Partitioned coupling of advection-diffusion-reaction systems and Brinkman flows

Pietro Lenarda (1) , Marco Paggi (1) , Ricardo Ruiz Baier (2)

1 IMT Institute for Advanced Studies [Lucca]
2 MI - Mathematical Institute [Oxford]

We present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection-diffusion-reaction systems and incompressible, viscous flow. The space dis-cretization of the governing equations is based on mixed finite element methods defined on unstructured meshes, whereas the time integration hinges on an operator splitting strategy that exploits the differences in scales between the reaction, advection, and diffusion processes, considering the global system as a number of sequentially linked sets of partial differential, and algebraic equations. The flow solver presents the advantage that all unknowns in the system (here vorticity, velocity, and pressure) can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective. The robustness of the proposed method is illustrated with a series of numerical tests in 2D and 3D, relevant in the modelling of bacterial bioconvection and Boussinesq systems.

Mots clés: coupling algorithms; operator splitting; primal-mixed finite element methods; viscous flow in porous media; Advection-reaction-diffusion processes

Domaines: Analyse numérique [cs.NA]; Mécanique des fluides [physics.class-ph]

Pietro Lenarda, Marco Paggi, Ricardo Ruiz Baier. Partitioned coupling of advection-diffusion-reaction systems and Brinkman flows. 2016. ⟨hal-01401903⟩