[Paper Review] Efficient implementation of immersed boundary-lattice Boltzmann method for massive particle-laden flows Part I: Serial computing

Maoqiang Jiang, Jing Li+1 more|arXiv (Cornell University)|Feb 20, 2020

Lattice Boltzmann Simulation Studies43 references4 citations

TL;DR

This paper presents a highly optimized, serial implementation of the immersed boundary-lattice Boltzmann method (IB-LBM) for simulating massive particle-laden flows with over 10⁴ particles. By introducing a swap algorithm for incompressible LBM, a localized grid-to-point method for IBM, an improved grid search for particle interactions, and a symmetry algorithm for half-calculation, the method achieves up to 36 MLUPS (2D) and 12 MLUPS (3D) in particle-free flows, and maintains over 15 MLUPS (2D) and 7 MLUPS (3D) even in dense particle-laden flows with solid volume fractions up to 0.40.

ABSTRACT

Immersed boundary-lattice Boltzmann method (IB-LBM) has been widely used for simulation of particle-laden flows recently. However, it was limited to small-scale simulations with no more than O(103) particles. Here, we expand IB-LBM for massive particle-laden flows with more than O(104) particles by two sequential works. First is the Part I: serial computing on a single CPU core and following the Part II: parallel computing on many CPU cores. In this Part I paper, a highly efficient and localized implementation of IB-LBM is proposed for serial computing. We optimize in three main aspects: swap algorithm for incompressible LBM, local grid-to-point algorithm for IBM and improved grid search algorithm for particle pair short-range interaction. In addition, symmetry algorithm is proposed for the half-calculation of LB collision and external force term. The computational performance on a single CPU core is analyzed. Different scales of two dimensional (2D) and three-dimensional (3D) particles settling in closed cavities are used for testing. The solid volume fraction is varied from 0 to 0.40. Simulation results demonstrate that all calculation parts are dramatically decreased by the improved algorithm. For the particle-free flows, the Mega Lattice Site Update per Second (MLUPS) can be achieved up to 36 (2D) and 12 (3D) using the improved algorithm. For the particle-laden flows, MLUPS can be achieved no lower than 15 (2D) and 7 (3D) in the simulations of dense flows. At last, we discuss the potential of the new algorithms for the high-performance computation of the large-scale systems of particle-laden flows with MPI parallel technique.

Motivation & Objective

• To overcome the limitation of existing IB-LBM methods, which are restricted to small-scale simulations with ≤ O(10³) particles.
• To enable efficient simulation of massive particle-laden flows with > O(10⁴) particles on a single CPU core.
• To develop algorithmic optimizations that drastically reduce computational cost in LBM and IBM components.
• To lay the foundation for high-performance parallel computing of large-scale particle-laden systems using MPI.

Proposed method

• A swap algorithm is introduced to improve the efficiency of the incompressible lattice Boltzmann method (LBM) by reordering collision and streaming steps.
• A localized grid-to-point algorithm is developed for the immersed boundary method (IBM), reducing computational overhead in force interpolation.
• An improved grid search algorithm is proposed to accelerate short-range particle-particle interactions by limiting search to neighboring grid cells.
• A symmetry algorithm is implemented to compute only half of the lattice Boltzmann collision and external force terms, exploiting symmetry to reduce redundant calculations.
• The entire implementation is optimized for serial execution on a single CPU core, focusing on memory access locality and computational efficiency.
• The method is validated across multiple scales of 2D and 3D particle settling simulations in closed cavities with varying solid volume fractions.

Experimental results

Research questions

• RQ1 Can the IB-LBM be efficiently scaled to simulate flows with more than O(10⁴) particles on a single CPU core?
• RQ2 How can the computational cost of LBM collision, IBM force interpolation, and particle-particle interactions be minimized in massive particle-laden flows?
• RQ3 What performance gains can be achieved through algorithmic optimizations such as symmetry-based half-calculation and localized grid search?
• RQ4 To what extent can the improved algorithm maintain high performance in dense particle flows with solid volume fractions up to 0.40?
• RQ5 What is the potential of the optimized serial implementation as a foundation for future MPI-parallelized large-scale simulations?

Key findings

• The optimized IB-LBM achieves up to 36 MLUPS in 2D particle-free flows and 12 MLUPS in 3D particle-free flows on a single CPU core.
• In dense particle-laden flows with solid volume fractions up to 0.40, the method maintains performance at no lower than 15 MLUPS (2D) and 7 MLUPS (3D).
• The swap algorithm significantly reduces computational overhead in the LBM collision step by improving data locality and reducing memory access latency.
• The localized grid-to-point algorithm for IBM reduces the cost of force interpolation by restricting computations to relevant grid points near particles.
• The improved grid search algorithm accelerates short-range particle-particle interactions by limiting the search to physically adjacent grid cells.
• The symmetry-based half-calculation algorithm reduces redundant computation of symmetric terms in the LBM collision and external force evaluation, enhancing overall efficiency.