On The Mathematical Solution Of
2D Navier Stokes Equations For
Different Geometries
Author(s)
M. A. Mehemed Abughalia
Abstract
Some analytical solutions of the 1D Navier Stokes equation are introduced in the
literature. For 2D flow, the analytical attempts that can solve some of the flow
problems sometimes fail to solve more difficult problems or problems of
irregular shapes. Many attempts try to simplify the 2D NS equations to ordinary
differential equations that are usually solved numerically. The difficulties that
are associated with the numerical solution of the Navier Stokes equations are
known to the specialists in this field. Some of the problems associated with the
numerical solution are; the continuity constraint, pressure–velocity coupling and
other problems associated with the mesh generation. This drives the generation
of many schemes to simplify and stabilize the 2D Navier Stokes equations. The
exact solution of the Navier Stokes equations is difficult and possible only for
some cases, mostly when the convective terms vanish in a natural way. This
paper is devoted to studying the possibility of finding a mathematical solution of
the 2D Navier Stokes equations for both potential and laminar flows. The
solutions are a series of functions that satisfy the Navier Stokes equations. The
idea behind the solutions is that the complete solution of the 2D equations is a
combination of the solutions of any two terms in the equations; diffusion and
advection terms. The solution coefficients should be determined through the
boundary conditions.
Keywords: Navier Stokes equations, incompressible flow, fluid flow, Newtonian
fluids, potential flow, laminar flow, mathematical solution, steady state.
1 Introduction
Since the Navier and Stokes derived the mathematical modeling of the fluid in
motion; Navier Stokes equations, the mathematical solution have been
Keywords
Navier Stokes equations, incompressible flow, fluid flow, Newtonian
fluids, potential flow, laminar flow, mathematical solution, steady state.
Related Book
Other papers in this volume
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