Analysis of physical processes in porous media is generally desired at the macroscopic level, though the processes themselves are fundamentally governed by microscopic constitutive relations. Direct numerical simulation of the macroscopic equations is prohibitively expensive in a computational sense for microscopic resolutions. The Heterogeneous Multiscale Framework offers an alternative formulation to incorporate the physics at multiple scales in an efficient manner. We expand upon a recent multiscale formulation of fluid flow in porous media to a more generalized multiscale scheme coupling continuous conservation laws at the macroscale and discrete constitutive relations at the microscale. We observe that the coupling assumption for fluid flow problems is sufficiently generalizable to steady state problems in heat diffusion and solid mechanics.

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