pith. sign in

arxiv: 2512.01251 · v1 · submitted 2025-12-01 · 💻 cs.CE · physics.comp-ph· physics.flu-dyn

GPU-native Embedding of Complex Geometries in Adaptive Octree Grids Applied to the Lattice Boltzmann Method

Khodr Jaber , Ebenezer E. Essel , Pierre E. Sullivan This is my paper

Pith reviewed 2026-05-17 03:40 UTC · model grok-4.3

classification 💻 cs.CE physics.comp-phphysics.flu-dyn
keywords GPU computingadaptive mesh refinementoctree gridslattice Boltzmann methodgeometry embeddingray castingtriangle meshcut cells
0
0 comments X

The pith

A GPU-native ray-casting algorithm embeds stationary triangle meshes into block-structured octree grids and builds cut-link tables for lattice Boltzmann boundary conditions entirely on the device.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a method that performs solid voxelization and near-wall refinement for complex geometries directly on the graphics processing unit. It uses local ray casting accelerated by spatial bins to classify cells cut by the surface and to compute distances needed for interpolated bounce-back rules in the lattice Boltzmann method. This removes the need for CPU intervention or hash tables while maintaining coalesced memory access on adaptive forest-of-octrees grids. A sympathetic reader would care because the approach allows high-resolution flow simulations around arbitrary objects to run efficiently on GPU hardware with only modest added cost.

Core claim

The central claim is that a GPU-native algorithm can incorporate stationary triangle-mesh geometries into block-structured forest-of-octrees grids by executing both solid voxelization and automated near-wall refinement entirely on the device, employing local ray casting accelerated by a hierarchy of spatial bins to eliminate index orderings and hash tables, and constructing a flattened lookup table of cut-link distances to support accurate interpolated bounce-back boundary conditions.

What carries the argument

Local ray-casting procedure with a hierarchy of spatial bins that classifies cut cells and computes cut-link distances for watertight meshes while enabling coalesced access on GPU-resident octree blocks.

If this is right

  • Geometry embedding and interpolation impose only modest overhead on the overall solver runtime.
  • Accurate force predictions are obtained for external flows past cylinders in 2D at Re=100 and spheres in 3D at Re=10,15,20.
  • Stable near-wall resolution is maintained on adaptive Cartesian grids for the tested stationary geometries.
  • The method is general and applies to other explicit solvers that require GPU-resident geometry embedding.
  • Benchmark results confirm correctness for both low-triangle-count and high-triangle-count models from the Stanford 3D Scanning Repository.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Extending the ray-casting bins to handle time-varying meshes could support moving-boundary problems without repeated CPU-GPU transfers.
  • The flattened cut-link table structure might integrate with other boundary-condition formulations beyond interpolated bounce-back.
  • Performance on multi-GPU systems with meshes larger than 7 million triangles remains an open scaling question.
  • Similar local classification techniques could reduce host-device synchronization in other adaptive-grid CFD codes.

Load-bearing premise

The local ray-casting procedure with a hierarchy of spatial bins correctly classifies all cut cells and produces accurate cut-link distances for arbitrary watertight meshes without requiring CPU intervention or post-processing.

What would settle it

Direct comparison of GPU-classified cut cells and distances against an independent CPU voxelization reference on the Stanford Bunny or XYZ RGB Dragon mesh would show whether any surface intersections are misclassified.

Figures

Figures reproduced from arXiv: 2512.01251 by Ebenezer E. Essel, Khodr Jaber, Pierre E. Sullivan.

