Numerical solutions of 2-dimensional burgers equation with finite difference methods

This thesis consists of six chapters. In the introduction chapter, some information about the aim of this study is presented. In the second chapter, after introducing classical finite difference methods, an application of the method has been carried out on 2-dimensional heat conduction equation to understand the method better. Moreover, after explaining von Neumann stability analysis, the stability analysis of finite difference schemes obtained by the application of the classical finite difference methods to 2-dimensional heat conduction equation. In the third chapter, after presenting the literature survey of 2-dimensional Burgers' equation, the problems with two different initial and boundary conditions are introduced. In the fourth chapter, numerical solutions of the model problems are obtained using classical explicit, implicit and Crank-Nicolson finite difference methods. The obtained results are compared with exact and other numerical results available in the literature. Moreover, the stability analysis of the weighted-average approximation for the 2-dimensional Burgers' equation has been made. The fifth chapter constitutes the original part of this thesis. In this section, numerical solutions of the model problems are obtained using different linearization techniques in place of the nonlinear terms UUx and UUy existing in the 2-dimensional Burgers' equation. The newly obtained results are compared with exact and other numerical results available in the literature. Moreover the numerical results obtained for FDA2 are presented graphically. In the sixth chapter, the error norms L2 and L∞ for all approximation taken into consideration in this thesis are compared and outstanding methods are determined.