Curvilinear Domains Research Articles

Chebyshev pseudospectral solution of the incompressible Navier-Stokes equations in curvilinear domains

A pseudospectral method for the calculation of 2-D flows of a viscous incompressible fluid in curvilinear domains is presented. The incompressible Navier-Stokes equations, expressed in terms of the primitive variables velocity and pressure, are solved in a non-orthogonal coordinate system. All the variables are expanded in double truncated series of Chebyshev polynomials. Time integration is performed by an implicit finite differences scheme for both the advective and diffusive terms. The pressure is calculated by the use of a truncated influence matrix involving all the collocation points in the field. A preconditioned iterative method is used to solve the system of linear equations resulting from the pseudospectral Chebyshev approximation. The algorithm is applied to the classical problem of the Green-Taylor vortices in order to check its accuracy; then 2 examples of viscous flow calculation are given in the case of a driven polar cavity and of a 2-D channel.

A saint-venant principle for the gradient in the Neumann problem

The maximum principle for subharmonic functions is used to obtain upper bounds for the gradient in the Neumann problem of potential theory. These bounds, which concern a curvilinear strip domain having nonzero boundary data only on an end, entail an exponential decay of the gradient magnitude with distance from that end.