الفهرس 
chapter 1Only 14 pages are availabe for public view
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Abstract
An exponential high order compact (EHOC) finite difference scheme for solving constant and variable coefficients steady convection-diffusion equations has been
developed for 3-dimentional space. The standard numerical methods perform poorly when there are sharp boundary and/or internal layers in the solution caused by the dominated convective coefficients. In this work, we show that the fundamental singularity in solution of a convection-dominated convective-diffusion equation is
independent on the right hand side of the equation and that the homogeneous equation itself is responsible for this singularity. The proposed EHoe scheme has the two features. firstly, it provides very accurate solution (exact in case of constant convection coefficients in ID) of the homogeneous equation while approximates the
particular part of the solution by fourth order accuracy. Secondly, it is a compact scheme. The key properties of this scheme are its stability, accuracy and efficiency so that high gradients near the boundary layers can be effectively resolved even on
coarse uniform meshes.
Application of the proposed EHOe scheme for convection diffusion equations IS
extended to solve the streamfunction-vorticity form of 2D steady viscous
incompressible Navier-Stokes equation which is a nonlinear system of partial
differential equations.
To validate the present scheme, a number of linear and non-linear problems, mostly with boundary or internal layers are solved. To demonstrate that the proposed scheme
is fourth order, comparisons are made for various convection-diffusion problems with known analytical solutions. In addition, comparisons are made between numerical results for the present EHOe scheme and other available methods in the literature.
The EHOe scheme produces excellent results for all test problems.