非定常对流扩散方程的高阶差分格式

对流扩散方程主要包含对流和扩散两项。在数值计算中，方程中的扩散项一般采用具有优良物理特性和计算精度的中心差分离散格式，而对对流项的处理就稍显困难，处理不当便会产生数值震荡或数值弥散，给数值计算带来困难。针对对流扩散方程，通过引入指数变换将对流扩散方程变为扩散方程，避免对对流项的直接处理。利用四阶紧致差分格式，首先建立三类特殊方程的高精度差分格式，在此基础上建立一维非定常含源对流扩散方程的高阶格式，并进行稳定性分析，所得格式精度高且绝对稳定。数值算例表明了该格式的有效性。

Highly Accurate Difference Scheme for the Unsteady Convection-Diffusion Equation

Convection-diffusion equation mainly contains two terms—convection and diffusion.In the numerical calculation,central difference scheme,with excellent physical properties and high accuracy is often employed to discretize the diffusion term,which has been fully able to meet the requirements for most practical problems,but somewhat difficult to handle convective term.If handled improperly,it will produce numerical oscillation or numerical dispersion,which will bring difficulties to the numerical calculation.To avoid handling the convection term directly,we change the convection-diffusion equation into a diffusion equation with an exponential transformation.According to fourth-order compact difference scheme,three types of special high-precision differential equation schemes are established firstly,then the process of the establishment of onedimensional unsteady convection diffusion equation with source term is derived with stability analysis.The scheme has high precision and absolute stability.In the end,the numerical result shows the effectiveness of the scheme.