A hybrid semi-Lagrangian cut cell method for advection-diffusion problems with Robin boundary conditions in moving domains

We present a new discretization approach to advection-diffusion problems with Robin boundary conditions on complex, time-dependent domains. The method is based on second order cut cell finite volume methods introduced by Bochkov et al.[8] to discretize the Laplace operator and Robin boundary condition. To overcome the small cell problem, we use a splitting scheme along with a semi-Lagrangian method to treat advection. We demonstrate second order accuracy in the L-1, L-2, and L-infinity norms for both analytic test problems and numerical convergence studies. We also demonstrate the ability of the scheme to convert one chemical species to another across a moving boundary. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

A new discretization approach for advection-diffusion problems with Robin boundary conditions on complex domains is presented, based on second-order cut cell finite volume methods. The method demonstrates second-order accuracy in various norms and the ability to convert chemical species across moving boundaries.