FluidX3D

The fastest and most memory efficient lattice Boltzmann CFD software, running on all GPUs via OpenCL.

Update History

v1.0 (04.08.2022)
- initial release
v1.1 (29.09.2022)
- added solid voxelization on GPU (slow algorithm)
- added tool to print current camera position (key_H)
- minor bug fix (workaround for Intel iGPU driver bug with triangle rendering)
v1.2 (24.10.2022)
- added functions to compute force/torque on objects
- added function to translate Mesh
- added Stokes drag validation setup
v1.3 (10.11.2022)
- added unit conversion functions for torque
- FORCE_FIELD and VOLUME_FORCE can now be used independently
- minor bug fix (workaround for AMD legacy driver bug with binary number literals)
v1.4 (14.12.2022)
- added interactive graphics mode on Linux with X11
- fixed streamline visualization bug in 2D
v2.0 (09.01.2023)
- added (cross-vendor) multi-GPU support on a single node (PC/laptop/server)
v2.1 (15.01.2023)
- made solid voxelization on GPU lightning fast (new algorithm, from minutes to milliseconds)
v2.2 (20.01.2023)
- added option to voxelize moving/rotating geometry on GPU, with automatic velocity initialization for each grid point based on center of rotation, linear velocity and rotational velocity
- cells that are converted from solid->fluid during re-voxelization now have their DDFs properly initialized
- added option to not auto-scale mesh during read_stl(...), with negative size parameter
- added kernel for solid boundary rendering with marching-cubes
v2.3 (30.01.2023)
- added particles with immersed-boundary method (either passive or 2-way-coupled, only supported with single-GPU)
- minor optimization to GPU voxelization algorithm (workgroup threads outside mesh bounding-box return after ray-mesh intersections have been found)
- displayed GPU memory allocation size is now fully accurate
- fixed bug in write_line() function in src/utilities.hpp
- removed .exe file extension for Linux/macOS
v2.4 (11.03.2023)
- added a help menu with key H that shows keyboard/mouse controls, visualization settings and simulation stats
- improvements to keyboard/mouse control (+/- for zoom, mouseclick frees/locks cursor)
- added suggestion of largest possible grid resolution if resolution is set larger than memory allows
- minor optimizations in multi-GPU communication (insignificant performance difference)
- fixed bug in temperature equilibrium function for temperature extension
- fixed erroneous double literal for Intel iGPUs in skybox color functions
- fixed bug in make.sh where multi-GPU device IDs would not get forwarded to the executable
- minor bug fixes in graphics engine (free cursor not centered during rotation, labels in VR mode)
- fixed bug in LBM::voxelize_stl() size parameter standard initialization
v2.5 (11.04.2023)
- implemented light absorption in fluid for raytracing graphics (no performance impact)
- improved raytracing framerate when camera is inside fluid
- fixed skybox pole flickering artifacts
- fixed bug where moving objects during re-voxelization would leave an erroneous trail of solid grid cells behind
v2.6 (16.04.2023)
- patched OpenCL issues of Intel Arc GPUs: now VRAM allocations >4GB are possible and correct VRAM capacity is reported

Compute Features - Getting the Memory Problem under Control

CFD model: lattice Boltzmann method (LBM)
- streaming (part 2/2)
  f₀^temp(x,t) = f₀(x, t)
  f_i^temp(x,t) = f_{(t%2 ? i : (i%2 ? i+1 : i-1))}(i%2 ? x : x-e_i, t) for i ∈ [1, q-1]
- collision
  ρ(x,t) = (Σ_i f_i^temp(x,t)) + 1
  
  u(x,t) = ¹∕_ρ(x,t) Σ_i c_i f_i^temp(x,t)
  
  f_i^eq-shifted(x,t) = w_i ρ · (^(u_°c_i)²∕_(2c⁴) - ^(u_°u)∕_(2c²) + ^(u_°c_i)∕_c²) + w_i (ρ-1)
  
  f_i^temp(x, t+Δt) = f_i^temp(x,t) + Ω_i(f_i^temp(x,t), f_i^eq-shifted(x,t), τ)
- streaming (part 1/2)
  f₀(x, t+Δt) = f₀^temp(x, t+Δt)
  f_{(t%2 ? (i%2 ? i+1 : i-1) : i)}(i%2 ? x+e_i : x, t+Δt) = f_i^temp(x, t+Δt) for i ∈ [1, q-1]
- velocity sets: D2Q9, D3Q15, D3Q19 (default), D3Q27
- collision operators: single-relaxation-time (SRT/BGK) (default), two-relaxation-time (TRT)

optimized to minimize VRAM footprint to 1/6 of other LBM codes

traditional LBM (D3Q19) with FP64 requires ~344 Bytes/cell
- 🟧🟧🟧🟧🟧🟧🟧🟧🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
  (density 🟧, velocity 🟦, flags 🟨, 2 copies of DDFs 🟩/🟥; each square = 1 Byte)
- allows for 3 Million cells per 1 GB VRAM
FluidX3D (D3Q19) requires only 55 Bytes/cell with Esoteric-Pull+FP16
- 🟧🟧🟧🟧🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩
  (density 🟧, velocity 🟦, flags 🟨, DDFs 🟩; each square = 1 Byte)
- allows for 19 Million cells per 1 GB VRAM
- in-place streaming with Esoteric-Pull: eliminates redundant copy B of density distribution functions (DDFs) in memory; almost cuts memory demand in half and slightly increases performance due to implicit bounce-back boundaries; offers optimal memory access patterns for single-cell in-place streaming
- decoupled arithmetic precision (FP32) and memory precision (FP32 or FP16S or FP16C): all arithmetic is done in FP32 for compatibility on all hardware, but DDFs in memory can be compressed to FP16S or FP16C: almost cuts memory demand in half again and almost doubles performance, without impacting overall accuracy for most setups
- only 8 flag bits per lattice point (can be used independently / at the same time)
  - TYPE_S (stationary or moving) solid boundaries
  - TYPE_E equilibrium boundaries (inflow/outflow)
  - TYPE_T temperature boundaries
  - TYPE_F free surface (fluid)
  - TYPE_I free surface (interface)
  - TYPE_G free surface (gas)
  - TYPE_X remaining for custom use or further extensions
  - TYPE_Y remaining for custom use or further extensions

large cost saving: comparison of maximum single-GPU grid resolution for D3Q19 LBM

