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SUMMARYA new finite element technique is developed for predicting the velocity and the pressure in transient incompressible viscous fluid flows at high Reynolds numbers. The new method is based on the generalized and simplified marker-and-cell met hod (GSMAC) and has two characteristics: one is an application of the Bernoulli function and the implicit pressure solution algorithm to the explicit fractional time step method, the other is a high-order flux calculation to prevent the pressure field from oscillating. Two examples, driven cavity flows at high Reynolds numbers and vortex shedding behind a circular cylinder, are presented. Satisfactory agreement with experiment is demonstrated.KEY WORDS GSMAC finite element method Incompressible Navier-Stokes solver High Reynolds number Driven cavity flow Vortex shedding behind a circular cylinder

The purpose of the present study is to clarify the mechanism of drag reduction for a sphere with arc type dimples. The sphere has 328 dimples of different depths uniformly distributed on its surface. The present study measured the pressure and velocity distributions inside and between the dimples, and visualized the flow on the sphere surface by an oil film method. The results indicated that separation bubbles were generated inside the dimples and transformed a laminar boundary layer into a turbulent boundary layer. Compared to a smooth sphere, the critical Reynolds number decreased and the separation point shifted further downstream. Therefore, the drag coefficient of a dimpled sphere was smaller than that of a smooth sphere. The magnitude of the decrease in the critical Reynolds number was found to increase with dimple depth. However, the separation point shifted to the upstream side and the drag coefficient became larger in the super-critical Reynolds number region.

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