High-order Exponential Methods For Solving Unsteady Convection-diffusion Equation

Unsteady convection-diffusion equation is a kind of basic equations of motion. There are a variety of methods for solving the unsteady convection-diffusion equation, such as finite difference method, finite element method, finite volume method and so on. But it will be trapped to solve the numerical solution of convection-diffusion equation due to the asymmetric wind effect of convection item, when the fluid convection term in the equation is dominant.In this paper, a high-order exponential method for solving unsteady convection-diffusion equation is developed based on literature[27]. There are the fourth-order compact exponential difference formula for the spatial discretization and the (2,2) Pade approximation for the temporal discretization, four-order accuracy in temporal and spatial variables can be achieved and the scheme is unconditional stable. The results of numerical experiments is verified the accuracy and reliability of the method. The author respectively used division method and direct derivation method to solve two dimensional unsteady convection-diffusion equation, and proved the stability of the constructed difference scheme, numerical examples is verified the effectiveness of the established difference scheme.