Multiscale simulations for multi-continuum Richards equations

Park, Jun Richard; Cheung, Siu Wun; Mai, Tina

doi:10.1016/j.cam.2021.113648

Title: Multiscale simulations for multi-continuum Richards equations

Journal Article · Mon May 17 00:00:00 EDT 2021 · Journal of Computational and Applied Mathematics

DOI:https://doi.org/10.1016/j.cam.2021.113648· OSTI ID:1810663

Park, Jun Richard ^[1];

^[2];

^[3]

Univ. of Iowa, Iowa City, IA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
Duy Tan Univ., Da Nang (Vietnam). Inst. of Research and Development

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

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); Vietnam National Foundation for Science and Technology Development (NAFOSTED)

Grant/Contract Number:: AC52-07NA27344; 101.99-2019.326

OSTI ID:: 1810663

Alternate ID(s):: OSTI ID: 1815329

Report Number(s):: LLNL-JRNL-822603; 1035173

Journal Information:: Journal of Computational and Applied Mathematics, Vol. 397; ISSN 0377-0427

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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