GPU VRAM capacity	1 GB	2 GB	3 GB	4 GB	6 GB	8 GB	10 GB	11 GB	12 GB	16 GB	20 GB	24 GB	32 GB	40 GB	48 GB	64 GB	80 GB	94 GB	128 GB	192 GB	256 GB
approximate GPU price	$25 GT 210	$25 GTX 950	$12 GTX 1060	$50 GT 730	$35 GTX 1060	$70 RX 470	$500 RTX 3080	$240 GTX 1080 Ti	$75 Tesla M40	$75 Instinct MI25	$900 RX 7900 XT	$205 Tesla P40	$600 Instinct MI60	$5500 A100	$2400 RTX 8000	$10k Instinct MI210	$11k A100	>$40k H100 NVL	? Max Series 1550	-	-
traditional LBM (FP64)	144³	182³	208³	230³	262³	288³	312³	322³	330³	364³	392³	418³	460³	494³	526³	578³	624³	658³	730³	836³	920³
FluidX3D (FP32/FP32)	224³	282³	322³	354³	406³	448³	482³	498³	512³	564³	608³	646³	710³	766³	814³	896³	966³	1018³	1130³	1292³	1422³
FluidX3D (FP32/FP16)	266³	336³	384³	424³	484³	534³	574³	594³	610³	672³	724³	770³	848³	912³	970³	1068³	1150³	1214³	1346³	1540³	1624³

cross-vendor multi-GPU support on a single PC/laptop/server

domain decomposition allows pooling VRAM from multiple GPUs for much larger grid resolution
each domain (GPU) can hold up to 4.29 billion (2³², 1624³) lattice points (225 GB memory)
GPUs don't have to be identical (not even from the same vendor), but similar VRAM capacity/bandwidth is recommended

domain communication architecture (simplified)

++   .-----------------------------------------------------------------.   ++
++   |                              GPU 0                              |   ++
++   |                          LBM Domain 0                           |   ++
++   '-----------------------------------------------------------------'   ++
++              |                 selective                /|\             ++
++             \|/               in-VRAM copy               |              ++
++        .-------------------------------------------------------.        ++
++        |               GPU 0 - Transfer Buffer 0               |        ++
++        '-------------------------------------------------------'        ++
!!                            |     PCIe     /|\                           !!
!!                           \|/    copy      |                            !!
@@        .-------------------------.   .-------------------------.        @@
@@        | CPU - Transfer Buffer 0 |   | CPU - Transfer Buffer 1 |        @@
@@        '-------------------------'\ /'-------------------------'        @@
@@                           pointer  X   swap                             @@
@@        .-------------------------./ \.-------------------------.        @@
@@        | CPU - Transfer Buffer 1 |   | CPU - Transfer Buffer 0 |        @@
@@        '-------------------------'   '-------------------------'        @@
!!                           /|\    PCIe      |                            !!
!!                            |     copy     \|/                           !!
++        .-------------------------------------------------------.        ++
++        |               GPU 1 - Transfer Buffer 1               |        ++
++        '-------------------------------------------------------'        ++
++             /|\                selective                 |              ++
++              |                in-VRAM copy              \|/             ++
++   .-----------------------------------------------------------------.   ++
++   |                              GPU 1                              |   ++
++   |                          LBM Domain 1                           |   ++
++   '-----------------------------------------------------------------'   ++
##                                    |                                    ##
##                      domain synchronization barrier                     ##
##                                    |                                    ##
||   -------------------------------------------------------------> time   ||

domain communication architecture (detailed)

++   .-----------------------------------------------------------------.   ++
++   |                              GPU 0                              |   ++
++   |                          LBM Domain 0                           |   ++
++   '-----------------------------------------------------------------'   ++
++     |  selective in- /|\  |  selective in- /|\  |  selective in- /|\    ++
++    \|/ VRAM copy (X)  |  \|/ VRAM copy (Y)  |  \|/ VRAM copy (Z)  |     ++
++   .---------------------.---------------------.---------------------.   ++
++   |    GPU 0 - TB 0X+   |    GPU 0 - TB 0Y+   |    GPU 0 - TB 0Z+   |   ++
++   |    GPU 0 - TB 0X-   |    GPU 0 - TB 0Y-   |    GPU 0 - TB 0Z-   |   ++
++   '---------------------'---------------------'---------------------'   ++
!!          | PCIe /|\            | PCIe /|\            | PCIe /|\         !!
!!         \|/ copy |            \|/ copy |            \|/ copy |          !!
@@   .---------. .---------.---------. .---------.---------. .---------.   @@
@@   | CPU 0X+ | | CPU 1X- | CPU 0Y+ | | CPU 3Y- | CPU 0Z+ | | CPU 5Z- |   @@
@@   | CPU 0X- | | CPU 2X+ | CPU 0Y- | | CPU 4Y+ | CPU 0Z- | | CPU 6Z+ |   @@
@@   '---------\ /---------'---------\ /---------'---------\ /---------'   @@
@@      pointer X swap (X)    pointer X swap (Y)    pointer X swap (Z)     @@
@@   .---------/ \---------.---------/ \---------.---------/ \---------.   @@
@@   | CPU 1X- | | CPU 0X+ | CPU 3Y- | | CPU 0Y+ | CPU 5Z- | | CPU 0Z+ |   @@
@@   | CPU 2X+ | | CPU 0X- | CPU 4Y+ | | CPU 0Y- | CPU 6Z+ | | CPU 0Z- |   @@
@@   '---------' '---------'---------' '---------'---------' '---------'   @@
!!         /|\ PCIe |            /|\ PCIe |            /|\ PCIe |          !!
!!          | copy \|/            | copy \|/            | copy \|/         !!
++   .--------------------..---------------------..--------------------.   ++
++   |   GPU 1 - TB 1X-   ||    GPU 3 - TB 3Y-   ||   GPU 5 - TB 5Z-   |   ++
++   :====================::=====================::====================:   ++
++   |   GPU 2 - TB 2X+   ||    GPU 4 - TB 4Y+   ||   GPU 6 - TB 6Z+   |   ++
++   '--------------------''---------------------''--------------------'   ++
++    /|\ selective in-  |  /|\ selective in-  |  /|\ selective in-  |     ++
++     |  VRAM copy (X) \|/  |  VRAM copy (Y) \|/  |  VRAM copy (Z) \|/    ++
++   .--------------------..---------------------..--------------------.   ++
++   |        GPU 1       ||        GPU 3        ||        GPU 5       |   ++
++   |    LBM Domain 1    ||    LBM Domain 3     ||    LBM Domain 5    |   ++
++   :====================::=====================::====================:   ++
++   |        GPU 2       ||        GPU 4        ||        GPU 6       |   ++
++   |    LBM Domain 2    ||    LBM Domain 4     ||    LBM Domain 6    |   ++
++   '--------------------''---------------------''--------------------'   ++
##              |                     |                     |              ##
##              |      domain synchronization barriers      |              ##
##              |                     |                     |              ##
||   -------------------------------------------------------------> time   ||

