An adaptive multiresolution Vortex Particle-Mesh method for the simulation of unbounded incompressible flows

Simulations of incompressible convection-dominated flows, such as vortical flows or wake flows, require accurate and efficient numerical methods. Among the various approaches, the vortex particle-mesh (VPM) method stands out for its ability to combine the strengths of mesh-based methods, such as efficient elliptic solvers and finite difference stencils, with the advantages of particle methods, which minimize numerical dispersion and dissipation errors. However, most VPM implementations consider a uniform grid. This can lead to a prohibitive computational cost, especially in three dimensions. This challenge can be addressed effectively through adaptive mesh refinement (AMR), which significantly reduces simulation costs by dynamically adjusting the local grid resolution to meet the requirements of the underlying physics. In this work, we present a novel VPM method that leverages the benefits of AMR. Building upon murphy, a wavelet-based block-structured AMR framework, we propose a new approach to represent the particles that allows for their refinement or coarsening. We show that our method achieves high-order accuracy, grid adaptation, and CFL relaxation at the same time. We then demonstrate the scalability of our method from 128 to 16,384 cores, and compare its performance with a uniform resolution framework for the simulation of aircraft wake vortices. We show that despite the increased complexity due to the overhead of the AMR operations, the resulting gains in computational efficiency and reductions in memory footprint are substantial.

Affiliations

UCLouvainSST/IMMC/TFL - Thermodynamics and fluid mechanics

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Balty, P., Duponcheel, M., & Chatelain, P. (2026). An adaptive multiresolution Vortex Particle-Mesh method for the simulation of unbounded incompressible flows. Computer Methods in Applied Mechanics and Engineering, 450(1), 118638. https://doi.org/10.1016/j.cma.2025.118638 (Original work published 2026)