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

TL;DR

This paper introduces a massively parallel Eulerian-Lagrangian method tailored for advection-dominated transport problems in viscous fluids, demonstrating high scalability and efficiency in complex, large-scale simulations relevant to Earth mantle convection.

Contribution

It presents a novel parallel implementation combining particle-based characteristics with finite-element methods for large-scale advection-diffusion problems.

Findings

Achieved scalability up to 147,456 processes

Successfully handled 52 billion degrees of freedom per time-step

Validated performance on complex geometries and coupled systems

Abstract

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.