FluidX3D Documentation

FluidX3D

The fastest and most memory efficient lattice Boltzmann CFD software, running on all GPUs and CPUs via OpenCL. Free for non-commercial use.

(click on images to show videos on YouTube)

Update History

• v1.0 (04.08.2022) changes (public release)
  • public release
• v1.1 (29.09.2022) changes (GPU voxelization)
  • added solid voxelization on GPU (slow algorithm)
  • added tool to print current camera position (key G)
  • minor bug fix (workaround for Intel iGPU driver bug with triangle rendering)
• v1.2 (24.10.2022) changes (force/torque computation)
  • added functions to compute force/torque on objects
  • added function to translate Mesh
  • added Stokes drag validation setup
• v1.3 (10.11.2022) changes (minor bug fixes)
  • 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) changes (Linux graphics)
  • complete rewrite of C++ graphics library to minimize API dependencies
  • added interactive graphics mode on Linux with X11
  • fixed streamline visualization bug in 2D
• v2.0 (09.01.2023) changes (multi-GPU upgrade)
  • added (cross-vendor) multi-GPU support on a single node (PC/laptop/server)
• v2.1 (15.01.2023) changes (fast voxelization)
  • made solid voxelization on GPU lightning fast (new algorithm, from minutes to milliseconds)
• v2.2 (20.01.2023) changes (velocity voxelization)
  • 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) changes (particles)
  • 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) changes (UI improvements)
  • 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) changes (raytracing overhaul)
  • 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) changes (Intel Arc patch)
  • patched OpenCL issues of Intel Arc GPUs: now VRAM allocations >4GB are possible and correct VRAM capacity is reported
• v2.7 (29.05.2023) changes (visualization upgrade)
  • added slice visualization (key 2 / key 3 modes, then switch through slice modes with key T, move slice with keys Q/E)
  • made flag wireframe / solid surface visualization kernels toggleable with key 1
  • added surface pressure visualization (key 1 when FORCE_FIELD is enabled and lbm.calculate_force_on_boundaries(); is called)
  • added binary .vtk export function for meshes with lbm.write_mesh_to_vtk(Mesh* mesh);
  • added time_step_multiplicator for integrate_particles() function in PARTICLES extension
  • made correction of wrong memory reporting on Intel Arc more robust
  • fixed bug in write_file() template functions
  • reverted back to separate cl::Context for each OpenCL device, as the shared Context otherwise would allocate extra VRAM on all other unused Nvidia GPUs
  • removed Debug and x86 configurations from Visual Studio solution file (one less complication for compiling)
  • fixed bug that particles could get too close to walls and get stuck, or leave the fluid phase (added boundary force)
• v2.8 (24.06.2023) changes (documentation + polish)
  • finally added more documentation
  • cleaned up all sample setups in setup.cpp for more beginner-friendliness, and added required extensions in defines.hpp as comments to all setups
  • improved loading of composite .stl geometries, by adding an option to omit automatic mesh repositioning, added more functionality to Mesh struct in utilities.hpp
  • added uint3 resolution(float3 box_aspect_ratio, uint memory) function to compute simulation box resolution based on box aspect ratio and VRAM occupation in MB
  • added bool lbm.graphics.next_frame(...) function to export images for a specified video length in the main_setup compute loop
  • added VIS_... macros to ease setting visualization modes in headless graphics mode in lbm.graphics.visualization_modes
  • simulation box dimensions are now automatically made equally divisible by domains for multi-GPU simulations
  • fixed Info/Warning/Error message formatting for loading files and made Info/Warning/Error message labels colored
  • added Ahmed body setup as an example on how body forces and drag coefficient are computed
  • added Cessna 172 and Bell 222 setups to showcase loading composite .stl geometries and revoxelization of moving parts
  • added optional semi-transparent rendering mode (#define GRAPHICS_TRANSPARENCY 0.7f in defines.hpp)
  • fixed flickering of streamline visualization in interactive graphics