Figure 1
Figure 1. Figure 1: Embedding of a 2D circular cylinder ( ) within an axis-aligned adaptive computational grid. Each square represents a 4 × 4 block of cells. Cells are classified as fluid ( ), boundary ( ), and solid ( ). The links between the boundary and solid nodes are illustrated with arrows ( ). The staircase approximation of the cylinder imposed by voxelization is shown with the dashed line ( ). or flows in complex geo… view at source ↗
Figure 2
Figure 2. Figure 2: Stencil for the interpolated bounce-back condition along a link that intersects a tesselation of a 2D circular cylinder [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left: Flow chart of proposed voxelization procedure. Right: Summary of our CUDA kernels for each subroutine. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Labeling and orientation of the geometry elements. Left: Edge in 2D. Right: Triangle in 3D. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Representations of the hierarchical grid: a) octree, b) flattened grid, c) hierarchical view of overlap. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Memory access patterns used to process cell and cell-block data. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The variable Nspec. enforces the potential range of bins that a face can occupy by restricting the maximum length of the edges. The actual set of bins considered at runtime is determined by face-AABB overlap tests, where the AABB is defined by the corners of each bin with an offset of cell-spacing ∆xL on grid level L. ( : potential bin, : overlapped bin, : overlap region) 12 [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 8
Figure 8. Figure 8: A sample 2D geometry with 16 faces and Nspec. = 1 that we used to illustrate the construction of bins on a given grid level. Shown also is the bin overlap used to include nearby faces that do not necessarily intersect the bin directly but still require inclusion to account for ray casts from cells at the edges. Step 3 is a stream compaction (via Thrust’s remove_if) of the two arrays zipped together. The re… view at source ↗
Figure 9
Figure 9. Figure 9: Application of the GPU-based uniform spatial binning algorithm to the sample set of faces from Figure [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Application of the GPU-based uniform spatial binning algorithm to the sample set of faces from Figure [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Application of the GPU-based uniform spatial binning algorithm to the sample set of faces from Figure [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: In a triangle-parallel approach to the current computational grid, threads may cross over several cell-blocks, requiring [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: (a) Cell classification is performed in the direct vicinity of the geometry. (b) Internal propagation begins; fluid cells [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Parallel accesses of the vertices of the first face in the different variants of the partial surface voxelization kernel. [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Warp-level approaches to the variants of the partial surface voxelization kernel (Figure [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: (a) Statuses are identified after cell masks have been loaded in the starting block. (b) Cell masks in the neighbor [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Steps for voxelization into and refinement of a single grid level. a) Initial state after partial surface voxelization [PITH_FULL_IMAGE:figures/full_fig_p023_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: (a) When cells need to sample data from neighbors, a lookup table is formed for the indices of the neighboring [PITH_FULL_IMAGE:figures/full_fig_p024_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Execution times for the hierarchical spatial binning tests. [PITH_FULL_IMAGE:figures/full_fig_p029_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Execution times for the voxelizer tests. [PITH_FULL_IMAGE:figures/full_fig_p030_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Illustration of the block-based sparse voxel octree representation of the Stanford bunny. Levels [PITH_FULL_IMAGE:figures/full_fig_p033_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Illustration of the block-based sparse voxel octree representation of the XYZ RGB dragon (flipped). Levels [PITH_FULL_IMAGE:figures/full_fig_p034_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Voxelizations of the Stanford bunny extracted from a single forest-of-octrees grid. [PITH_FULL_IMAGE:figures/full_fig_p034_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Voxelizations of the XYZ RGB dragon extracted from a single forest-of-octrees grid. [PITH_FULL_IMAGE:figures/full_fig_p035_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Voxelization of the XYZ RGB dragon on level [PITH_FULL_IMAGE:figures/full_fig_p036_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Illustrations of 2:1 balanced computational grids with an embedded a) XYZ RGB dragon, and b) sphere. [PITH_FULL_IMAGE:figures/full_fig_p037_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Illustration of the computational domain for the 2D flow past a circular cylinder with four levels of refinement (i.e., [PITH_FULL_IMAGE:figures/full_fig_p038_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Illustration of the computational domain for the 3D flow past a sphere with three levels of refinement (i.e., [PITH_FULL_IMAGE:figures/full_fig_p039_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Vorticity plots with overlaid AMR grid outline extracted from the final time step. [PITH_FULL_IMAGE:figures/full_fig_p040_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Velocity magnitude plots (top) with overlaid streamlines (bottom) for the circular (left) and square (right) 2D [PITH_FULL_IMAGE:figures/full_fig_p041_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Time-averaged drag coefficients for flow past a sphere over the range Re [PITH_FULL_IMAGE:figures/full_fig_p042_31.png] view at source ↗
read the original abstract

Adaptive mesh refinement (AMR) reduces computational costs in CFD by concentrating resolution where needed, but efficiently embedding complex, non-aligned geometries on GPUs remains challenging. We present a GPU-native algorithm for incorporating stationary triangle-mesh geometries into block-structured forest-of-octrees grids, performing both solid voxelization and automated near-wall refinement entirely on the device. The method employs local ray casting accelerated by a hierarchy of spatial bins, leveraging efficient grid-block traversal to eliminate the need for index orderings and hash tables commonly used in CPU pipelines, and enabling coalesced memory access without CPU-GPU synchronization. A flattened lookup table of cut-link distances between fluid and solid cells is constructed to support accurate interpolated bounce-back boundary conditions for the lattice Boltzmann method (LBM). We implement this approach as an extension of the AGAL framework for GPU-based AMR and benchmark the geometry module using the Stanford Bunny (112K triangles) and XYZ RGB Dragon (7.2M triangles) models from the Stanford 3D Scanning Repository. The extended solver is validated for external flows past a circular/square cylinder (2D, $Re = 100$), and a sphere (3D, $\text{Re}\in\{10, 15, 20\}$). Results demonstrate that geometry handling and interpolation impose modest overhead while delivering accurate force predictions and stable near-wall resolution on adaptive Cartesian grids. The approach is general and applicable to other explicit solvers requiring GPU-resident geometry embedding.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a GPU-native algorithm for embedding stationary triangle-mesh geometries into block-structured forest-of-octrees grids for the Lattice Boltzmann Method. It performs solid voxelization and automated near-wall refinement entirely on the GPU using local ray casting accelerated by a hierarchy of spatial bins. This eliminates the need for CPU-GPU synchronization and common CPU data structures like hash tables. A flattened lookup table of cut-link distances is constructed to support interpolated bounce-back boundary conditions. The method is implemented as an extension to the AGAL framework, benchmarked on complex models such as the Stanford Bunny with 112K triangles and the XYZ RGB Dragon with 7.2M triangles, and validated on external flows past 2D cylinders and a 3D sphere at low Reynolds numbers, demonstrating accurate force predictions with modest overhead.

