Numerical Study of a Strongly Coupled Two-scale System with Nonlinear Dispersion
<|reference_start|>Numerical Study of a Strongly Coupled Two-scale System with Nonlinear Dispersion: Thinking of flows crossing through regular porous media, we numerically explore the behavior of weak solutions to a two-scale elliptic-parabolic system that is strongly coupled by means of a suitable nonlinear dispersion term. The two-scale system of interest originates from the fast-drift periodic homogenization of a nonlinear convective-diffusion-reaction problem, where the structure of the non-linearity in the drift fits to the hydrodynamic limit of a totally asymmetric simple exclusion process for a population of particles. In this article, we focus exclusively on numerical simulations that employ two decoupled approximation schemes, viz. 'scheme 1' - a Picard-type iteration - and 'scheme 2' - a time discretization decoupling. Additionally, we describe a computational strategy which helps to drastically improve computation times. Finally, we provide several numerical experiments to illustrate what dispersion effects are introduced by a specific choice of microstructure and model ingredients.<|reference_end|>
@article{nepal2024numerical,
    title={Numerical Study of a Strongly Coupled Two-scale System with Nonlinear
  Dispersion},
    author={Surendra Nepal, Vishnu Raveendran, Michael Eden, Rainey Lyons, Adrian
  Muntean},
    journal={arXiv preprint arXiv:2402.09607},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.09607},
    primaryClass={math.NA cs.NA math.AP}
}