Nonlocal Artificial Boundary Conditions for the Incompressible Viscous Flow in a Channel Using Spectral Techniques

for linear partial differential equations in cylinders, which was applied to solve some nonlinear problems. In this paper the numerical simulation of the steady incompressible viscous flow in a no-slip channel is considered. A sequence The purpose of this paper is to design nonlocal artificial of approximate nonlocal artificial boundary conditions on a given boundary conditions for steady incompressible viscous flow segment artificial boundary is derived by a system of linearized in the vorticity streamfunction formulation in the case Navier–Stokes equations and spectral techniques. Then the original when the domain is a no-slip channel. We introduce twoproblem is reduced to a boundary value problem in a bounded segment artificial boundaries in the physical domain. The computational domain. The numerical examples show that these artificial boundary conditions are very effective and are also more spectral Chebyshev Tau method [14] is used to design the accurate than Dirichlet and Neumann boundary conditions, which artificial boundary condition. Then the original problem is are often used in the engineering literature. Q 1996 Academic Press, Inc. reduced to a problem on a bounded computational domain. Finally numerical examples show that the artificial boundary conditions given in this paper are very effective.