一类变系数非稳态对流扩散方程的四阶紧致差分格式

A Fourth-order Compact Difference Scheme for Unsteady Convection-diffusion Equations with Variant Coefficients

针对一类变系数非稳态对流扩散问题,构造了一种四阶Runge-Kutta高阶紧致有限差分格式.该格式具有时空四阶收敛精度,即O(h4,4τ),而且构造方法简单、易推广应用到其他问题.最后给出数值算例验证了所提出方法在求解非齐次对流扩散问题上的有效性和可靠性.

A fourth-order Runge-Kutta CFD scheme is constructed for a class of unsteady convection-diffusion equations with variant coefficients.The proposed method has fourth-order accuracy both in space and time variables,i.e.O（h4,τ4）.The scheme is constructed simply and effectively,and this scheme is easy to be applied in other equations.Numerical experiments are performed to test its high accuracy,reliability and efficiency in solving convection-diffusion equations.