Significance. This work has the potential to significantly impact GPU-based computational fluid dynamics by providing a fully device-resident approach to handling complex geometries in adaptive mesh refinement settings. The strengths include the self-contained implementation without fitted parameters, the use of efficient grid-block traversal for coalesced memory access, and practical benchmarks on large triangle counts. If the ray-casting accuracy holds for complex meshes, it offers a general method applicable to other explicit solvers.

major comments (2)
  1. [§4.3] §4.3: Performance benchmarks for the Stanford Bunny (112K triangles) and Dragon (7.2M triangles) report only execution times and memory usage; no quantitative measures of voxelization accuracy, cut-cell classification rates, or cut-link distance errors are provided for these complex cases (unlike the cylinder and sphere results in §4.1–4.2). This directly bears on the central claim of reliable, CPU-free operation for arbitrary watertight meshes.
  2. [§4.1] §4.1: The 2D cylinder (Re=100) and square cylinder force-coefficient comparisons lack reported uncertainty from grid-convergence studies or explicit baseline references, limiting assessment of the interpolated bounce-back accuracy on adaptive grids.
minor comments (2)
  1. The description of the spatial bin hierarchy in the methods section would benefit from an explicit equation or pseudocode listing the bin traversal order and intersection test.
  2. Figure captions for the Dragon and Bunny visualizations should note the number of refinement levels and the near-wall cell size to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We address each major comment point by point below, indicating the revisions we will make to strengthen the presentation of results and validation.

read point-by-point responses

  1. Referee: [§4.3] §4.3: Performance benchmarks for the Stanford Bunny (112K triangles) and Dragon (7.2M triangles) report only execution times and memory usage; no quantitative measures of voxelization accuracy, cut-cell classification rates, or cut-link distance errors are provided for these complex cases (unlike the cylinder and sphere results in §4.1–4.2). This directly bears on the central claim of reliable, CPU-free operation for arbitrary watertight meshes.

    Authors: We agree that quantitative accuracy metrics for the complex models would provide additional support for the method's reliability. The Bunny and Dragon benchmarks in §4.3 are intended to demonstrate scalability, performance, and memory usage of the fully GPU-resident pipeline on large, real-world triangle counts (up to 7.2M triangles) rather than to serve as primary accuracy validation. These models are taken from the Stanford 3D Scanning Repository and treated as watertight. Obtaining independent ground-truth voxelizations or precise cut-link errors for such intricate geometries is non-trivial without a separate reference discretization. The correctness of the ray-casting, binning, and cut-link construction is instead established through the controlled validation cases in §4.1–4.2, where force coefficients match literature values. In the revised manuscript we will add an explicit statement in §4.3 clarifying the purpose of these benchmarks and note that accuracy for arbitrary meshes is inferred from the validated algorithm plus the watertight-mesh assumption. revision: partial

  2. Referee: [§4.1] §4.1: The 2D cylinder (Re=100) and square cylinder force-coefficient comparisons lack reported uncertainty from grid-convergence studies or explicit baseline references, limiting assessment of the interpolated bounce-back accuracy on adaptive grids.

    Authors: We acknowledge that explicit grid-convergence data and uncertainty estimates would improve the assessment of the interpolated bounce-back implementation on adaptive grids. The reported force coefficients are compared to established literature values obtained with other LBM and CFD methods at Re=100. To address this point, we will add a grid-convergence study for the circular-cylinder case in the revised manuscript. This will include results at successive refinement levels, the observed order of convergence, and estimated uncertainties in the drag and lift coefficients, thereby providing a quantitative basis for the accuracy of the boundary treatment on the forest-of-octrees grids. revision: yes

Circularity Check

0 steps flagged

Algorithmic implementation is self-contained with no reduction of claims to fitted inputs or self-citation chains

full rationale

The paper describes a GPU-native algorithm for voxelization and refinement using local ray-casting with spatial binning hierarchies, without any equations that derive performance metrics, accuracy measures, or boundary conditions from quantities fitted to the same data or meshes. Validation uses separate simple geometries (cylinders, sphere) for quantitative checks and complex models (Bunny, Dragon) only for performance benchmarks. No self-citations are invoked as load-bearing uniqueness theorems or ansatzes; the method is presented as a direct implementation extension of the AGAL framework. The central claims rest on explicit algorithmic steps and empirical timing/force results rather than any definitional or fitted equivalence. This is a standard honest non-finding for an implementation-focused methods paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on standard assumptions from computational geometry and LBM boundary-condition literature; no new free parameters or invented entities are introduced.

axioms (1)
  • domain assumption Input triangle meshes are closed, watertight, and stationary.
    Required for reliable ray-casting voxelization and cut-cell classification.

pith-pipeline@v0.9.0 · 5577 in / 1137 out tokens · 71981 ms · 2026-05-17T03:40:20.418939+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

74 extracted references · 74 canonical work pages

  1. [1]

    M. J. Berger, J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, Journal of Computational Physics 53 (3) (1984) 484–512. doi:10.1016/0021-9991(84)90073-1

    work page doi:10.1016/0021-9991(84)90073-1 1984

  2. [2]

    M. J. Berger, R. J. LeVeque, Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems , SIAM Journal on Numerical Analysis 35 (6) (1998) 2298–2316. doi:10.1137/S0036142997315974. URL http://epubs.siam.org/doi/10.1137/S0036142997315974

    work page doi:10.1137/s0036142997315974 1998

  3. [3]