peak performance on GPUs (datacenter/gaming/professional/laptop), validated with roofline model
DDF-shifting and other algebraic optimization to minimize round-off error
powerful model extensions
- boundary types
  - stationary mid-grid bounce-back boundaries (stationary solid boundaries)
  - moving mid-grid bounce-back boundaries (moving solid boundaries)
  - equilibrium boundaries (non-reflective inflow/outflow)
  - temperature boundaries (fixed temperature)
- global force per volume (Guo forcing), can be modified on-the-fly
- local force per volume (force field)
  - optional computation of forces from the fluid on solid boundaries
- state-of-the-art free surface LBM (FSLBM) implementation:
  - volume-of-fluid model
  - fully analytic PLIC for efficient curvature calculation
  - improved mass conservation
  - ultra efficient implementation with only 4 kernels additionally to stream_collide() kernel
- thermal LBM to simulate thermal convection
  - D3Q7 subgrid for thermal DDFs
  - in-place streaming with Esoteric-Pull for thermal DDFs
  - optional FP16S or FP16C compression for thermal DDFs with DDF-shifting
- Smagorinsky-Lilly subgrid turbulence LES model to keep simulations with very large Reynolds number stable
  Π_αβ = Σ_i e_iα e_iβ (f_i - f_i^eq-shifted)
  
  Q = Σ_αβ Π_αβ²
  ______________________
  τ = ½ (τ₀ + √ τ₀² + ^(16√2)∕_(3π²) ^√Q∕_ρ )
- particles with immersed-boundary method (either passive or 2-way-coupled, only supported with single-GPU)

Solving the Visualization Problem

FluidX3D can do simulations so large that storing the volumetric data for later rendering becomes unmanageable (like 120GB for a single frame, hundreds of TeraByte for a video)
instead, FluidX3D allows rendering raw simulation data directly in VRAM, so no large volumetric files have to be exported to the hard disk (see my technical talk)
the rendering is so fast that it works interactively in real time for both rasterization and raytracing
if no monitor is available (like on a remote Linux server), there is an ASCII rendering mode to interactively visualize the simulation in the terminal (even in WSL and/or through SSH)
rendering is fully multi-GPU-parallelized via seamless domain decomposition rasterization
with interactive graphics mode disabled, image resolution can be as large as VRAM allows for (4K/8K/16K and above)
(interacitive) visualization modes:
- flags (and force vectors on solid boundary cells if the extension is used)
- velocity field
- streamlines
- velocity-colored Q-criterion isosurface
- rasterized free surface with marching-cubes
- raytraced free surface with fast ray-grid traversal and marching-cubes, either 1-4 rays/pixel or 1-10 rays/pixel

Solving the Compatibility Problem

FluidX3D is written in OpenCL 1.2, so it runs on any hardware from any vendor (Nvidia, AMD, Intel, ...):
- world's fastest datacenter GPUs, like H100, A100, MI250(X), MI210, MI100, V100(S), P100, ...
- gaming GPUs (desktop or laptop), like Nvidia GeForce, AMD Radeon, Intel Arc
- professional/workstation GPUs, like Nvidia Quadro, AMD Radeon Pro / FirePro
- integrated GPUs
- Intel Xeon Phi (requires installation of the Intel OpenCL CPU Runtime ("oclcpuexp"))
- Intel/AMD CPUs (requires installation of the Intel OpenCL CPU Runtime ("oclcpuexp"))
- even smartphone ARM GPUs
supports parallelization across multiple GPUs on a single PC/laptop/server with PCIe communication, no SLI/Crossfire/NVLink/InfinityFabric or MPI installation required; the GPUs don't even have to be from the same vendor, but similar memory capacity and bandwidth is recommended
works in Windows and Linux with C++17, with limited support also for MacOS and Android
supports importing and voxelizing triangle meshes from binary .stl files, with fast GPU voxelization
supports exporting volumetric data as binary .vtk files with lbm.<field>.write_device_to_vtk();
supports exporting rendered frames as .png/.qoi/.bmp files with lbm.graphics.write_frame();, encoding is handled in parallel on the CPU while the simulation on GPU can continue without delay

How to get started?

