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ABSTRACT
The solution of the Navier-Stokes equations by finite differences method is presented. Various concepts are presented as well as the mathematical model governing the behavior of a fluid; particular cases of formulation of the Navier-Stokes equations are indicated. Two distinct formulations are considered to solve the target problem; on the one hand the current- vorticity formulation to compute a 2D flow where one has to solve simply a Poisson equation coupled to a convection-diffusion equation. Another method also allows to solve the target equations formulated in velocity-pressure. In both cases the numerical analysis of the algorithms is presented. The last part presents the solution of the Navier-Stokes equations in turbulent regime.
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Pierre SPITERI: Professor Emeritus - University of Toulouse, INP – ENSEEIHT – IRIT, Toulouse, France
INTRODUCTION
The Navier-Stokes equations model many of the phenomena involved in flow studies. These include flows in the cooling circuits of boilers and jet engines, the external aerodynamics of vehicles such as automobiles, trains and airplanes during take-off, the internal aerodynamics of engines, particularly in nozzles and combustion chambers, the study of blood flow in veins in cardiology, and to some extent, weather forecasting, ocean currents, hydrology, etc.
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KEYWORDS
current-vorticity formulation | convection-diffusion equation | behavior of a fluid | formulation velocity-pressure
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Numerical solution of the Navier-Stokes equations using the finite difference method
Mathematical model of a compressible or incompressible fluid
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