ISSN:
0271-2091
Keywords:
Incompressible flows
;
Navier-Stokes equations
;
Primitive variables
;
Vorticity-Streamfunction
;
Compatibility conditions
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
This paper deals with the non-stationary incompressible Navier--Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H1 for the velocity, as in most current numerical schemes relying on spatial discretizations of local type.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650180504
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