  • improved smooth positioning of streamlines in slice mode
  • fixed bug where mass and massex in SURFACE extension were also allocated in CPU RAM (not required)
  • fixed bug in Q-criterion rendering of halo data in multi-GPU mode, reduced gap width between domains
  • removed shared memory optimization from mesh voxelization kernel, as it crashes on Nvidia GPUs with new GPU drivers and is incompatible with old OpenCL 1.0 GPUs
  • fixed raytracing attenuation color when no surface is at the simulation box walls with periodic boundaries
• v2.9 (31.07.2023) changes (multithreading)
  • added cross-platform parallel_for implementation in utilities.hpp using std::threads
  • significantly (>4x) faster simulation startup with multithreaded geometry initialization and sanity checks
  • faster calculate_force_on_object() and calculate_torque_on_object() functions with multithreading
  • added total runtime and LBM runtime to lbm.write_status()
  • fixed bug in voxelization ray direction for re-voxelizing rotating objects
  • fixed bug in Mesh::get_bounding_box_size()
  • fixed bug in print_message() function in utilities.hpp
• v2.10 (05.11.2023) changes (frustum culling)
  • improved rasterization performance via frustum culling when only part of the simulation box is visible
  • improved switching between centered/free camera mode
  • refactored OpenCL rendering library
  • unit conversion factors are now automatically printed in console when units.set_m_kg_s(...) is used
  • faster startup time for FluidX3D benchmark
  • miner bug fix in voxelize_mesh(...) kernel
  • fixed bug in shading(...)
  • replaced slow (in multithreading) std::rand() function with standard C99 LCG
  • more robust correction of wrong VRAM capacity reporting on Intel Arc GPUs
  • fixed some minor compiler warnings
• v2.11 (07.12.2023) changes (improved Linux graphics)
  • interactive graphics on Linux are now in fullscreen mode too, fully matching Windows
  • made CPU/GPU buffer initialization significantly faster with std::fill and enqueueFillBuffer (overall ~8% faster simulation startup)
  • added operating system info to OpenCL device driver version printout
  • fixed flickering with frustum culling at very small field of view
  • fixed bug where rendered/exported frame was not updated when visualization_modes changed
• v2.12 (18.01.2024) changes (faster startup)
  • ~3x faster source code compiling on Linux using multiple CPU cores if make is installed
  • significantly faster simulation initialization (~40% single-GPU, ~15% multi-GPU)
  • minor bug fix in Memory_Container::reset() function
• v2.13 (11.02.2024) changes (improved .vtk export)
  • data in exported .vtk files is now automatically converted to SI units
  • ~2x faster .vtk export with multithreading
  • added unit conversion functions for TEMPERATURE extension
  • fixed graphical artifacts with axis-aligned camera in raytracing
  • fixed get_exe_path() for macOS
  • fixed X11 multi-monitor issues on Linux
  • workaround for Nvidia driver bug: enqueueFillBuffer is broken for large buffers on Nvidia GPUs
  • fixed slow numeric drift issues caused by -cl-fast-relaxed-math
  • fixed wrong Maximum Allocation Size reporting in LBM::write_status()
  • fixed missing scaling of coordinates to SI units in LBM::write_mesh_to_vtk()
• v2.14 (03.03.2024) changes (visualization upgrade)
  • coloring can now be switched between velocity/density/temperature with key Z
  • uniform improved color palettes for velocity/density/temperature visualization
  • color scale with automatic unit conversion can now be shown with key H
  • slice mode for field visualization now draws fully filled-in slices instead of only lines for velocity vectors
  • shading in VIS_FLAG_SURFACE and VIS_PHI_RASTERIZE modes is smoother now
  • make.sh now automatically detects operating system and X11 support on Linux and only runs FluidX3D if last compilation was successful
  • fixed compiler warnings on Android
  • fixed make.sh failing on some systems due to nonstandard interpreter path
  • fixed that make would not compile with multiple cores on some systems
• v2.15 (09.04.2024) changes (framerate boost)
  • eliminated one frame memory copy and one clear frame operation in rendering chain, for 20-70% higher framerate on both Windows and Linux
