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A FULLY CONSERVATIVE EULERIAN-LAGRANGIAN STREAM-TUBE METHOD FOR
 

Summary: A FULLY CONSERVATIVE EULERIAN-LAGRANGIAN
STREAM-TUBE METHOD FOR
ADVECTION-DIFFUSION PROBLEMS
TODD ARBOGAST, CHIEH-SEN HUANG, AND CHEN-HUI HUNG
Abstract. We present a new method for the linear advection-diffusion problem, the fully conser-
vative Eulerian-Lagrangian stream-tube method. It combines the volume corrected characteristics-
mixed method (VCCMM) with the use of a stream-tube mesh. It has the advantages that it is fully
locally conservative (both tracer and ambient fluid mass is conserved locally), has low numerical dif-
fusion overall and no numerical cross diffusion between stream-tubes, can use very large time steps
(perhaps 20 to 30 times the CFL limited step), and can use a very coarse mesh, since it is tailored
to the flow pattern. Because advection is approximated within stream-tubes, it is essentially one di-
mensional, making it relatively easy to implement and computationally efficient. The new method is
important to many applications, but especially to flow and transport in porous media, such as in the
modeling of groundwater contaminant migration, petroleum production, and carbon sequestration.
Key words. Eulerian-Lagrangian, stream-tube, finite volume, locally conservative, characteris-
tics, hyperbolic transport, porous media
1. Introduction. We consider the linear hyperbolic transport problem in which
one component (say a tracer) is advected and diffuses within an ambient fluid. For
such problems, characteristic or Eulerian-Lagrangian (or semi-Lagrangian) methods
have the advantages that long time steps can be used without loss of stability, nu-

  

Source: Arbogast, Todd - Center for Subsurface Modeling & Department of Mathematics, University of Texas at Austin

 

Collections: Mathematics; Geosciences