A HIGHT-ORDER COMBINED COMPACT UPWIND DIFFERENCE SCHEME FOR SOLVING 1D UNSTEADY CONVECTION-DIFFUSION EQUATION
Zhao Bingxin (Department Mechanics and Engineering Science,Fudan University,Shanghai 200433,China; School of Mathematics and Computer Science,Ningxia University,Yinchuan 750021,China)
A fourth-order combined compact upwind(CCU) finite difference scheme was proposed for solving 1D unsteady convection-diffusion equation.Convection terms were discretized by combined fourth-order and fifth-order compact upwind schemes.Viscous terms were discretized by fourth-order compact symmetric finite difference scheme.After that,the semi-discretized equation was solved by fourth-order Runge-Kutta formula in time.The truncation error of the CCU scheme is O(h~4 + t~4).Its excellent properties are proved by Fourier analyses and three numerical examples,which include linear and nonlinear convection-diffusion equations and rectangular wave problem.The results show that the CCU scheme is capable of capturing the minute physical changes for its high resolution,and is applicable to high Reynolds number problems.
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