  • enabled g++ compiler optimizations for faster startup and higher rendering framerate
  • fixed bug in multithreaded sanity checks
  • fixed wrong unit conversion for thermal expansion coefficient
  • fixed density to pressure conversion in LBM units
  • fixed bug that raytracing kernel could lock up simulation
  • fixed minor visual artifacts with raytracing
  • fixed that console sometimes was not cleared before INTERACTIVE_GRAPHICS_ASCII rendering starts
• v2.16 (02.05.2024) changes (bug fixes)
  • simplified 10% faster marching-cubes implementation with 1D interpolation on edges instead of 3D interpolation, allowing to get rid of edge table
  • added faster, simplified marching-cubes variant for solid surface rendering where edges are always halfway between grid cells
  • refactoring in OpenCL rendering kernels
  • fixed that voxelization failed in Intel OpenCL CPU Runtime due to array out-of-bounds access
  • fixed that voxelization did not always produce binary identical results in multi-GPU compared to single-GPU
  • fixed that velocity voxelization failed for free surface simulations
  • fixed terrible performance on ARM GPUs by macro-replacing fused-multiply-add (fma) with a*b+c
  • fixed that Y/Z keys were incorrect for QWERTY keyboard layout in Linux
  • fixed that free camera movement speed in help overlay was not updated in stationary image when scrolling
  • fixed that cursor would sometimes flicker when scrolling on trackpads with Linux-X11 interactive graphics
  • fixed flickering of interactive rendering with multi-GPU when camera is not moved
  • fixed missing XInitThreads() call that could crash Linux interactive graphics on some systems
  • fixed z-fighting between graphics_rasterize_phi() and graphics_flags_mc() kernels
• v2.17 (05.06.2024) changes (unlimited domain resolution)
  • domains are no longer limited to 4.29 billion (2³², 1624³) grid cells or 225 GB memory; if more are used, the OpenCL code will automatically compile with 64-bit indexing
  • new, faster raytracing-based field visualization for single-GPU simulations
  • added GPU Driver and OpenCL Runtime installation instructions to documentation
  • refactored INTERACTIVE_GRAPHICS_ASCII
  • fixed memory leak in destructors of floatN, floatNxN, doubleN, doubleNxN (all unused)
  • made camera movement/rotation/zoom behavior independent of framerate
  • fixed that smart_device_selection() would print a wrong warning if device reports 0 MHz clock speed
• v2.18 (21.07.2024) changes (more bug fixes)
  • added support for high refresh rate monitors on Linux
  • more compact OpenCL Runtime installation scripts in Documentation
  • driver/runtime installation instructions will now be printed to console if no OpenCL devices are available
  • added domain information to LBM::write_status()
  • added LBM::index function for uint3 input parameter
  • fixed that very large simulations sometimes wouldn't render properly by increasing maximum render distance from 10k to 2.1M
  • fixed mouse input stuttering at high screen refresh rate on Linux
  • fixed graphical artifacts in free surface raytracing on Intel CPU Runtime for OpenCL
  • fixed runtime estimation printed in console for setups with multiple lbm.run(...) calls
  • fixed density oscillations in sample setups (too large lbm_u)
  • fixed minor graphical artifacts in raytrace_phi()
  • fixed minor graphical artifacts in ray_grid_traverse_sum()
  • fixed wrong printed time step count on raindrop sample setup
• v2.19 (07.09.2024) changes (camera splines)
  • the camera can now fly along a smooth path through a list of provided keyframe camera placements, using Catmull-Rom splines
  • more accurate remaining runtime estimation that includes time spent on rendering
  • enabled FP16S memory compression by default
  • printed camera placement using key G is now formatted for easier copy/paste
  • added benchmark chart in Readme using mermaid gantt chart
  • placed memory allocation info during simulation startup at better location
  • fixed threading conflict between INTERACTIVE_GRAPHICS and lbm.graphics.write_frame();
  • fixed maximum buffer allocation size limit for AMD GPUs and in Intel CPU Runtime for OpenCL
  • fixed wrong Re<Re_max info printout for 2D simulations
  • minor fix in bandwidth_bytes_per_cell_device()
