1. Introduction. Recently A. Chorin has found a numerical scheme for solving the Navier-Stokes equations which has the pleasing feature of not breaking down at high Reynolds numbers R [5]. The purpose of this announcement is to present a formula «2) below) which is designed to establish the convergence of Chorin's time step iteration procedure, assuming that the relevant equations (heat equatio...

We propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. The scheme is based on the general ideas proposed in [1] for the two dimensional incompressible Navier-Stokes equations and is then extended to three space dim...

The usual time integration approach for solving steady viscous free surface flow problems has several drawbacks. We propose instead an efficient iterative method, which relies on a different but equivalent formulation of the free surface flow problem, involving a so-called quasi free-surface condition. Furthermore, we present a method for analyzing the properties of wave solutions of the discre...

A new Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite-element Galerkin approximation, which can be shown to be equivalent to a finite-volume approximation for regular equilateral triangular meshes. Integration to steady state is performed using a multistage time-stepping scheme, and conv...

A new high spectral accuracy compact difference scheme is proposed here. This has been obtained by constrained optimization of error in spectral space for discretizing first derivative for problems with non-periodic boundary condition. This produces a scheme with the highest spectral accuracy among all known compact schemes, although this is formally only second-order accurate. Solution of Navi...

In the current study, the effects of interactions of the moving loads and the attached mass-spring-damper systems of the composite plates on the resulting dynamic responses are investigated comprehensively, for the first time, using the classical plate theory. The solution of the coupled governing system of equations is accomplished through tracing the spatial variations using a Navier-type sol...

In this paper, we describe recent developments in the design and implementation of Navier-Stokes solvers based on nite element discretization. The most important ingredients are residual driven a posteriori mesh reenement, fully coupled defect-correction iteration for linearization, and optimal multigrid precondi-tioning. These techniques were systematically developed for computing incompressib...