A massively parallel Eulerian-Lagrangian method for advection-dominated transport in viscous fluids

Motivated by challenges in Earth mantle convection, we present a massively parallel implementation of an Eulerian-Lagrangian method for the advection-diffusion equation in the advection-dominated regime. The advection term is treated by a particle-based, characteristics method coupled to a block-structured finite-element framework. Its numerical and computational performance is evaluated in multiple, two- and three-dimensional benchmarks, including curved geometries, discontinuous solutions, pure advection, and it is applied to a coupled non-linear system modeling buoyancy-driven convection in Stokes flow. We demonstrate the parallel performance in a strong and weak scaling experiment, with scalability to up to $147,456$ parallel processes, solving for more than $5.2 \times 10^10$ (52 billion) degrees of freedom per time-step.

@article{id2677,
  author = {Kohl, Nils and Mohr, Marcus and Eibl, Sebastian and R\"ude, Ulrich},
  doi = {10.48550/arXiv.2103.02388},
  eid = {2103.02388v1},
  journal = {arXiv},
  language = {en},
  number = {22},
  title = {A massively parallel Eulerian-Lagrangian method for advection-dominated transport in viscous fluids},
  url = {https://doi.org/10.48550/arXiv.2103.02388},
  year = {2021},
}

%O Journal Article
%A Kohl, Nils
%A Mohr, Marcus
%A Eibl, Sebastian
%A Rüde, Ulrich
%R 10.48550/arXiv.2103.02388
%1 2103.02388v1
%J arXiv
%G en
%N 22
%T A massively parallel Eulerian-Lagrangian method for advection-dominated transport in viscous fluids
%U https://doi.org/10.48550/arXiv.2103.02388
%D 2021