Modeling of hydrodynamic dispersion and two-phase flow in the complex variable boundary element method Original Research Article

This study aims at extending the applicability of the complex variable boundary element method (CVBEM) to convective–dispersive flow and simultaneous two-phase flow problems. In order to utilize the analytical solutions obtained for one-dimensional (1D) problems, two-dimensional (2D) flow is decomposed into flow along multiple 1D streamlines. Varying velocity along the streamlines can be taken into account with the aid of a series of coordinate transformations τ and ω, which are accurately evaluated by the CVBEM. The complete 2D solution is recovered by composing the individual 1D solutions. For convective–dispersive flow, tracer concentration profiles and effluent concentration curves are directly constructed from the Gelhar–Collins solution. For two-phase flow, displacing fluid profiles and recovery efficiency curves are directly constructed from the self-similar solution. The numerical results for example problems confirm that the developed model enables flow computations devoid of discretization effects.