    Journal of Computational Physics , keywords =

    M. Berger, P. Colella, Local adaptive mesh refinement for shock hydrodynamics , Journal of Computational Physics 82 (1) (1989) 64–84. doi:10.1016/0021-9991(89)90035-1 . URL https://www.jstor.org/stable/10.2307/3323192?origin=crossrefhttps://linkinghub.elsevier.com/retrieve/ pii/0021999189900351

    work page doi:10.1016/0021-9991(89)90035-1 1989

  4. [4]

    Dubey, A

    A. Dubey, A. Almgren, J. Bell, M. Berzins, S. Brandt, G. Bryan, P. Colella, D. Graves, M. Lijewski, F. Löffler, B. O’Shea, E. Schnetter, B. Van Straalen, K. Weide, A survey of high level frameworks in block-structured adaptive mesh refinement packages, Journal of parallel and distributed computing 74 (12) (2014) 3217–3227. 45

    work page 2014

  5. [5]

    Dubey, M

    A. Dubey, M. Berzins, C. Burstedde, M. L. Norman, D. Unat, M. Wahib, K. Hinsen, A. Dubey, I. U. S. Argonne National Lab. (ANL), Argonne, Structured adaptive mesh refinement adaptations to retain performance portability with increasing heterogeneity, Computing in science & engineering 23 (5) (2021) 62–66

    work page 2021

  6. [6]

    Burstedde, L

    C. Burstedde, L. C. Wilcox, O. Ghattas, p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees, SIAM Journal on Scientific Computing 33 (3) (2011) 1103–1133. doi:10.1137/100791634

    work page doi:10.1137/100791634 2011

  7. [7]

    Holke, J

    J. Holke, J. Markert, D. Knapp, L. Dreyer, S. Elsweijer, N. Böing, I. Lilikakis, J. Fussbroich, T. Leistikow, F. Becker, V. Uenlue, O. Albers, C. Burstedde, A. Basermann, C. Hergl, W. Julia, K. Schoenlein, J. Ackerschott, A. Evgenii, Z. Csati, A. Dutka, B. Geihe, P. Kestener, A. Kirby, H. Ranocha, S.-L. Michael, t8code - modular adaptive mesh refinement i...

    work page doi:10.21105/joss.06887 2025

  8. [8]

    Wahib, N

    M. Wahib, N. Maruyama, T. Aoki, Daino: A High-Level Framework for Parallel and Efficient AMR on GPUs, International Conference for High Performance Computing, Networking, Storage and Analysis, SC 0 (November) (2016) 621–632. doi:10.1109/SC.2016.52

    work page doi:10.1109/sc.2016.52 2016

  9. [9]

    481(4):4815--4840

    H.-Y. Schive, J. A. ZuHone, N. J. Goldbaum, M. J. Turk, M. Gaspari, C.-Y. Cheng, GAMER-2: a GPU-accelerated adaptive mesh refinement code – accuracy, performance, and scalability , Monthly Notices of the Royal Astronomical Society 481 (4) (2018) 4815–4840. doi:10.1093/mnras/sty2586. URL https://academic.oup.com/mnras/article/481/4/4815/5106358

    work page doi:10.1093/mnras/sty2586 2018

  10. [10]

    X. Luo, L. Wang, W. Ran, F. Qin, Gpu accelerated cell-based adaptive mesh refinement on unstructured quadrilateral grid, Computer physics communications 207 (2016) 114–122

    work page 2016

  11. [11]

    Giuliani, L

    A. Giuliani, L. Krivodonova, Adaptive mesh refinement on graphics processing units for applications in gas dynamics , Journal of Computational Physics 381 (2019) 67–90. doi:10.1016/j.jcp.2018.12.019. URL https://doi.org/10.1016/j.jcp.2018.12.019

    work page doi:10.1016/j.jcp.2018.12.019 2019

  12. [12]

    Menshov, P

    I. Menshov, P. Pavlukhin, GPU-native gas dynamic solver on octree-based AMR grids, Journal of Physics: Conference Series 1640 (1) (2020). doi:10.1088/1742-6596/1640/1/012017

    work page doi:10.1088/1742-6596/1640/1/012017 2020

  13. [13]

    P. V. Pavlukhin, I. S. Menshov, Gpu-native dynamic octree-based grid adaptation to moving bodies, Lobachevskii journal of mathematics 45 (1) (2024) 308–318

    work page 2024

  14. [14]

    Jaber, E

    K. Jaber, E. E. Essel, P. E. Sullivan, GPU-native adaptive mesh refinement with application to lattice Boltzmann simu- lations, Computer Physics Communications (2025) 109543

    work page 2025

  15. [15]

    Mierke, C

    D. Mierke, C. Janßen, T. Rung, An efficient algorithm for the calculation of sub-grid distances for higher-order lbm boundary conditions in a gpu simulation environment , Computers & Mathematics with Applications 79 (1) (2020) 66–87, mesoscopic Methods in Engineering and Science. doi:https://doi.org/10.1016/j.camwa.2018.04.022. URL https://www.sciencedirec...

    work page doi:10.1016/j.camwa.2018.04.022 2020

  16. [16]

