Vorticity dynamics and numerical resolution of Navier-Stokes equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 2, p. 313-330

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
@article{M2AN_2001__35_2_313_0,
     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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {2},
     year = {2001},
     pages = {313-330},
     zbl = {0987.35122},
     mrnumber = {1825701},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2001__35_2_313_0}
}
Ben-Artzi, Matania; Fishelov, Dalia; Trachtenberg, Shlomo. Vorticity dynamics and numerical resolution of Navier-Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 2, pp. 313-330. http://www.numdam.org/item/M2AN_2001__35_2_313_0/

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