Unsteady viscous flow over a grooved wall: A comparison of two numerical methods

Abstract

SUMMARYA numerical study is made of the unsteady two-dimensional laminar flow of an incompressible fluid over a periodically grooved wall. Two independent finite difference techniques are employed. One is based on the vorticity-stream function and the other on the vorticity-velocity (i.e. induction law) formulation. The fluid motion is initiated impulsively from rest and is assumed to be spatially periodic in the streamwise direction. The numerical formulations are derived in detail. The generation of vorticity at the solid surface is modelled differently in the two approaches, and this is found to play an important role in determining the surface pressure distribution and the drag coefficient. The flow field is examined during the early transient phase of development, during which the greatest changes occur. Results are presented for a moderate Reynolds number (based on groove depth) equal to 100. It is found that the vorticity-stream function approach does not produce a spatially periodic wall pressure distribution, and therefore global conservation of total vorticity is not achieved. This results in substantial errors in the predictions for the drag coefficient. These deficiencies are not found in the results obtained by the vorticity-velocity formulation.

Time‐dependent natural convection in a square cavity: Application of a new finite volume method

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Accuracy considerations for implementing velocity boundary condiditons in vorticity formulations

“…The above formulations rely on kinematics to describe vorticity creation. Other approaches use dynamics (the Navier-Stokes equations) on the boundary (Kinney et al [16], [13], Wu (J.-Z.) [43]).…”