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The convection and diffusion are the basic processes in fluid flow and heat& mass transfer. The upwind and evolution functions for the convection term are introduced to give a comprehensive transformation to one-dimensional unsteady convection-diffusion equation involving source term. The corresponding compact fourth-order finite difference methed is developed. With the trans formation, the authors overcome the difficultyin dealing with the convection term, and the high-order expression for the convection-diffusion term can be conveniently obtained. The proposed difference scheme with thefourth-order accuracy and unconditional stability can fully reflect the upwind and evolutioneffects of the convection. The calculated results show that the errors of the referencescheme are 600 or 6000 times those of the proposed scheme for the same computationalgrid. With the one time decrease of the space grid, the errors of the proposed scheme andthe reference scheme reduce about 20 times and 2 times respectively. It is evident that theaccuracy of the proposed scheme is remarkably higher than that of the reference scheme.
The convection and diffusion are the basic processes in fluid flow and heat & mass transfer. The upwind and evolution functions for the convection term are introduced to give a comprehensive transformation to one-dimensional unsteady convection-diffusion equation involving source term. The respective compact fourth- order finite difference methed is developed. With the trans formation, the authors overcome the difficulty of dealing with the convection term, and the high-order expression for convection-diffusion term can be derived. The proposed difference scheme with the fourth-order accuracy and unconditional stability can fully reflect the upwind and evolutioneffects of the convection. The calculated results show that the errors of the referencescheme are 600 or 6000 times those of the proposed scheme for the same computationalgrid. With the one time decrease of the space grid, the errors of the proposed scheme and the reference scheme reduce about 20 times and 2 time s respectively. It is evident that theaccuracy of the proposed scheme is remarkably higher than that of the reference scheme.