Geodesic
Vorticity dynamics and numerical resolution of Navier-Stokes equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 2, pp. 313-330

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We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data for some test cases to which we apply the computational scheme.

Classification : 35Q30, 65M06, 76D17
Keywords: Navier-Stokes equations, vorticity-streamfunction, numerical algorithm, vorticity boundary conditions 
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     author = {Ben-Artzi, Matania and Fishelov, Dalia and Trachtenberg, Shlomo},
     title = {Vorticity dynamics and numerical resolution of {Navier-Stokes} equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {313--330},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {2},
     year = {2001},
     mrnumber = {1825701},
     zbl = {0987.35122},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_2_313_0/}
}
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Ben-Artzi, Matania; Fishelov, Dalia; Trachtenberg, Shlomo. Vorticity dynamics and numerical resolution of Navier-Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 2, pp. 313-330. http://geodesic.mathdoc.fr/item/M2AN_2001__35_2_313_0/