Computer-implemented systems and methods for modeling behavior of at least one fluid in a reservoir are disclosed. The techniques can include obtaining measurements of physical parameters, including pressure, at locations within the reservoir, and discretizing, based on a three-dimensional fine grid, a system of partial differential mass balance equations that model, based on the measurements, at least the physical parameters at the locations within the reservoir, such that a system of nonlinear equations is produced. The techniques can include iterating from a current time step to a next time step, such that a solution to the system of nonlinear equations for a time interval that includes the current time step and the next time step is produced. The iterating can include an adaptive multi-fidelity multiscale technique that employs multiple restriction operators, prolongation operators, and coarse grids, to model various computationally challenging reservoir features, behaviors, or both.
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