To develop an efficient numerical scheme for two-dimensional convection diffusion equation using Crank-Nicholson and ADI, time-dependent nonlinear system is discussed. These schemes are of second order accurate in apa...To develop an efficient numerical scheme for two-dimensional convection diffusion equation using Crank-Nicholson and ADI, time-dependent nonlinear system is discussed. These schemes are of second order accurate in apace and time solved at each time level. The procedure was combined with Iterative methods to solve non-linear systems. Efficiency and accuracy are studied in term of L2, L∞ norms confirmed by numerical results by choosing two test examples. Numerical results show that proposed alternating direction implicit scheme was very efficient and reliable for solving two dimensional nonlinear convection diffusion equation. The proposed methods can be implemented for solving non-linear problems arising in engineering and physics.展开更多
This paper presents a kind of new Crank-Nicolson difference scheme for one and two dimensional convection-diffusion equations. It also gives the alternating direction method for two-dimensional problems. Because the c...This paper presents a kind of new Crank-Nicolson difference scheme for one and two dimensional convection-diffusion equations. It also gives the alternating direction method for two-dimensional problems. Because the coefficient matrix formed by the scheme is always diagonally dominant, the scheme can be solved by general iteration method. In this paper, we prove that the new CN scheme for one dimensional problems is convergent with respect to discrete L^2 norm with orderO(△t^2+△th+h^2). We also prove that the new CN scheme for two dimensional problems is stable by discrete Fourier method. Finally, numerical examples show that the method in this paper is very effective for solving convection-diffusion equations.展开更多
文摘To develop an efficient numerical scheme for two-dimensional convection diffusion equation using Crank-Nicholson and ADI, time-dependent nonlinear system is discussed. These schemes are of second order accurate in apace and time solved at each time level. The procedure was combined with Iterative methods to solve non-linear systems. Efficiency and accuracy are studied in term of L2, L∞ norms confirmed by numerical results by choosing two test examples. Numerical results show that proposed alternating direction implicit scheme was very efficient and reliable for solving two dimensional nonlinear convection diffusion equation. The proposed methods can be implemented for solving non-linear problems arising in engineering and physics.
文摘This paper presents a kind of new Crank-Nicolson difference scheme for one and two dimensional convection-diffusion equations. It also gives the alternating direction method for two-dimensional problems. Because the coefficient matrix formed by the scheme is always diagonally dominant, the scheme can be solved by general iteration method. In this paper, we prove that the new CN scheme for one dimensional problems is convergent with respect to discrete L^2 norm with orderO(△t^2+△th+h^2). We also prove that the new CN scheme for two dimensional problems is stable by discrete Fourier method. Finally, numerical examples show that the method in this paper is very effective for solving convection-diffusion equations.
