separation is a prerequisite for rotor formation. The numerical simu...