Check the settings and extensions in src/defines.hpp by uncommenting corresponding lines.
Write a C++ setup skript as main_setup() function in src/setup.cpp (get inspiration from existing setups):
- For unit conversion, use the units struct.
- For initializing the box, use call LBM lbm(Nx, Ny, Nz, nu, ...); constructor. To use multiple GPUs, use LBM lbm(Nx, Ny, Nz, Dx, Dy, Dz, nu, ...);, with Dx/Dy/Dz indicating how many domains (GPUs) there are in each spatial direction.
- Set the initial condition in a loop that iterates over the entire lattice by writing to lbm.rho[n]/lbm.u.x[n]/lbm.u.y[n]/lbm.u.z[n]/lbm.flags[n].
- Call lbm.run(); to initialize and execute the setup (infinite time steps) or lbm.run(time_steps); to execute only a specific number of time steps.
- As long as the lbm object is in scope, you can access the memory. As soon as it goes out of scope, all memory associated to the current simulation is freed again.
When done with the setup, on Windows in Visual Studio Community select "Release" and "x64" and hit compile+run, or on Linux execute chmod +x make.sh and ./make.sh; this will automatically select the fastest installed GPU(s). Alternatively, you can add the device ID(s) as command-line arguments, for example ./make.sh 2 to compile+run on device 2, or bin/FluidX3D 1 3 to run the executable on devices 1 and 3. Compile time for the entire code is about 10 seconds. If you use INTERACTIVE_GRAPHICS on Linux, change to the "compile on Linux with X11" command in make.sh.
Keyboard/mouse controls with INTERACTIVE_GRAPHICS/INTERACTIVE_GRAPHICS_ASCII enabled:
- P: start/pause the simulation
- H: show/hide help
- 1: flags (and force vectors on solid boundary cells if the extension is used)
- 2: velocity field
- 3: streamlines
- 4: vorticity / velocity-colored Q-criterion isosurface
- 5: rasterized free surface
- 6: raytraced free surface
- 7: particles
- Mouse or I/J/K/L: rotate camera
- Scrollwheel or +/-: zoom (centered camera mode) or camera movement speed (free camera mode)
- Mouseclick or U: toggle rotation with Mouse and angle snap rotation with I/J/K/L
- Y/X: adjust camera field of view
- G: print current camera position/rotation in console as copy/paste command
- R: toggle camera autorotation
- F: toggle centered/free camera mode
- W/A/S/D/Space/C: move free camera
- V: toggle stereoscopic rendering for VR
- B: toggle VR-goggles/3D-TV mode for stereoscopic rendering
- N/M: adjust eye distance for stereoscopic rendering
- Esc/Alt+F4: quit

Single-GPU Benchmarks

Here are performance benchmarks on various hardware in MLUPs/s, or how many million lattice points are updated per second. The settings used for the benchmark are D3Q19 SRT with no extensions enabled (only LBM with implicit mid-grid bounce-back boundaries) and the setup consists of an empty cubic box with sufficient size (typically 256³). Without extensions, a single lattice point requires:

a memory capacity of 93 (FP32/FP32) or 55 (FP32/FP16) Bytes
a memory bandwidth of 153 (FP32/FP32) or 77 (FP32/FP16) Bytes per time step
363 (FP32/FP32) or 406 (FP32/FP16S) or 1275 (FP32/FP16C) FLOPs per time step (FP32+INT32 operations counted combined)

In consequence, the arithmetic intensity of this implementation is 2.37 (FP32/FP32) or 5.27 (FP32/FP16S) or 16.56 (FP32/FP16C) FLOPs/Byte. So performance is only limited by memory bandwidth.

If your GPU is not on the list yet, you can report your benchmarks here.

Colors: 🔴 AMD, 🔵 Intel, 🟢 Nvidia, 🟣 Apple, 🟡 Samsung

Device	FP32 [TFlops/s]	Mem [GB]	BW [GB/s]	FP32/FP32 [MLUPs/s]	FP32/FP16S [MLUPs/s]	FP32/FP16C [MLUPs/s]

🔴 Instinct MI250 (1 GCD)	45.26	64	1638	5638 (53%)	9030 (42%)	8506 (40%)
🔴 Radeon VII	13.83	16	1024	4898 (73%)	7778 (58%)	5256 (40%)
🟢 H100 PCIe 80GB	51.01	80	2000	11128 (85%)	20624 (79%)	13862 (53%)
🟢 A100 SXM4 80GB	19.49	80	2039	10228 (77%)	18448 (70%)	11197 (42%)
🟢 A100 SXM4 40GB	19.49	40	1555	8522 (84%)	16013 (79%)	11251 (56%)
🟢 A100 PCIe 40GB	19.49	40	1555	8526 (84%)	16035 (79%)	11088 (55%)
🟢 Tesla V100 SXM2 32GB	15.67	32	900	4471 (76%)	8947 (77%)	7217 (62%)
🟢 Tesla V100 PCIe 16GB	14.13	16	900	5128 (87%)	10325 (88%)	7683 (66%)
🟢 Quadro GV100	16.66	32	870	3442 (61%)	6641 (59%)	5863 (52%)
🟢 Titan V	14.90	12	653	3601 (84%)	7253 (86%)	6957 (82%)
🟢 Tesla P100 16GB	9.52	16	732	3295 (69%)	5950 (63%)	4176 (44%)
🟢 Tesla P100 12GB	9.52	12	549	2427 (68%)	4141 (58%)	3999 (56%)
🟢 Tesla K40m	4.29	12	288	1131 (60%)	1868 (50%)	912 (24%)
🟢 Tesla K80 (1 GPU)	4.11	12	240	916 (58%)	1642 (53%)	943 (30%)
🟢 Tesla K20c	3.52	5	208	861 (63%)	1507 (56%)	720 (27%)

