A Massively Parallel Eulerian-Lagrangian Method for Advection-Dominated Transport in Viscous Fluids

Motivated by challenges in the Earth's 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, and pure advection, and it is applied to a coupled nonlinear 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 x 10^{10} (52 billion) degrees of freedom per time-step.

@article{id2823,
  author = {Nils Kohl and Marcus Mohr and Sebastian Eibl and Ulrich R\"ude},
  doi = {10.1137/21M1402510},
  journal = {SIAM Journal on Scientific Computing},
  language = {en},
  number = {3},
  pages = {C260-C285},
  title = {A Massively Parallel Eulerian-Lagrangian Method for Advection-Dominated Transport in Viscous Fluids},
  volume = {44},
  year = {2022},
}

%O Journal Article
%A Nils Kohl
%A Marcus Mohr
%A Sebastian Eibl
%A Ulrich Rüde
%R 10.1137/21M1402510
%J SIAM Journal on Scientific Computing
%G en
%N 3
%P C260-C285
%T A Massively Parallel Eulerian-Lagrangian Method for Advection-Dominated Transport in Viscous Fluids
%V 44
%D 2022