We consider the free fall of a sphere above a wall in a viscous incompressible fluid. Weinvestigate the influence of boundary conditions on the finite-time occurrence of contactbetween the sphere and the wall. We prove that slip boundary conditions enable tocircumvent the ”no-collision” paradox associated with no-slip boundary conditions. Wealso examine the case of mixed bou...

A numerical scheme for treating fluid–land boundaries in inviscid shallow water flows is derived that conserves the domain-summed mass, energy, vorticity, and potential enstrophy in domains with arbitrarily shaped boundaries. The boundary scheme is derived from a previous scheme that conserves all four domain-summed quantities only in periodic domains without boundaries. It consists of a method...

We consider Laplace and Stokes operators in domains with rough boundaries and search for an effective boundary condition. The method of homogenization, coupled with the boundary layers, is used to obtain it. In the case of the homogeneous Dirichlet condition at the rough boundary, the effective law is Navier’s slip condition, used in the computations of viscous flows in complex geometries. The ...

A simple mechanical model and dimensional analysis are used to derive a scaling law for the partitioning between slip rate on a strike-slip fault and distributed deformation in the far-field. The depth of the fault, the distributions of stress, strain rate and slip rate are solved for a given far-field force or displacement in a 2-D medium with a linear temperature-dependent viscous rheology. A...

We consider 3D Navier-Stokes flows with no-slip boundary condition in an infinitely long pipe with circular cross section. The velocity fields we consider are independent of the variable parametrizing the axis of the pipe, and the component of the velocity normal to the axis is arranged to be circularly symmetric, though we impose no such symmetry on the component of velocity parallel to the ax...

Meshfree point collocation method is developed for the stream-vorticity formulation of two-dimensional incompressible Navier– Stokes equations. Particular emphasis is placed on the novel formulation of effective vorticity condition on no-slip boundaries. The moving least square approximation is employed to construct shape functions in conjunction with the framework of point collocation method. ...

Molecular dynamics (MD) and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate dependence of the intrinsic slip length in the flow over an atomically flat surface is computed by MD simulations. We describe laminar flow away from a curved boundar...