  In this paper, we propose a computational framework,which is based on a
domain decomposition technique, to employ both finite element method (which is
a popular continuum modeling approach) and lattice Boltzmann method (which is a
popular pore-scale modeling approach) in the same computational domain. To
bridge the gap across the disparate length and time-scales, we first propose a
new method to enforce continuum-scale boundary conditions (i.e., Dirichlet and
Neumann boundary conditions) onto the numerical solution from the lattice
Boltzmann method. This method are based on maximization of entropy and preserve
the non-negativity of discrete distributions under the lattice Boltzmann
method. The proposed computational framework allows different grid sizes,
orders of interpolation, and time-steps in different subdomains. This allows
for different desired resolutions in the numerical solution in different
subdomains. Through numerical experiments, the effect of grid and time-step
refinement, disparity of time-steps in different subdomains, domain
partitioning, and the number of iteration steps on the accuracy and rate of
convergence of the proposed methodology are studied. Finally, to showcase the
performance of this framework in porous media applications, we use it to
simulate the dissolution of calcium carbonate in a porous structure.
