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Abstract <p>A solver for simulation of 2D and 3D flows of incompressible viscous fluids using the Particle Finite Element Method is presented. We consider a Eulerian–Lagrangian approach called PFEM-2 instead of purely Lagrangian PFEM. A detailed description of the numerical method and its algorithm is given. Both solution using finite element method on a fixed Eulerian grid and operations with particles are covered. Implementation of the algorithm presented in this paper is done for graphics processing units using NVIDIA CUDA technology. The solver performs all the operations on GPU without any copy to CPU, except for data export. To our knowledge this is the first GPU implementation of the PFEM-2 method. Quantitative and qualitative results are given for test problems of 3D flows past a sphere and a NACA-0012 airfoil of finite thickness. The solver is also shown to be several times faster on a single GPU as opposed to a cluster with several CPUs. The source code is available online and does not include any third-party software apart from libraries of the NVIDIA CUDA Toolkit.</p>

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Simulation of 3D Flows of Incompressible Viscous Fluids Using PFEM-2 Method on GPU

  • 期刊论文

  • 发表日期：

    2026年5月23日

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  • A. Popov

摘要

Abstract

A solver for simulation of 2D and 3D flows of incompressible viscous fluids using the Particle Finite Element Method is presented. We consider a Eulerian–Lagrangian approach called PFEM-2 instead of purely Lagrangian PFEM. A detailed description of the numerical method and its algorithm is given. Both solution using finite element method on a fixed Eulerian grid and operations with particles are covered. Implementation of the algorithm presented in this paper is done for graphics processing units using NVIDIA CUDA technology. The solver performs all the operations on GPU without any copy to CPU, except for data export. To our knowledge this is the first GPU implementation of the PFEM-2 method. Quantitative and qualitative results are given for test problems of 3D flows past a sphere and a NACA-0012 airfoil of finite thickness. The solver is also shown to be several times faster on a single GPU as opposed to a cluster with several CPUs. The source code is available online and does not include any third-party software apart from libraries of the NVIDIA CUDA Toolkit.