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The application of a finite element scheme to full three-dimensional (3D) incompressible viscous flow around a circular cylinder is presented in this paper. The scheme is based on the Petrov-Galerkin weak formulation using exponential weighting functions and on the second-order accurate Adams-Bashforth strategy as a time integration. As a typical example of the problems, flow around a circular cylinder involving an interesting phenomenon of the drag crisis is performed numerically. Numerical results demonstrate the workability and the validity of the present approach.

The application of a finite element scheme to three-dimensional Rayleigh-Benard convection in a horizontal fluid layer heated from below is presented. The scheme is based on the Petrov-Galerkin weak formulation using exponential weighting functions. The incompressible Navier-Stokes equations and energy equation with the Boussinesq approximation are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth scheme for both convection and diffusion terms. Numerical results obtained are compared through the Rayleigh-Benard convection of air for Rayleigh numbers up to 87300 with the experimental data and other existing numerical data, and demonstrate the workability and validity of the present approach.

In previous papers, we proposed finite element schemes based on the Petrov-Galerkin weak formulation using exponential weighting functions for solving accurately, and in a stable manner, the flow field of an incompressible viscous fluid. In this paper, we present the Petrov-Galerkin finite element scheme for turbulent flow fields based on large eddy simulation using the standard Smagorinsky model with the Van Driest damping function. The filtered incompressible Navier-Stokes equations are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth explicit differencing for both convection an diffusion terms. In order to evaluate more accurately a mass matrix, the well-known multi-pass algorithm was also adopted in this study. Numerical results obtained are compared through flow around a rectangular cylinder at Re = 22,000 with the experimental data and other existing numerical data.