Three-Dimensional Eulerian-Lagrangian Transport Model

by A. K. M. Quamrul Ahsan, HydroQual, Inc, Mahwah, United States,
M. S. Bruno, HydroQual, Inc, Mahwah, United States,

Abstract: An Eulerian-Lagrangian algorithm, based on operator-splitting techniques has been formulated for the three-dimensional advection-diffusion equation. This combines the advantage of a fixed Eulerian grid and computationally powerful Lagrangian technique. Using the operator splitting algorithm, the full transport equation has been split into two successive initial value problems of pure advection and pure diffusion. For the advection equation, solutions are found by the Backward Method of Characteristics (BMC) and for the diffusion equation, an Alternating Direction Implicit (ADI) scheme is employed. Lagrangian solution of the advection equation involves the tracking of characteristics lines backward in time from a fixed Eulerian nodal point. A tri-cubic hermitian interpolation scheme is used to interpolate the concentration and its derivatives at the foot of the characteristic lines. Amplitude and phase error portraits for the Backward Method of Characteristics have been constructed using the von Neumann fourier analysis. Extensive numerical testing has been performed, with results compared to solutions obtained by analytical and other existing numerical techniques.

Subject Headings: Advection | Three-dimensional models | Sediment transport | Algorithms | Diffusion | Numerical analysis | Lagrangian functions

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