    Laine, T

    S. Laine, T. Karras, Efficient sparse voxel octrees, IEEE transactions on visualization and computer graphics 17 (8) (2011) 1048–1059

    work page 2011

  17. [17]

    Sundar, R

    H. Sundar, R. S. Sampath, G. Biros, Bottom-up construction and 2:1 balance refinement of linear octrees in parallel, SIAM journal on scientific computing 30 (5) (2008) 2675–2708

    work page 2008

  18. [18]

    S. C. G. Laboratory, The stanford 3d scanning repository, http://graphics.stanford.edu/data/3Dscanrep/, accessed: 2025-11-05

    work page 2025

  19. [19]

    Schwarz, H.-P

    M. Schwarz, H.-P. Seidel, Fast parallel surface and solid voxelization on gpus , ACM Trans. Graph. 29 (6) (Dec. 2010). doi:10.1145/1882261.1866201. URL https://doi.org/10.1145/1882261.1866201

    work page doi:10.1145/1882261.1866201 2010

  20. [20]

    Jasak, Openfoam: open source cfd in research and industry, International Journal of Naval Architecture and Ocean Engineering 1 (2) (2009) 89–94

    H. Jasak, Openfoam: open source cfd in research and industry, International Journal of Naval Architecture and Ocean Engineering 1 (2) (2009) 89–94

    work page 2009

  21. [21]

    Holke, Scalable algorithms for parallel tree-based adaptive mesh refinement with general element types, Ph.D

    J. Holke, Scalable algorithms for parallel tree-based adaptive mesh refinement with general element types, Ph.D. thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, Mathematisch-Naturwissenschaftliche Fakultät, Bonn, Germany, disser- tation zur Erlangung des Doktorgrades (Dr. rer. nat.) (Mar. 2018)

    work page 2018

  22. [22]

    Schornbaum, U

    F. Schornbaum, U. Rüde, Extreme-scale block-structured adaptive mesh refinement, SIAM journal on scientific computing 40 (3) (2018) C358–C387

    work page 2018

  23. [23]

    Stewart, C

    C. Stewart, C. Feichtinger, C. Godenschwager, C. Rettinger, C. Schwarzmeier, D. Ritter, D. Anderl, D. Staubach, D. Bar- tuschat, E. Fattahi, F. Winterhalter, F. Schornbaum, F. Hennig, G. Drozdov, H. Schottenhamml, I. Ostanin, J. Götz, J. Hönig, J. V. T. Risso, J. Habich, K. Iglberger, K. Pickl, L. Hufnagel, L. Werner, M. Holzer, M. Bauer, M. Markl, M. Kur...

    work page doi:10.5281/zenodo.10054460 2023

  24. [24]

    L. Wang, F. Witherden, A. Jameson, An efficient gpu-based h-adaptation framework via linear trees for the flux recon- struction method, Journal of computational physics 502 (2024) 112823

    work page 2024

  25. [25]

    Y. Wang, Y. Wu, Y. Zeng, M. Jiang, Z. Liu, An immersed boundary lattice boltzmann method on block-structured adaptive grids for the simulation of particle-laden flows on cpus/gpus , Computer Physics Communications 314 (2025) 109674. doi:https://doi.org/10.1016/j.cpc.2025.109674. URL https://www.sciencedirect.com/science/article/pii/S0010465525001766

    work page doi:10.1016/j.cpc.2025.109674 2025

  26. [26]

    Y. Wang, C. Zhong, J. Cao, C. Zhuo, S. Liu, A simplified finite volume lattice boltzmann method for simulations of fluid flows from laminar to turbulent regime, part i: Numerical framework and its application to laminar flow simulation , Computers & Mathematics with Applications 79 (5) (2020) 1590–1618. doi:https://doi.org/10.1016/j.camwa.2019. 09.017. 46...

    work page doi:10.1016/j.camwa.2019 2020

  27. [27]

    J. A. Reyes Barraza, R. Deiterding, Towards a generalised lattice boltzmann method for aerodynamic simulations, Journal of Computational Science 45 (2020) 101182

    work page 2020

  28. [28]

    Dupuis, B

    A. Dupuis, B. Chopard, Theory and applications of an alternative lattice Boltzmann grid refinement algorithm , Physical Review E 67 (6) (2003) 066707. doi:10.1103/PhysRevE.67.066707. URL https://link.aps.org/doi/10.1103/PhysRevE.67.066707

    work page doi:10.1103/physreve.67.066707 2003

  29. [29]

    Rohde, D

    M. Rohde, D. Kandhai, J. J. Derksen, H. E. A. van den Akker, A generic, mass conservative local grid refinement technique for lattice-Boltzmann schemes , International Journal for Numerical Methods in Fluids 51 (4) (2006) 439–468. doi:10.1002/fld.1140. URL https://onlinelibrary.wiley.com/doi/10.1002/fld.1140

    work page doi:10.1002/fld.1140 2006

  30. [30]

    Lagrava, O

    D. Lagrava, O. Malaspinas, J. Latt, B. Chopard, Advances in multi-domain lattice boltzmann grid refinement, Journal of computational physics 231 (14) (2012) 4808–4822

    work page 2012

  31. [31]

    Springer (2017)

