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A LOCALLY CONSERVATIVE STREAMLINE METHOD FOR A MODEL TWO-PHASE FLOW PROBLEM
 

Summary: A LOCALLY CONSERVATIVE STREAMLINE METHOD
FOR A MODEL TWO-PHASE FLOW PROBLEM
IN A ONE-DIMENSIONAL POROUS MEDIUM
TODD ARBOGAST, CHIEH-SEN HUANG, AND THOMAS F. RUSSELL
Abstract. Motivated by possible generalizations to more complex multiphase multicomponent
systems in higher dimensions, we develop a numerical approximation for a system of two conservation
laws in one space dimension modeling two-phase flow in a porous medium. The method is based on
tracing streamlines, so it is stable independent of any CFL constraint. The main difficulty is that it is
not possible to trace individual streamlines independently. We approximate streamline tracing using
local mass conservation principles and self-consistency. The two-phase flow problem is governed by
a system of equations representing mass conservation of each phase, so there are two local mass
conservation principles. Our numerical method respects both of these conservation principles over
the computational mesh (i.e., locally), and so is a fully conservative streamline method. We present
numerical results that demonstrate the ability of the method to handle problems with shocks and
rarefactions, and to do so with very coarse spatial grids and time steps larger than the CFL limit.
Key words. advection-diffusion, characteristics, streamlines, local conservation, two-phase,
shocks, rarefactions
1. Introduction. We consider the problem of numerical approximation of a
system of two conservation laws modeling two-phase flow in a one-dimensional porous
medium. We develop a streamline method with particular attention given to local

  

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

 

Collections: Mathematics; Geosciences