We study a 2D and a 3D incompressible magnetohydrodynamic (MHD) channel flow, also known as Hartmann flow, which is electrically conducting and subject to an external transverse magnetic field. We consider periodic boundary condition along one axis (two axis, for the three-dimensional case). We consider the flow at low magnetic Reynolds number and obtain the so-called simplified magnetohydrodyn...

0021-9991/$ see front matter 2012 Elsevier Inc http://dx.doi.org/10.1016/j.jcp.2012.04.017 ⇑ Corresponding author. Tel./fax: +86 10 6278 16 E-mail address: [email protected] (B.-Y. Ca A uniform momentum source-and-sink scheme of nonequilibrium molecular dynamics (NEMD) is developed to calculate the shear viscosity of fluids in this paper. The uniform momentum source and sink are realized by...

A large number of differential equation problems which admit traveling waves are usually defined on very large or infinite domains. To numerically solve these problems on smaller subdomains of the original domain, artificial boundary conditions must be defined for these subdomains. One type of artificial boundary condition which can minimize the size of such subdomains is the absorbing boundary...

A method is presented for planning obstacle-avoiding paths for a system which exhibits nonholonomic constraints. The method is based on the use of harmonic functions. Linear constraints on the velocity of a nonholonomic system can be directly expressed as Neumann boundary conditions for a harmonic function. Such boundary conditions are easily represented in a resistive network. The resulting po...

We derive general conditions of slip of a fluid on the boundary. Under these conditions the velocity of the fluid on the immovable boundary is a function of the normal and tangential components of the force acting on the surface of the fluid. A problem on stationary flow of an electrorheological fluid in which the terms of slip are specified on one part of the boundary and surface forces are gi...

In this paper, we study strong solutions to the steady compressible heat-conductive fluid near a non-zero constant flow with the Dirichlet boundary condition for the velocity on the inflow and outflow part of the boundary. We also consider the Dirichlet boundary condition for the temperature, and we do not need the thermal conductivity coefficient κ to be large. The existence of strong solution...

Boundary value problems for steady-state flow in elastoplasticity are a topic of mathematical and physical interest. In particular, the underlying PDE may be hyperbolic, and uncertainties surround the choice of physically appropriate stress and velocity boundary conditions. The analysis and numerical simulations of this paper address this issue for a model problem, a system of equations describ...

I apply Fourier and Chebyshev spectral methods to derive accurate and efficient algorithms for velocity continuation. As expected, the accuracy of the spectral methods is noticeably superior to that of the finite-difference approach. Both methods apply a transformation of the time axis to squared time. The Chebyshev method is slightly less efficient than the Fourier method, but has less problem...

A diffusion’s induced transport is defined for a linear model of a Fokker-Plank equation under periodic boundary conditions in one-dimensional geometry. The flow is generated by a diffusion and a periodic deriving force induced by a velocity potential. An inverse problem is suggested for evaluating the deriving force in terms of the response function associated with the flow. It is also shown t...

A numerical procedure for the determination of equivalent grid block permeability tensors for heterogeneous porous media is presented. The method entails solution of the fine scale pressure equation subject o periodic boundary conditions to yield, upon appropriate averaging of the fine scale velocity field, the coarse scale or equivalent grid block permeability. When the region over which this ...