• v3.0 (16.11.2024) changes (larger CPU/iGPU simulations)
  • reduced memory footprint on CPUs and iGPU from 72 to 55 Bytes/cell (fused OpenCL host+device buffers for rho/u/flags), allowing 31% higher resolution in the same RAM capacity
  • faster hardware-supported and faster fallback emulation atomic floating-point addition for PARTICLES extension
  • hardened calculate_f_eq() against bad user input for D2Q9
  • fixed velocity voxelization for overlapping geometry with different velocity
  • fixed Remaining Time printout during paused simulation
  • fixed CPU/GPU memory printout for CPU/iGPU simulations
• v3.1 (08.02.2025) changes (more bug fixes)
  • faster enqueueReadBuffer() on modern CPUs with 64-Byte-aligned host_buffer
  • hardened ray intersection functions against planar ray edge case
  • updated OpenCL headers
  • better OpenCL device specs detection using vendor ID and Nvidia compute capability
  • better VRAM capacity reporting correction for Intel dGPUs
  • improved styling of performance mermaid gantt chart in Readme
  • added multi-GPU performance mermaid gantt chart in Readme
  • updated driver install guides
  • fixed voxelization being broken on some GPUs
  • added workaround for compiler bug in Intel CPU Runtime for OpenCL that causes Q-criterion isosurface rendering corruption
  • fixed TFlops estimate for Intel Battlemage GPUs
  • fixed wrong device name reporting for AMD GPUs
• v3.2 (09.03.2025) changes (fast force/torque summation)
  • implemented GPU-accelerated force/torque summation (~20x faster than CPU-multithreaded implementation before)
  • simplified calculating object force/torque in setups
  • improved coloring in VIS_FIELD/ray_grid_traverse_sum()
  • updated OpenCL-Wrapper now compiles OpenCL C code with -cl-std=CL3.0 if available
  • fixed compiling on macOS with new OpenCL headers
• v3.3 (17.05.2025) changes (faster .vtk export)
  • .vtk export now converts and writes data in chunks, to reduce memory footprint and time for large memory allocation
  • .vtk files now contain original file name as metadata in title
  • INTERACTIVE_GRAPHICS_ASCII now renders in 2x vertical resolution but less colors
  • updated OpenCL-Wrapper: more robust dp4a detection, fixed core count reporting for RDNA4 GPUs
  • fixed update_moving_boundaries() kernel not being called with flags other than TYPE_S
  • fixed corrupted first frame until resizing with INTERACTIVE_GRAPHICS_ASCII
  • fixed resolution() function for D2Q9
  • fixed missing <chrono> header on some compilers
  • fixed bug in split_regex()
  • fixed compiler warning with min_int
• v3.4 (02.07.2025) changes (bug fixes)
  • updated OpenCL driver install versions
  • minor refactoring in stream_collide()
  • fixed bug in insertion-sort in voxelize_mesh() kernel causing crash on AMD GPUs
  • fixed bug in voxelize_mesh_on_device() host code causing initialization corruption on AMD GPUs
  • fixed dual CU and IPC reporting on AMD RDNA 1-4 GPUs
• v3.5 (01.10.2025) changes (multi-GPU particles)
  • PARTICLES extension now also works with multi-GPU
  • faster force spreading if volume force is axis-aligned
  • added more documentation for boundary conditions
  • updated FAQs
  • improved "hydraulic jump" sample setup
  • updated GPU driver install instructions
  • disabled zero-copy on ARM iGPUs because CL_MEM_USE_HOST_PTR is broken there
• v3.6 (24.03.2026) changes (improved macOS graphics)
  • improved INTERACTIVE_GRAPHICS support on macOS with XQuartz
  • added Mesh::get_center_of_mass() function, for easy rotation of any balanced rotor
  • made performance mermaid gantt chart in Readme properly colored
  • more robust Intel GPU core/CU detecton via CL_DEVICE_IP_VERSION_INTEL
  • OpenCL code refactoring
  • set nvidia_compute_capability only for Nvidia GPUs not Nvidia CPUs
  • fixed TFLOPs/s estimate for AMD CDNA3/4 GPUs
  • fixed Device Name and CU reporting for AMD GPUs with rusticl
• v3.7 (14.05.2026) changes (faster Q-criterion rendering)
  • up to 2x faster Q-criterion isosurface rendering on some GPUs
  • reduced assembly spaghettification by simpler condition for VR rendering and disabling loop unrolling in rasterization
  • micro-optimization in convert_triangle/_interpolated()
  • fixed empty kernel name and workgroup size error printout in OpenCL-Wrapper

