Phase reduction is a reduced-order modeling technique that can express the high-dimensional periodic dynamics with single scalar phase variable. We develop an adjoint-based framework for incompressible flows. This analysis reveals high-fidelity spatial sensitivity fields respect to perturbation over limit cycle of flow in computationally efficient manner.

in oil industry, spontaneous imbibition is an important phenomenon in recovery from fractured reservoirs which can be defined as spontaneous uptake of a wetting fluid into a porous solid. spontaneous imbibition involves both cocurrent and countercurrent flows. when a matrix block is partially covered by water, oil recovery is dominated by cocurrent imbibition i.e. the production of non wetting ...