PATCHING METHODS IN FLUID MECHANICS

Abstract

The thesis comprises six chapters. In the thesis a new method has been deduced to solve Navier- Stokes equations for compressible and incompressible fluid flows the results have been compared to those resulted by using Beam and Warming techniques. In the first chapter exhibits most of the known methods in question such as

1- The Non- Primitive variable Approach

(i)The Velocity- Vorticity Approach

(ii)The Vorticity- Stream function Approach

2- The Primitive variable Approach

(a) The Artificial Compressibility Approach

(b) The Primitive- Variable Approach with Pressure Poisson Equation

(c) Compatibility Condition

(d) The present Approach

In the second chapter the Navier- Stokes equations are derived together with the continuity equation, momentum equation and energy equation. In the third chapter the author shows the way of deriving a new method in two-dimensional and in three- dimensionai(Cartesian and generalized curvilinear coordinate systems) , in the foUowing cases:-