چكيده به لاتين
The motion equations for a fluid are known as the Navier-Stokes equations. In general, the problem of finding exact solutions of the Navier-Stokes equations presents insurmountable mathematical difficulties. This is primarily due to the fact that these equations are nonlinear. The Navier-Stokes equations cover a wide variety of problems, depending on the use of different physical conditions and their various applications. An important category of these problems is named as the stagnation point flow. The stagnation flow has been studied during past decades because of technical importance in many industrial applications.
In this thesis, an efficient and precise spectral method known as the rational Chebyshev collocation (RCC) approach has been developed to solve the stagnation flow problems. In this research, the technique of using this method has been shown in the analysis of two important categories of stagnation flow problems, including stagnation flow on a flat plate with a semi-infinite interval [0, ∞], and a stagnation flow on a cylinder with a semi-infinite domain [1, ∞].
The Navier-Stokes equations which govern the stagnation flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper similarity transformations and this nonlinear differential equation has been analyzed using the rational Chebyshev collocation method. This approach would reduce the nonlinear ordinary differential equation solution to the solution of a system of algebraic equations. Using this method to solve boundary value problems on infinite or semi-infinite intervals, effectively and efficiently eliminates the defects in other numerical methods, such as truncating the domain or dependence of the results on the value of the initial guess, and provides very good results.
The comparison between the numerical results provided by other references, the fourth-order Runge-Kutta and approximated by this study for two categories of the stagnation flow problems, indicates that the results of the RCC approach are in good agreement with other methods. This shows the validity of the current method for boundary value problems.
Also, in this thesis, by presenting the definitions for spectral series convergence, the exponential convergence of the spectral series used in the two present problems has been shown.
