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

Abstract: 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.