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Home  >  Volume 21 (2012)

Simulation of Hamiltonian Function for Contaminant Fluid Flow by I.M. Echi, A. N. Amah, and E. Anthony Volume 21 (July, 2012), pp 121 – 134
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Hamiltonian function for the transport of contaminants was constructed and simulated for different forms of flow velocities and diffusion models. The flow velocities vary in space and time while the diffusion models are functions of contaminant concentration leading to nonlinearity in the transport equation for the contaminant distribution. Explicit space centre and forward time finite difference approximation was applied to solve the equations. Graphical outputs of the contaminant distribution in space and time for the space varying carrier velocity show that diffusion plays significant role in the contaminant distribution in the half integer and one quarter  power models, where the peclet number is greater than unity contrary to the prediction of linear theory. Advection dominates the contaminant distribution only when the peclet number, Pe is of several orders of magnitude greater than unity (Pe =149,  229). In the harmonic diffusion models and space varying advection both diffusion and advection contribute to contaminant distribution when Pe < 1, which according to linear theory should be diffusion, dominated.

Keywords: Hamiltonian, Advection, Diffusion, Contaminant and models