A Kriging-based Multiscale Interface for Flow and Reactive Transport

Flow and solute transport in natural environments are fundamental processes that occur and interact across scales. Hybrid multiscale simulation, which generally employs an interface to couple heterogeneous solvers at two adjacent scales, is an effective way to describe micro-scale processes in a macro-scale domain when/where needed. Therefore, it is important to develop an accurate and computationally efficient hybrid multiscale modeling approach. A Kriging-based Multiscale Interface (KMI), which is developed for scale coupling on the basis of a recently developed C++ library, i.e. Multiscale Universal Interface (MUI, Tang et al. J. Comp. Phys. 297:13-31), is presented in this work. The main difference between the MUI and KMI lies in the way to obtain the unknown values at the coupling interface. In the MUI, the unknown variables on the coupling boundaries are obtained by a simple/weighted (e.g. Gaussian weighting function) average of the known values at their surrounding nodes. While in the KMI, the kriging (known as the best linear unbiased predictor) is employed to predict the unknown values based on a limited number of observations. To validate the KMI, force-driven flows as well as heat transfer between two parallel plates are tested using different solvers (e.g. lattice Boltzmann method, finite difference method). As applications, pore- and Darcy-scale flow and flow-induced mixing in homogeneous/heterogeneous porous media are coupled through the KMI to further validate the model and investigate the effect of micro-scale processes on macroscopic properties. Finally, the overall model performance among the KMI-, MUI- and single-scale simulations are evaluated.