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We investigate a two-scale system featuring an upscaled parabolicdispersion-reaction equation intimately linked to a family of elliptic cellproblems. The system is strongly coupled through a dispersion tensor, whichdepends on the solutions to the cell problems, and via the cell problemsthemselves, where the solution of the parabolic problem interacts nonlinearlywith the drift term. This particular mathematical structure is motivated by arigorously derived upscaled reaction-diffusion-convection model that describesthe evolution of a population of interacting particles pushed by a large driftthrough an array of periodically placed obstacles (i.e., through a regularporous medium).  We prove the existence of weak solutions to our system by means of aniterative scheme, where particular care is needed to ensure the uniformpositivity of the dispersion tensor. Additionally, we use finite element-basedapproximations for the same iteration scheme to perform multiple simulationstudies. Finally, we highlight how the choice of micro-geometry (building theregular porous medium) and of the nonlinear drift coupling affects themacroscopic dispersion of particles.

Strongly Coupled Two-scale System with Nonlinear Dispersion: Weak Solvability and Numerical Simulation