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 advection-diffusion equation advection-dominated regime. The advection term is treated particle-based characteristics coupled to block-structured finite element framework. Its numerical and computational performance evaluated multiple two- three-dimensional benchmarks, including curved geometries, discontinuous solutions, pure advection, it applied nonlinear system modeling buoyancy-driven convection Stokes flow. We demonstrate strong weak scaling experiment, with scalability up 147,456 processes, solving more than 5.2 x 10^{10} (52 billion) degrees freedom per time-step.