🔴 Radeon RX 7900 XTX	61.44	24	960	3665 (58%)	7644 (61%)	7716 (62%)
🔴 Radeon RX 7900 XT	51.61	20	800	3013 (58%)	5856 (56%)	5986 (58%)
🔴 Radeon RX 6900 XT	23.04	16	512	1968 (59%)	4227 (64%)	4207 (63%)
🔴 Radeon RX 6800 XT	20.74	16	512	2008 (60%)	4241 (64%)	4224 (64%)
🔴 Radeon RX 5700 XT	9.75	8	448	1368 (47%)	3253 (56%)	3049 (52%)
🔴 Radeon RX Vega 64	13.35	8	484	1875 (59%)	2878 (46%)	3227 (51%)
🔴 Radeon RX 580 4GB	6.50	4	256	946 (57%)	1848 (56%)	1577 (47%)
🔴 Radeon HD 7850	1.84	2	154	112 (11%)	120 ( 6%)	635 (32%)
🔵 Arc A770 LE	19.66	16	560	2741 (75%)	4591 (63%)	4626 (64%)
🔵 Arc A750 LE	17.20	8	512	2625 (78%)	4184 (63%)	4238 (64%)
🟢 GeForce RTX 4090	82.58	24	1008	5624 (85%)	11091 (85%)	11496 (88%)
🟢 RTX 6000 Ada	91.10	48	960	4997 (80%)	10249 (82%)	10293 (83%)
🟢 GeForce RTX 4080	55.45	16	717	3914 (84%)	7626 (82%)	7933 (85%)
🟢 GeForce RTX 3090 Ti	40.00	24	1008	5717 (87%)	10956 (84%)	10400 (79%)
🟢 GeForce RTX 3090	39.05	24	936	5418 (89%)	10732 (88%)	10215 (84%)
🟢 GeForce RTX 3080 Ti	37.17	12	912	5202 (87%)	9832 (87%)	9347 (79%)
🟢 RTX A6000	40.00	48	768	4421 (88%)	8814 (88%)	8533 (86%)
🟢 GeForce RTX 3080	29.77	10	760	4230 (85%)	8118 (82%)	7714 (78%)
🟢 GeForce RTX 3070	20.31	8	448	2578 (88%)	5096 (88%)	5060 (87%)
🟢 GeForce RTX 3060 Ti	16.49	8	448	2644 (90%)	5129 (88%)	4718 (81%)
🟢 RTX A5000M	16.59	16	448	2228 (76%)	4461 (77%)	3662 (63%)
🟢 GeForce RTX 3060	13.17	12	360	2108 (90%)	4070 (87%)	3566 (76%)
🟢 GeForce RTX 3060M	10.94	6	336	2019 (92%)	4012 (92%)	3572 (82%)
🟢 GeForce RTX 3050M	7.13	4	192	1180 (94%)	2339 (94%)	2016 (81%)
🟢 Titan RTX	16.31	24	672	3471 (79%)	7456 (85%)	7554 (87%)
🟢 Quadro RTX 6000	16.31	24	672	3307 (75%)	6836 (78%)	6879 (79%)
🟢 Quadro RTX 8000 Pass.	14.93	48	624	2591 (64%)	5408 (67%)	5607 (69%)
🟢 GeForce RTX 2080 Ti	13.45	11	616	3194 (79%)	6700 (84%)	6853 (86%)
🟢 GeForce RTX 2080 Sup.	11.34	8	496	2434 (75%)	5284 (82%)	5087 (79%)
🟢 Quadro RTX 5000	11.15	16	448	2341 (80%)	4766 (82%)	4773 (82%)
🟢 GeForce RTX 2060 Sup.	7.18	8	448	2503 (85%)	5035 (87%)	4463 (77%)
🟢 Quadro RTX 4000	7.12	8	416	2284 (84%)	4584 (85%)	4062 (75%)
🟢 GeForce RTX 2060 KO	6.74	6	336	1643 (75%)	3376 (77%)	3266 (75%)
🟢 GeForce RTX 2060	6.74	6	336	1681 (77%)	3604 (83%)	3571 (82%)
🟢 GeForce GTX 1660 Sup.	5.03	6	336	1696 (77%)	3551 (81%)	3040 (70%)
🟢 Tesla T4	8.14	15	300	1356 (69%)	2869 (74%)	2887 (74%)
🟢 GeForce GTX 1660 Ti	5.48	6	288	1467 (78%)	3041 (81%)	3019 (81%)
🟢 GeForce GTX 1660	5.07	6	192	1016 (81%)	1924 (77%)	1992 (80%)
🟢 GeForce GTX 1650M	3.20	4	128	706 (84%)	1214 (73%)	1400 (84%)
🟢 Titan Xp	12.15	12	548	2919 (82%)	5495 (77%)	5375 (76%)
🟢 GeForce GTX 1080 Ti	12.06	11	484	2631 (83%)	4837 (77%)	4877 (78%)
🟢 GeForce GTX 1080	9.78	8	320	1623 (78%)	3100 (75%)	3182 (77%)
🟢 GeForce GTX 1060M	4.44	6	192	983 (78%)	1882 (75%)	1803 (72%)
🟢 GeForce GTX 1050M Ti	2.49	4	112	631 (86%)	1224 (84%)	1115 (77%)
🟢 Quadro P1000	1.89	4	82	426 (79%)	839 (79%)	778 (73%)
🟢 GeForce GTX 970	4.17	4	224	980 (67%)	1721 (59%)	1623 (56%)
🟢 Quadro M4000	2.57	8	192	899 (72%)	1519 (61%)	1050 (42%)
🟢 Tesla M60 (1 GPU)	4.82	8	160	853 (82%)	1571 (76%)	1557 (75%)
🟢 GeForce GTX 960M	1.51	4	80	442 (84%)	872 (84%)	627 (60%)
🟢 Quadro K2000	0.73	2	64	312 (75%)	444 (53%)	171 (21%)
🟢 GeForce GT 630 (OEM)	0.46	2	29	151 (81%)	185 (50%)	78 (21%)
🟢 Quadro NVS 290	0.03	0.256	6	1 ( 2%)	1 ( 1%)	1 ( 1%)