How to get started? Copy Chapter

Read the FluidX3D Documentation!

Compute Features - Getting the Memory Problem under Control Copy Chapter

• CFD model: lattice Boltzmann method (LBM)

  • streaming (part 2/2)

  • collision

  • streaming (part 1/2)

  • variables and notation

    variable	SI units	defining equation	description
    x	m	x = (x,y,z)T	3D position in Cartesian coordinates
    t	s	-	time
    ρ	kg∕m³	ρ = (Σi fi)+1	mass density of fluid
    p	kg∕m s²	p = c² ρ	pressure of fluid
    u	m∕s	u = 1∕ρ Σi ci fi	velocity of fluid
    ν	m²∕s	ν = μ∕ρ	kinematic shear viscosity of fluid
    μ	kg∕m s	μ = ρ ν	dynamic viscosity of fluid
    fi	kg∕m³	-	shifted density distribution functions (DDFs)
    Δx	m	Δx = 1	lattice constant (in LBM units)
    Δt	s	Δt = 1	simulation time step (in LBM units)
    c	m∕s	c = 1∕√3 Δx∕Δt	lattice speed of sound (in LBM units)
    i	1	0 ≤ i < q	LBM streaming direction index
    q	1	q ∈ { 9,15,19,27 }	number of LBM streaming directions
    ei	m	D2Q9 / D3Q15/19/27	LBM streaming directions
    ci	m∕s	ci = ei∕Δt	LBM streaming velocities
    wi	1	Σi wi = 1	LBM velocity set weights
    Ωi	kg∕m³	SRT or TRT	LBM collision operator
    τ	s	τ = ν∕c² + Δt∕2	LBM relaxation time

  • velocity sets: D2Q9, D3Q15, D3Q19 (default), D3Q27

  • collision operators: single-relaxation-time (SRT/BGK) (default), two-relaxation-time (TRT)

  • DDF-shifting and other algebraic optimization to minimize round-off error

• 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 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	180 GB	192 GB	256 GB	288 GB	6 TB
    approximate GPU price	$25GT 210	$25GTX 950	$12GTX 1060	$50GT 730	$35GTX 1060	$70RX 470	$500RTX 3080	$240GTX 1080 Ti	$75Tesla M40	$75Instinct MI25	$900RX 7900 XT	$205Tesla P40	$600Instinct MI60	$5500A100	$2400RTX 8000	$10kInstinct MI210	$11kA100	>$40kH100 NVL	?GPU Max 1550	~$80kB200	~$15kMI300X	~$25kMI325X	~$25kMI350X	~$80k2x Xeon 6960P
    traditional LBM (FP64)	144³	182³	208³	230³	262³	288³	312³	322³	330³	364³	392³	418³	460³	494³	526³	578³	624³	658³	730³	818³	836³	920³	956³	2654³
    FluidX3D (FP32/FP32)	224³	282³	322³	354³	406³	448³	482³	498³	512³	564³	608³	646³	710³	766³	814³	896³	966³	1018³	1130³	1266³	1292³	1422³	1480³	4106³
    FluidX3D (FP32/FP16)	266³	336³	384³	424³	484³	534³	574³	594³	610³	672³	724³	770³	848³	912³	970³	1068³	1150³	1214³	1346³	1508³	1540³	1696³	1764³	4892³

• cross-vendor multi-GPU support on a single computer/server

  • domain decomposition allows pooling VRAM from multiple GPUs for much larger grid resolution
  • GPUs don't have to be identical, not even from the same vendor - any combination of AMD+Intel+Nvidia GPUs will work - but similar VRAM capacity/bandwidth is recommended
  • domain communication architecture (simplified)
    text Copy

