Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by Richards equation (for pressure head), and these equations are coupled to one another transfer terms. On its own, already nonlinear partial differential equation, it exceedingly difficult solve numerically due extra dependencies involving soil water. To deal with multiple scales, our strategy that starting from microscopic scale, upscale system via homogenization two-scale asymptotic expansion, obtain homogenized system, at an intermediate scale (level). Based on hierarchical approach, homogenization’s effective coefficients computed through solving arising cell problems. tackle nonlinearity, after time discretization, use Picard iteration procedure linearization equations. At iteration, some degree still remains level, so utilize generalized finite element (GMsFEM) combining multi-continuum macroscopic (coarse-grid) level. This scheme involves building uncoupled basis functions, which used not only construct coarse-grid solution approximation high accuracy but also (with basis) capture interactions among continua. These prospects convergence demonstrated several numerical results proposed method.