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For miscible displacements in porous media, the volume fraction of the concentration is between 0 and 1. The main idea of my current work is to numerically preserve the two bound and keep the high-order accuracy. Then the numerical scheme is stable. The idea can be applied to other similar areas such as seawater intrusion, and contaminant transportation, etc.
Yang, Yang, "Numerical methods of miscible displacements in porous media" (2017). TechTalks. 55.