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In this paper, we propose a computational framework,which is based on adomain decomposition technique, to employ both finite element method (which isa popular continuum modeling approach) and lattice Boltzmann method (which is apopular pore-scale modeling approach) in the same computational domain. Tobridge the gap across the disparate length and time-scales, we first propose anew method to enforce continuum-scale boundary conditions (i.e., Dirichlet andNeumann boundary conditions) onto the numerical solution from the latticeBoltzmann method. This method are based on maximization of entropy and preservethe non-negativity of discrete distributions under the lattice Boltzmannmethod. The proposed computational framework allows different grid sizes,orders of interpolation, and time-steps in different subdomains. This allowsfor different desired resolutions in the numerical solution in differentsubdomains. Through numerical experiments, the effect of grid and time-steprefinement, disparity of time-steps in different subdomains, domainpartitioning, and the number of iteration steps on the accuracy and rate ofconvergence of the proposed methodology are studied. Finally, to showcase theperformance of this framework in porous media applications, we use it tosimulate the dissolution of calcium carbonate in a porous structure.

A hybrid multi-time-step framework for pore-scale and continuum-scale modeling of solute transport in porous media