    T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, E. M. Viggen, The Lattice Boltzmann Method , Graduate Texts in Physics, Springer International Publishing, Cham, 2017. doi:10.1007/978-3-319-44649-3 . URL https://link.springer.com/book/10.1007/978-3-319-44649-3http://link.springer.com/10.1007/ 978-3-319-44649-3

    work page doi:10.1007/978-3-319-44649-3 2017

  32. [32]

    Filippova, D

    O. Filippova, D. Hänel, Grid Refinement for Lattice-BGK Models , Journal of Computational Physics 147 (1) (1998) 219–

    work page 1998

  33. [33]

    URL https://linkinghub.elsevier.com/retrieve/pii/S0021999198960892

    doi:10.1006/jcph.1998.6089. URL https://linkinghub.elsevier.com/retrieve/pii/S0021999198960892

    work page doi:10.1006/jcph.1998.6089 1998

  34. [34]

    Bouzidi, M

    M. Bouzidi, M. Firdaouss, P. Lallemand, Momentum transfer of a boltzmann-lattice fluid with boundaries, Physics of fluids (1994) 13 (11) (2001) 3452–3459

    work page 1994

  35. [35]

    Ginzburg, D

    I. Ginzburg, D. d’Humières, Multireflection boundary conditions for lattice boltzmann models, Physical review. E, Statis- tical, nonlinear, and soft matter physics 68 (6 Pt 2) (2003) 066614–066614

    work page 2003

  36. [36]

    M. L. Sætra, A. R. Brodtkorb, K. A. Lie, Efficient GPU-Implementation of Adaptive Mesh Refinement for the Shallow- Water Equations, Journal of Scientific Computing 63 (1) (2015) 23–48. doi:10.1007/s10915-014-9883-4

    work page doi:10.1007/s10915-014-9883-4 2015

  37. [37]

    Beckingsale, W

    D. Beckingsale, W. Gaudin, A. Herdman, S. Jarvis, Resident block-structured adaptive mesh refinement on thousands of graphics processing units, in: 2015 44th International Conference on Parallel Processing, IEEE, 2015, pp. 61–70

    work page 2015

  38. [38]

    Zhang, A

    W. Zhang, A. Almgren, V. Beckner, J. Bell, J. Blaschke, C. Chan, M. Day, B. Friesen, K. Gott, D. Graves, M. Katz, A. Myers, T. Nguyen, A. Nonaka, M. Rosso, S. Williams, M. Zingale, AMReX: a framework for block-structured adaptive mesh refinement, Journal of Open Source Software 4 (37) (2019) 1370

    work page 2019

  39. [39]

    Pavlukhin, I

    P. Pavlukhin, I. Menshov, GPU-Aware AMR on Octree-Based Grids, in: V. Malyshkin (Ed.), Parallel Computing Tech- nologies, Springer International Publishing, Cham, 2019, pp. 214–220

    work page 2019

  40. [40]

    S. Fang, H. Chen, Hardware accelerated voxelization, Computers & graphics 24 (3) (2000) 433–442

    work page 2000

  41. [41]

    W. Li, Z. Fan, X. Wei, A. Kaufman, Flow simulation with complex boundaries, in: M. Pharr (Ed.), GPU Gems 2: Pro- gramming Techniques for High-Performance Graphics and General-Purpose Computation, Addison Wesley Professional, 2005, pp. 747–764

    work page 2005

  42. [42]

    Eisemann, X

    E. Eisemann, X. Décoret, Fast scene voxelization and applications , in: Proceedings of the 2006 Symposium on Interactive 3D Graphics and Games, I3D ’06, Association for Computing Machinery, New York, NY, USA, 2006, p. 71–78. doi: 10.1145/1111411.1111424. URL https://doi.org/10.1145/1111411.1111424

    work page doi:10.1145/1111411.1111424 2006

  43. [43]

    Eisemann, X

    E. Eisemann, X. Décoret, Single-pass gpu solid voxelization for real-time applications, in: Proceedings of Graphics Interface 2008, GI ’08, Canadian Information Processing Society, CAN, 2008, p. 73–80

    work page 2008

  44. [44]

    Crassin, S

    C. Crassin, S. Green, Octree-based sparse voxelization using the gpu hardware rasterizer, in: P. Cozzi, C. Riccio (Eds.), OpenGL Insights, CRC Press, 2012. doi:10.1201/b12288

    work page doi:10.1201/b12288 2012

  45. [45]

    Aleksandrov, S

    M. Aleksandrov, S. Zlatanova, D. J. Heslop, Voxelisation algorithms and data structures: A review , Sensors 21 (24) (2021). doi:10.3390/s21248241. URL https://www.mdpi.com/1424-8220/21/24/8241

    work page doi:10.3390/s21248241 2021

  46. [46]

    Akenine-Möller, Fast 3d triangle-box overlap testing , J

    T. Akenine-Möller, Fast 3d triangle-box overlap testing , J. Graph. Tools 6 (1) (2002) 29–33. doi:10.1080/10867651.2001. 10487535. URL https://doi.org/10.1080/10867651.2001.10487535

    work page doi:10.1080/10867651.2001 2002

  47. [47]

    S. Park, H. Shin, Efficient generation of adaptive cartesian mesh for computational fluid dynamics using gpu, International journal for numerical methods in fluids 70 (11) (2012) 1393–1404

    work page 2012

  48. [48]

