 
Summary: A LOCALLY CONSERVATIVE STREAMLINE METHOD
FOR A MODEL TWOPHASE FLOW PROBLEM
IN A ONEDIMENSIONAL POROUS MEDIUM
TODD ARBOGAST, CHIEHSEN 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 twophase 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 selfconsistency. The twophase 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. advectiondiffusion, characteristics, streamlines, local conservation, twophase,
shocks, rarefactions
1. Introduction. We consider the problem of numerical approximation of a
system of two conservation laws modeling twophase flow in a onedimensional porous
medium. We develop a streamline method with particular attention given to local
