A Sharp Analytical Bound on the Spatiotemporal Locality in General Two-phase Flow and Transport Phenomena

The objective is to understand, for any two-phase flow situation, the instantaneous spatiotemporal nature of the domain-of- dependence. The focal setting is generally nonlinear and heterogeneous, compressible two-phase flow and transport in porous media. The analytical approach develops a sequence of approximations that ultimately recast the general conservation equa- tions into an infinite-dimensional Newton process. Within this process, the spatiotemporal evolution is dictated by linear dif- ferential equations that are easily analyzed. We develop sharp conservative estimates for the support of instantaneous changes to flow and transport variables. Several computational examples are used to illustrate the analytical results.