Mass-Conserving Front Tracking for Miscible Two-Phase Flow

Abstract

A critical analysis of the mass conservation properties of the jump discontinuity propagating algorithms in the front-tracking method of Glimm et al. is performed in the context of miscible, two-phase, incompressible flow in porous media. These algorithms do not enforce the conservation of mass properties of the hyperbolic system on any grid of finite discretization size. For the curve propagation algorithm, which is the core of the suite of discontinuity movement algorithms, we show that mass conservation errors vanish linearly with maximum mesh size of the moving grids. We present new curve propagation and redistribution algorithms which conserve mass for any grid of finite spacing. Analogously mass-conserving untangling routines have also been developed. We investigate the performance of these new algorithms for diagonal five-spot computations.