    J. J. Hasbestan, I. Senocak, Binarized-octree generation for cartesian adaptive mesh refinement around immersed geome- tries, Journal of Computational Physics 368 (2018) 179–195. doi:https://doi.org/10.1016/j.jcp.2018.04.039. URL https://www.sciencedirect.com/science/article/pii/S002199911830264X

    work page doi:10.1016/j.jcp.2018.04.039 2018

  49. [49]

    C. F. Janßen, N. Koliha, T. Rung, A fast and rigorously parallel surface voxelization technique for gpu-accelerated cfd simulations, Communications in computational physics 17 (5) (2015) 1246–1270

    work page 2015

  50. [50]

    T. Ma, P. Li, T. Ma, A three-dimensional cartesian mesh generation algorithm based on the gpu parallel ray casting method, Applied sciences 10 (1) (2020) 58–

    work page 2020

  51. [51]

    Shukla, N

    R. Shukla, N. Arora, D. S. Banerjee, Voxelization of moving geometries on gpu, in: 2022 IEEE 24th Int Conf on High Performance Computing & Communications; 8th Int Conf on Data Science & Systems; 20th Int Conf on Smart City; 8th Int Conf on Dependability in Sensor, Cloud & Big Data Systems & Application (HPCC/DSS/SmartCity/DependSys), 2022, pp. 904–913. do...

    work page doi:10.1109/hpcc-dss-smartcity-dependsys57074.2022.00146 2022

  52. [52]

    Kumar, R

    R. Kumar, R. Deep, D. S. Banerjee, N. Arora, Voxelization of moving deformable geometries on gpu, in: 2024 23rd International Symposium on Parallel and Distributed Computing (ISPDC), 2024, pp. 1–8. doi:10.1109/ISPDC62236. 47 2024.10705394

    work page doi:10.1109/ispdc62236 2024

  53. [53]

    K. Zhou, Q. Hou, R. Wang, B. Guo, Real-time kd-tree construction on graphics hardware , ACM Trans. Graph. 27 (5) (Dec. 2008). doi:10.1145/1409060.1409079. URL https://doi.org/10.1145/1409060.1409079

    work page doi:10.1145/1409060.1409079 2008

  54. [54]

    Kalojanov, P

    J. Kalojanov, P. Slusallek, A parallel algorithm for construction of uniform grids , in: Proceedings of the Conference on High Performance Graphics 2009, HPG ’09, Association for Computing Machinery, New York, NY, USA, 2009, p. 23–28. doi:10.1145/1572769.1572773. URL https://doi.org/10.1145/1572769.1572773

    work page doi:10.1145/1572769.1572773 2009

  55. [55]

    Lauterbach, M

    C. Lauterbach, M. Garland, S. Sengupta, D. Luebke, D. Manocha, Fast bvh construction on gpus, Computer graphics forum 28 (2) (2009) 375–384

    work page 2009

  56. [56]

    Pantaleoni, D

    J. Pantaleoni, D. Luebke, Hlbvh: hierarchical lbvh construction for real-time ray tracing of dynamic geometry, in: Pro- ceedings of the Conference on High Performance Graphics, Eurographics Association, Goslar Germany, Germany, 2010, pp. 87–95

    work page 2010

  57. [57]

    Garanzha, J

    K. Garanzha, J. Pantaleoni, D. McAllister, S. N. Spencer, Simpler and faster hlbvh with work queues, in: Proceedings HPG 2011 : ACM SIGGRAPH Symposium on High Performance Graphics, Vancouver, British Columbia, Canada, August 5-7, 2011, ACM, New York, NY, USA, 2011, pp. 59–64

    work page 2011

  58. [58]

    Kalojanov, M

    J. Kalojanov, M. Billeter, P. Slusallek, Two-level grids for ray tracing on gpus, Computer graphics forum 30 (2) (2011) 307–314

    work page 2011

  59. [59]

    T. Karras, Maximizing parallelism in the construction of bvhs, octrees, and k-d trees, in: Proceedings of the Fourth ACM SIGGRAPH / Eurographics Conference on High-Performance Graphics, EGGH-HPG’12, Eurographics Association, Goslar, DEU, 2012, p. 33–37

    work page 2012

  60. [60]

    Keller, A

    S. Keller, A. Cavelan, R. Cabezon, L. Mayer, F. Ciorba, Cornerstone: Octree construction algorithms for scalable particle simulations, in: Proceedings of the Platform for Advanced Scientific Computing Conference, PASC ’23, Association for Computing Machinery, New York, NY, USA, 2023. doi:10.1145/3592979.3593417. URL https://doi.org/10.1145/3592979.3593417

    work page doi:10.1145/3592979.3593417 2023

  61. [61]

    Stanford Bunny.stl, https://commons.wikimedia.org/wiki/File:Stanford_Bunny.stl, downloaded from Wikimedia Commons, licensed under CC‑BY‑3.0 (Jan 23 2020)

    work page 2020

  62. [62]

