Navier-Stokes equations for incompressible fluids
In this short chapter, the Navier-Stokes equations governing the motion of a viscous incompressible fluid are recalled. Two formulations are considered: the velocity-pressure formulation (also called “primitive variables” formulation) and the vorticity-streamfunction formulation. The formulation using vorticity and velocity as dependent variables will not be addressed here. This formulation, commonly used with finite-difference methods, has not yet received large attention in the field of spectral methods. However, recent works (Clercx, 1997; Trujillo and Karniadakis, 1999) have shown that Chebyshev solutions of the vorticity-velocity equations could be envisaged with success.
KeywordsCompatibility Condition Incompressible Fluid Vorticity Vector Associate Boundary Condition Outflow Boundary Condition
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