🟣 M1 Max GPU 24C 32GB	6.14	22	400	2369 (91%)	4496 (87%)	2777 (53%)
🟣 M1 Pro GPU 16C 16GB	4.10	11	200	1204 (92%)	2329 (90%)	1855 (71%)
🔴 Radeon Vega 8 (4750G)	2.15	27	57	263 (71%)	511 (70%)	501 (68%)
🔴 Radeon Vega 8 (3500U)	1.23	7	38	157 (63%)	282 (57%)	288 (58%)
🔵 UHD Graphics 630	0.46	7	51	151 (45%)	301 (45%)	187 (28%)
🔵 HD Graphics 5500	0.35	3	26	75 (45%)	192 (58%)	108 (32%)
🔵 HD Graphics 4600	0.38	2	26	105 (63%)	115 (35%)	34 (10%)
🟡 ARM Mali-G72 MP18	0.24	4	29	14 ( 7%)	17 ( 5%)	12 ( 3%)

🔴 2x EPYC 9654	29.49	1536	922	1381 (23%)	1814 (15%)	1801 (15%)
🔵 Xeon Phi 7210	5.32	192	102	415 (62%)	193 (15%)	223 (17%)
🔵 4x Xeon E5-4620 v4	2.69	512	273	460 (26%)	275 ( 8%)	239 ( 7%)
🔵 2x Xeon E5-2630 v4	1.41	64	137	264 (30%)	146 ( 8%)	129 ( 7%)
🔵 2x Xeon E5-2623 v4	0.67	64	137	125 (14%)	66 ( 4%)	59 ( 3%)
🔵 2x Xeon E5-2680 v3	1.92	64	137	209 (23%)	305 (17%)	281 (16%)
🔵 Core i9-10980XE	3.23	128	94	286 (47%)	251 (21%)	223 (18%)
🔵 Core i5-9600	0.60	16	43	146 (52%)	127 (23%)	147 (27%)
🔵 Core i7-8700K	0.71	16	51	152 (45%)	134 (20%)	116 (17%)
🔵 Core i7-7700HQ	0.36	12	38	81 (32%)	82 (16%)	108 (22%)
🔵 Core i7-4770	0.44	16	26	104 (62%)	69 (21%)	59 (18%)
🔵 Core i7-4720HQ	0.33	16	26	58 (35%)	13 ( 4%)	47 (14%)

Multi-GPU Benchmarks

Multi-GPU benchmarks are done at the largest possible grid resolution with a cubic domain, and either 2x1x1, 2x2x1 or 2x2x2 of these cubic domains together. The percentages in brackets are single-GPU roofline model efficiency, and the multiplicator numbers in brackets are scaling factors relative to benchmarked single-GPU performance.

Colors: 🔴 AMD, 🔵 Intel, 🟢 Nvidia, 🟣 Apple, 🟡 Samsung

Device	FP32 [TFlops/s]	Mem [GB]	BW [GB/s]	FP32/FP32 [MLUPs/s]	FP32/FP16S [MLUPs/s]	FP32/FP16C [MLUPs/s]

🔴 1x Instinct MI250 (1 GCD)	45.26	64	1638	5638 (53%)	9030 (42%)	8506 (40%)
🔴 1x Instinct MI250 (2 GCD)	90.52	128	3277	9460 (1.7x)	14313 (1.6x)	17338 (2.0x)
🔴 2x Instinct MI250 (4 GCD)	181.04	256	6554	16925 (3.0x)	29163 (3.2x)	29627 (3.5x)
🔴 4x Instinct MI250 (8 GCD)	362.08	512	13107	27350 (4.9x)	52258 (5.8x)	53521 (6.3x)

🔴 1x Radeon VII	13.83	16	1024	4898 (73%)	7778 (58%)	5256 (40%)
🔴 2x Radeon VII	27.66	32	2048	8113 (1.7x)	15591 (2.0x)	10352 (2.0x)
🔴 4x Radeon VII	55.32	64	4096	12911 (2.6x)	24273 (3.1x)	17080 (3.2x)
🔴 8x Radeon VII	110.64	128	8192	21946 (4.5x)	30826 (4.0x)	24572 (4.7x)

🟢 1x A100 SXM4 40GB	19.49	40	1555	8543 (84%)	15917 (79%)	8748 (43%)
🟢 2x A100 SXM4 40GB	38.98	80	3110	14311 (1.7x)	23707 (1.5x)	15512 (1.8x)
🟢 4x A100 SXM4 40GB	77.96	160	6220	23411 (2.7x)	42400 (2.7x)	29017 (3.3x)
🟢 8x A100 SXM4 40GB	155.92	320	12440	37619 (4.4x)	72965 (4.6x)	63009 (7.2x)

🟢 1x A100 SXM4 40GB	19.49	40	1555	8522 (84%)	16013 (79%)	11251 (56%)
🟢 2x A100 SXM4 40GB	38.98	80	3110	13629 (1.6x)	24620 (1.5x)	18850 (1.7x)
🟢 4x A100 SXM4 40GB	77.96	160	6220	17978 (2.1x)	30604 (1.9x)	30627 (2.7x)

🟢 1x Tesla V100 SXM2 32GB	15.67	32	900	4471 (76%)	8947 (77%)	7217 (62%)
🟢 2x Tesla V100 SXM2 32GB	31.34	64	1800	7953 (1.8x)	15469 (1.7x)	12932 (1.8x)
🟢 4x Tesla V100 SXM2 32GB	62.68	128	3600	13135 (2.9x)	26527 (3.0x)	22686 (3.1x)

🟢 1x Tesla K40m	4.29	12	288	1131 (60%)	1868 (50%)	912 (24%)
🟢 2x Tesla K40m	8.58	24	577	1971 (1.7x)	3300 (1.8x)	1801 (2.0x)
🟢 3x K40m + 1x Titan Xp	17.16	48	1154	3117 (2.8x)	5174 (2.8x)	3127 (3.4x)

🟢 1x RTX A6000	40.00	48	768	4421 (88%)	8814 (88%)	8533 (86%)
🟢 2x RTX A6000	80.00	96	1536	8041 (1.8x)	15026 (1.7x)	14795 (1.7x)
🟢 4x RTX A6000	160.00	192	3072	14314 (3.2x)	27915 (3.2x)	27227 (3.2x)
🟢 8x RTX A6000	320.00	384	6144	19311 (4.4x)	40063 (4.5x)	39004 (4.6x)

