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This paper considers two-dimensional hierarchical locally-refined rect-angular meshes with dynamic adaptation to the solution. A parallel algorithm with dynamic load balancing has been developed. Adaptive meshes have been used for the problem of passive contaminant transport in an oil-bearing stratum at water flooding. A model neglecting the capillary and gravity forces (the Buckley — Leverett model) has been used.

Adaptive Cartesian Mesh Refinement For Simulating Multiphase Lows In Porous Media