Abstract
The primary difficulty encountered in the numerical solution of non-Fickian diffusion problems is numerical oscillations in the vicinity of sharp discontinuities. The present study applies a hybrid numerical scheme of the Laplace transform technique and the controlvolume method in conjunction with the hyperbolic shape functions to investigate the one-dimensional non-Fickian diffusion problems in the presence of a potential field for finite or semi-infinite geometry. The Laplace transform method used to remove the time-dependent terms in the governing differential equation and boundary conditions, and then the transformed equations are discretized by the control-volume scheme. To show the accuracy of the present numerical method, a comparison of the mass concentration distribution between the present numerical results and the analytic solutions is made. Results show that the present numerical results agree well with the analytic solutions and do not exhibit numerical oscillations in the vicinity of the jump discontinuity for various potential values. The potential gradient dV/dx has a great effect on the mass concentration distribution. The strength of the jump discontinuity is reduced as the value of the dimensionless potential gradient is increased.
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