🟢 1x Quadro RTX 8000 Pa.	14.93	48	624	2591 (64%)	5408 (67%)	5607 (69%)
🟢 2x Quadro RTX 8000 Pa.	29.86	96	1248	4767 (1.8x)	9607 (1.8x)	10214 (1.8x)

🟢 1x GeForce RTX 2080 Ti	13.45	11	616	3194 (79%)	6700 (84%)	6853 (86%)
🟢 2x GeForce RTX 2080 Ti	26.90	22	1232	5085 (1.6x)	10770 (1.6x)	10922 (1.6x)
🟢 4x GeForce RTX 2080 Ti	53.80	44	2464	9117 (2.9x)	18415 (2.7x)	18598 (2.7x)
🟢 7x 2080 Ti + 1x A100 40GB	107.60	88	4928	16146 (5.1x)	33732 (5.0x)	33857 (4.9x)

FAQs

General

What physical model does FluidX3D use?

FluidX3D implements the lattice Boltzmann method, a type of direct numerical simulation (DNS), the most accurate type of fluid simulation, but also the most computationally challenging. Optional extension models include volume force (Guo forcing), free surface (volume-of-fluid and PLIC), a temperature model and Smagorinsky-Lilly subgrid turbulence model.
FluidX3D only uses FP32 or even FP32/FP16, in contrast to FP64. Are simulation results physically accurate?

Yes, in all but extreme edge cases. The code has been specially optimized to minimize arithmetic round-off errors and make the most out of lower precision. With these optimizations, accuracy in most cases is indistinguishable from FP64 double-precision, even with FP32/FP16 mixed-precision. Details can be found in this paper.
Why is the domain size limited to 2³² grid points?

The 32-bit unsigned integer grid index will overflow above this number. Using 64-bit index calculation would slow the simulation down by ~20%, as 64-bit uint is calculated on special function units and not the regular GPU cores. 2³² grid points with FP32/FP16 mixed-precision is equivalent to 225GB memory and single GPUs currently are only at 128GB, so it should be fine for a while to come. For higher resolutions above the single-domain limit, use multiple domains (typically 1 per GPU, but multiple domains on the same GPU also work).
Comparted to the benchmark numbers stated here, efficiency seems much lower but performance is slightly better for most devices. How can this be?

In that paper, the One-Step-Pull swap algorithm is implemented, using only misaligned reads and coalesced writes. On almost all GPUs, the performance penalty for misaligned writes is much larger than for misaligned reads, and sometimes there is almost no penalty for misaligned reads at all. Because of this, One-Step-Pull runs at peak bandwidth and thus peak efficiency.
Here, a different swap algorithm termed Esoteric-Pull is used, a type of in-place streaming. This makes the LBM require much less memory (93 vs. 169 (FP32/FP32) or 55 vs. 93 (FP32/FP16) Bytes/cell for D3Q19), and also less memory bandwidth (153 vs. 171 (FP32/FP32) or 77 vs. 95 (FP32/FP16) Bytes/cell per time step for D3Q19) due to so-called implicit bounce-back boundaries. However memory access now is half coalesced and half misaligned for both reads and writes, so memory access efficiency is lower. For overall performance, these two effects approximately cancel out. The benefit of Esoteric-Pull - being able to simulate domains twice as large with the same amount of memory - clearly outweights the cost of slightly lower memory access efficiency, especially since performance is not reduced overall.
Why don't you use CUDA? Wouldn't that be more efficient?

No, that is a wrong myth. OpenCL is exactly as efficient as CUDA on Nvidia GPUs if optimized properly. Here I did roofline model and analyzed OpenCL performance on various hardware. OpenCL efficiency on modern Nvidia GPUs can be 100% with the right memory access pattern, so CUDA can't possibly be any more efficient. Without any performance advantage, there is no reason to use proprietary CUDA over OpenCL, since OpenCL is compatible with a lot more hardware.
Why no multi-relaxation-time (MRT) collision operator?

The idea of MRT is to linearly transform the DDFs into "moment space" by matrix multiplication and relax these moments individually, promising better stability and accuracy. In practice, in the vast majority of cases, it has zero or even negative effects on stability and accuracy, and simple SRT is much superior. Apart from the kinematic shear viscosity and conserved terms, the remaining moments are non-physical quantities and their tuning is a blackbox. Although MRT can be implemented in an efficient manner with only a single matrix-vector multiplication in registers, leading to identical performance compared to SRT by remaining bandwidth-bound, storing the matrices vastly elongates and over-complicates the code for no real benefit.

Hardware

Can FluidX3D run on multiple GPUs at the same time?

Yes. The simulation grid is then split in domains, one for each GPU (domain decomposition method). The GPUs essentially pool their memory, enabling much larger grid resolution and higher performance. Rendering is parallelized across multiple GPUs as well; each GPU renders its own domain with a 3D offset, then rendered frames from all GPUs are overlayed with their z-buffers. Communication between domains is done over PCIe, so no SLI/Crossfire/NVLink/InfinityFabric is required. All GPUs must however be installed in the same node (PC/laptop/server). Even unholy combinations of Nvidia/AMD/Intel GPUs will work, although it is recommended to only use GPUs with similar memory capacity and bandwidth together. Using a fast gaming GPU and slow integrated GPU together would only decrease performance due to communication overhead.
I'm on a budget and have only a cheap computer. Can I run FluidX3D on my toaster PC/laptop?

Absolutely. Today even the most inexpensive hardware, like integrated GPUs or entry-level gaming GPUs, support OpenCL. You might be a bit more limited on memory capacity and grid resolution, but you should be good to go. I've tested FluidX3D on very old and inexpensive hardware and even on my Samsung S9+ smartphone, and it runs just fine, although admittedly a bit slower.
I don't have an expensive workstation GPU, but only a gaming GPU. Will performance suffer?

