Abstract: Under certain physically reasonable assumptions, three-phase flow of immiscible, incompressible fluids can be described by a $2\times2$ nongenuinely nonlinear, hyperbolic system. We combine analytical solutions to the corresponding Riemann problem with an efficient front-tracking method to study Cauchy and initial-boundary value problems. Unlike finite difference methods, the front-tracking method treats all waves as discontinuities by evolving shocks exactly and approximating rarefactions by small entropy-violating discontinuities. This way, the method can track individual waves and give very accurate (or even exact) resolution of discontinuities. We demonstrate the applicability of the method through several numerical examples, including a streamline simulation of a water-alternating-gas (WAG) injection process in a three-dimensional, heterogeneous, shallow-marine formation.
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