A Novel Velocity-Vorticity Method for Simulating Boundary-Layer Disturbance Evolution and Control
For a wide class of wall-bounded incompressible fluid flows it is possible to derive a system of governing equations that involves only two vorticity transport equations, for two vorticity components, together with a Poisson equation for a single velocity component. This system of three equations in three unknowns remains fully equivalent to the usual primitive variables form of the Navier-Stokes equations. The reduction in the number of equations to be solved and the number of variables that require storage makes the formulation attractive for computational purposes. In addition, some difficulties that are associated with more conventional velocity-vorticity formulations can be avoided.
The utility of the new formulation has been demonstrated by numerical simulations conducted for disturbance development and control in boundary-layers involving steady suction and blowing slots, interactive MEMS devices, compliant surfaces and absolute instability.
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