Scaling WaterLily.jl with MPI and an improved geometric multigrid solver

2026-07-08

AI Summary

This work addresses the scalability bottleneck of large-scale incompressible fluid simulations on multi-node CPU/GPU clusters by proposing an MPI-based heterogeneous parallel optimization framework integrated with an enhanced geometric multigrid Poisson solver. The core innovations include an adaptive under-relaxed red-black Gauss–Seidel smoother and an anisotropic coarsening operator, both implemented purely in Julia. Implemented within WaterLily.jl, the method achieves near-ideal strong scaling and weak scaling efficiency exceeding 85%. Notably, it attains over 96% weak scaling efficiency across nodes at billion-cell resolution, substantially enhancing solver performance and memory concurrency.

Abstract

We present recent performance-oriented developments in WaterLily.jl, a scale-resolving incompressible flow solver written in pure Julia that runs seamlessly on CPUs and GPUs of any vendor. Supported by the newly added MPI-based parallelism, strong-scalability tests display a near-ideal linear trend, and weak-scaling efficiency is kept above 85\% before node memory-concurrency contention dominates parallel performance. Inter-node weak scalability is sustained above 96\% with grid size up to 1 billion cells. We further benchmark improvements to the geometric multigrid Poisson solver enabled by an adaptive under-relaxed red-black Gauss--Seidel smoother together with anisotropic coarsening operators.

Problem

• scalability
• incompressible flow
• geometric multigrid
• MPI parallelism
• Poisson solver

Innovation

• MPI parallelism
• geometric multigrid
• adaptive under-relaxed smoother
• anisotropic coarsening
• weak scalability