    J. Latt, O. Malaspinas, D. Kontaxakis, A. Parmigiani, D. Lagrava, F. Brogi, M. B. Belgacem, Y. Thorimbert, S. Leclaire, S. Li, F. Marson, J. Lemus, C. Kotsalos, R. Conradin, C. Coreixas, R. Petkantchin, F. Raynaud, J. Beny, B. Chopard, Palabos: Parallel lattice boltzmann solver, Computers & mathematics with applications 81 (1) (2021) 334–350

    work page 2021

  63. [63]

    Russell, Z

    D. Russell, Z. Jane Wang, A cartesian grid method for modeling multiple moving objects in 2d incompressible viscous flow, Journal of Computational Physics 191 (1) (2003) 177–205. doi:https://doi.org/10.1016/S0021-9991(03)00310-3 . URL https://www.sciencedirect.com/science/article/pii/S0021999103003103

    work page doi:10.1016/s0021-9991(03)00310-3 2003

  64. [64]

    Calhoun, A cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions, Journal of Computational Physics 176 (2) (2002) 231–275

    D. Calhoun, A cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions, Journal of Computational Physics 176 (2) (2002) 231–275. doi:https://doi.org/10.1006/jcph.2001.6970. URL https://www.sciencedirect.com/science/article/pii/S0021999101969700

    work page doi:10.1006/jcph.2001.6970 2002

  65. [65]

    C. Liu, X. Zheng, C. Sung, Preconditioned multigrid methods for unsteady incompressible flows , Journal of Computational Physics 139 (1) (1998) 35–57. doi:https://doi.org/10.1006/jcph.1997.5859. URL https://www.sciencedirect.com/science/article/pii/S0021999197958599

    work page doi:10.1006/jcph.1997.5859 1998

  66. [66]

    J.-I. Choi, R. C. Oberoi, J. R. Edwards, J. A. Rosati, An immersed boundary method for complex incompressible flows , Journal of Computational Physics 224 (2) (2007) 757–784. doi:https://doi.org/10.1016/j.jcp.2006.10.032. URL https://www.sciencedirect.com/science/article/pii/S0021999106005481

    work page doi:10.1016/j.jcp.2006.10.032 2007

  67. [67]

    J. Kim, D. Kim, H. Choi, An immersed-boundary finite-volume method for simulations of flow in complex geometries , Journal of Computational Physics 171 (1) (2001) 132–150. doi:https://doi.org/10.1006/jcph.2001.6778. URL https://www.sciencedirect.com/science/article/pii/S0021999101967786

    work page doi:10.1006/jcph.2001.6778 2001

  68. [68]

    A. K. Saha, K. Muralidhar, G. Biswas, Transition and chaos in two-dimensional flow past a square cylinder, Journal of engineering mechanics 126 (5) (2000) 523–532

    work page 2000

  69. [69]

    Fakhari, T

    A. Fakhari, T. Lee, Finite-difference lattice boltzmann method with a block-structured adaptive-mesh-refinement tech- nique, Phys. Rev. E 89 (2014) 033310. doi:10.1103/PhysRevE.89.033310. URL https://link.aps.org/doi/10.1103/PhysRevE.89.033310

    work page doi:10.1103/physreve.89.033310 2014

  70. [70]

    A. P. Singh, A. K. De, V. K. Carpenter, V. Eswaran, K. Muralidhar, Flow past a transversely oscillating square cylinder in free stream at low reynolds numbers , International Journal for Numerical Methods in Fluids 61 (6) (2009) 658–682. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.1979, doi:https://doi.org/10.1002/fld.1979. URL https://onlin...

    work page doi:10.1002/fld.1979 2009

  71. [71]

    Pavlov, S

    A. Pavlov, S. Sazhin, R. Fedorenko, M. Heikal, A conservative finite difference method and its application for the analysis of a transient flow around a square prism , International Journal of Numerical Methods for Heat & Fluid Flow 10 (1) (2000) 6–47. arXiv:https://www.emerald.com/hff/article-pdf/10/1/6/650843/09615530010306894.pdf, doi:10.1108/ 09615530...

    work page doi:10.1108/09615530010306894 2000

  72. [72]

    Mikhailov, A

    M. Mikhailov, A. S. Freire, The drag coefficient of a sphere: An approximation using shanks transform , Powder Technology 237 (2013) 432–435. doi:https://doi.org/10.1016/j.powtec.2012.12.033. URL https://www.sciencedirect.com/science/article/pii/S0032591012008327

    work page doi:10.1016/j.powtec.2012.12.033 2013

  73. [73]

    F. W. Roos, W. W. Willmarth, Some experimental results on sphere and disk drag , AIAA Journal 9 (2) (1971) 285–291. arXiv:https://doi.org/10.2514/3.6164, doi:10.2514/3.6164. URL https://doi.org/10.2514/3.6164 48

    work page doi:10.2514/3.6164 1971

  74. [74]

    P. P. Brown, D. F. Lawler, Sphere drag and settling velocity revisited , Journal of Environmental Engineering 129 (3) (2003) 222–231. arXiv:https://ascelibrary.org/doi/pdf/10.1061/\%28ASCE\%290733-9372\%282003\%29129\ %3A3\%28222\%29, doi:10.1061/(ASCE)0733-9372(2003)129:3(222). URL https://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9372%282003%29129%...

    work page doi:10.1061/(asce)0733-9372(2003)129:3(222 2003