No. Efficiency on gaming GPUs is exactly as good as on their "professional"/workstation counterparts. Performance often is even better as gaming GPUs have higher boost clocks.
Do I need a GPU with ECC memory?

No. Gaming GPUs work just fine. Some Nvidia GPUs automatically reduce memory clocks for compute applications to almost entirely eliminate memory errors.
My GPU does not support CUDA. Can I still use FluidX3D?

Yes. FluidX3D uses OpenCL 1.2 and not CUDA, so it runs on any GPU from any vendor since around 2012.
I don't have a dedicated graphics card at all. Can I still run FluidX3D on my PC/laptop?

Yes. FluidX3D also runs on all integrated GPUs since around 2012, and also on CPUs.
I need more memory than my GPU can offer. Can I run FluidX3D on my CPU as well?

Yes. You only need to install the OpenCL Runtime for Intel CPUs.
In the benchmarks you list some very expensive hardware. How do you get access to that?

I'm a scientist (PhD candidate in computational physics) and I use FluidX3D for my research, so I have access to BZHPC, SuperMUC-NG and JURECA-DC supercomputers.

Graphics

I don't have an RTX/DXR GPU that supports raytracing. Can I still use raytracing graphics in FluidX3D?

Yes, and at full performance. FluidX3D does not use a bounding volume hierarchy (BVH) to accelerate raytracing, but fast ray-grid traversal instead, implemented directly in OpenCL C. This is much faster than BVH for moving isosurfaces in the LBM grid (~N vs. ~N²+log(N) runtime; LBM itself is ~N³), and it does not require any dedicated raytracing hardware. Raytracing in FluidX3D runs on any GPU that supports OpenCL 1.2.
I have a datacenter/mining GPU without any video output or graphics hardware. Can FluidX3D still render simulation results?

Yes. FluidX3D does all rendering (rasterization and raytracing) in OpenCL C, so no display output and no graphics features like OpenGL/Vulkan/DirectX are required. Rendering is just another form of compute after all. Rendered frames are passed to the CPU over PCIe and then the CPU can either draw them on screen through dedicated/integrated graphics or write them to the hard drive.
I'm running FluidX3D on a remote (super-)computer and only have an SSH terminal. Can I still use graphics somehow?

Yes, either directly as interactive ASCII graphics in the terminal or by storing rendered frames on the hard drive and then copying them over via `scp -r user@server.url:"~/path/to/images/folder" .`.

Licensing

I want to learn about programming/software/physics/engineering. Can I use FluidX3D for free?

Yes. Anyone can use FluidX3D for free for public research, education or personal use. Use by scientists, students and hobbyists is free of charge and well encouraged.
I am a scientist/teacher with a paid position at a public institution. Can I use FluidX3D for my research/teaching?

Yes, you can use FluidX3D free of charge. This is considered research/education, not commercial use. To give credit, the references listed below should be cited. If you publish data/results generated by altered source versions, the altered source code must be published as well.
I work at a company in CFD/consulting/R&D or related fields. Can I use FluidX3D commercially?

No. Commercial use is not allowed with the current license.
Is FluidX3D open-source?

No. "Open-source" as a technical term is defined as freely available without any restriction on use, but I am not comfortable with that. I have written FluidX3D in my spare time and no one should milk it for profits while I remain uncompensated, especially considering what other CFD software sells for. The technical term for the type of license I choose is "source-available no-cost non-commercial". The source code is freely available, and you are free to use, to alter and to redistribute it, as long as you do not sell it or make a profit from derived products/services, and as long as you do not use it for any military purposes (see the license for details).
Will FluidX3D at some point be available with a commercial license?

Maybe I will add the option for a second, commercial license later on. If you are interested in commercial use, let me know. For non-commercial use in science and education, FluidX3D is and will always be free.

External Code/Libraries/Images used in FluidX3D

OpenCL-Headers for GPU parallelization (Khronos Group)
Win32 API for interactive graphics in Windows (Microsoft)
X11/Xlib for interactive graphics in Linux (The Open Group)
marching-cubes tables for isosurface generation on GPU (Paul Bourke)
src/lodepng.cpp and src/lodepng.hpp for .png encoding and decoding (Lode Vandevenne)
SimplexNoise class in src/utilities.hpp for generating continuous noise in 2D/3D/4D space (Stefan Gustavson)
skybox/skybox8k.png for free surface raytracing (HDRI Hub)

References

Lehmann, M.: Esoteric Pull and Esoteric Push: Two Simple In-Place Streaming Schemes for the Lattice Boltzmann Method on GPUs. Computation, 10, 92, (2022)
Lehmann, M., Krause, M., Amati, G., Sega, M., Harting, J. and Gekle, S.: Accuracy and performance of the lattice Boltzmann method with 64-bit, 32-bit, and customized 16-bit number formats. Phys. Rev. E 106, 015308, (2022)
Lehmann, M.: Combined scientific CFD simulation and interactive raytracing with OpenCL. IWOCL'22: International Workshop on OpenCL, 3, 1-2, (2022)
Lehmann, M., Oehlschlägel, L.M., Häusl, F., Held, A. and Gekle, S.: Ejection of marine microplastics by raindrops: a computational and experimental study. Micropl.&Nanopl. 1, 18, (2021)
Lehmann, M.: High Performance Free Surface LBM on GPUs. Master's thesis, (2019)
Lehmann, M. and Gekle, S.: Analytic Solution to the Piecewise Linear Interface Construction Problem and Its Application in Curvature Calculation for Volume-of-Fluid Simulation Codes. Computation, 10, 21, (2022)

Contact

For any questions, feedback or other inquiries, don't hesitate to contact me at moritz.lehmann@uni-bayreuth.de.
Updates will be posted on Twitter via @FluidX3D and @ProjectPhysX, under the hashtag #FluidX3D or on my YouTube channel.

Heavy02011 / FluidX3D