  /* Detailed source-code truncated for AI context efficiency. */

- domain communication architecture (detailed)
    ```
/* Detailed source-code truncated for AI context efficiency. */

• peak performance on GPUs (datacenter/gaming/professional/laptop)

  • single-GPU/CPU benchmarks
  • multi-GPU benchmarks

• 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

  • particles with immersed-boundary method (either passive or 2-way-coupled)

Solving the Visualization Problem Copy Chapter

• 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
• rasterization and raytracing are done in OpenCL and work on all GPUs, even the ones without RTX/DXR raytracing cores or without any rendering hardware at all (like A100, MI200, ...)
• 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:
  • flag wireframe / solid surface (and force vectors on solid cells or surface pressure if the extension is used)
  • velocity field (with slice mode)
  • streamlines (with slice mode)
  • 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 Copy Chapter

• FluidX3D is written in OpenCL, so it runs on all hardware from all vendors (Nvidia, AMD, Intel, ...):
  • world's fastest datacenter GPUs: B300, B200, MI355X, MI300X, H200, H100 (NVL), A100, MI200, GPU Max 1100, ...
  • gaming GPUs (desktop/laptop): Nvidia GeForce, AMD Radeon, Intel Arc
  • professional/workstation GPUs: Nvidia Quadro, AMD Radeon Pro / FirePro, Intel Arc Pro
  • integrated GPUs
  • CPUs (requires installation of Intel CPU Runtime for OpenCL)
  • Intel Xeon Phi (requires installation of Intel CPU Runtime for OpenCL)
  • smartphone ARM GPUs
• native cross-vendor multi-GPU implementation
  • uses PCIe communication, so no SLI/Crossfire/NVLink/InfinityFabric required
  • single-node parallelization, so no MPI installation required
  • GPUs don't even have to be from the same vendor, but similar memory capacity and bandwidth are recommended
• works on 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 / triangle meshes as binary .vtk files
• supports exporting rendered images as .png/.qoi/.bmp files; encoding runs in parallel on the CPU while the simulation on GPU can continue without delay

Single-GPU/CPU Benchmarks Copy Chapter

Here are performance benchmarks on various hardware in MLUPs/s, or how many million lattice cells 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 cell 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. The table in the left 3 columns shows the hardware specs as found in the data sheets (theoretical peak FP32 compute performance, memory capacity, theoretical peak memory bandwidth). The right 3 columns show the measured FluidX3D performance for FP32/FP32, FP32/FP16S, FP32/FP16C floating-point precision settings, with the (roofline model efficiency) in round brackets, indicating how much % of theoretical peak memory bandwidth are being used.

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

/* Detailed source-code truncated for AI context efficiency. */

Single-GPU/CPU Benchmark Table

Colors: 🔴 AMD, 🔵 Intel, 🟢 Nvidia, ⚪ Apple, 🟣 ARM, 🟡 Glenfly

Multi-GPU Benchmarks Copy Chapter

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

/* Detailed source-code truncated for AI context efficiency. */

Multi-GPU Benchmark Table

Colors: 🔴 AMD, 🔵 Intel, 🟢 Nvidia, ⚪ Apple, 🟣 ARM, 🟡 Glenfly

FAQs Copy Chapter

General Copy Section

• How to learn using FluidX3D?Follow the FluidX3D Documentation!

• 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 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.

• FluidX3D in Blender?FluidX3D is a standalone software, with integrated in-situ rendering engine that directly accesses the raw simulation data in VRAM. Integration into Blender or other software packages is not planned.

• Checkpoint support?FluidX3D does not support saving/loading checkpoints. I have made the software so robust that it does not crash, and so fast that restarting a simulation does not take longer than a few hours at most on a GPU system.

Model Copy Section

• 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 implemented in FluidX3D include volume force (Guo forcing), free surface (volume-of-fluid and PLIC), a temperature model and Smagorinsky-Lilly subgrid turbulence model for DNS-LES simulations.

• What boundary types are available in FluidX3D?Periodic boundaries, solid boundaries, equilibrium boundaries, and moving solid boundaries.See the section on initial/boundary conditions in the FluidX3D Documentation!

• Does FluidX3D support adaptive mesh refinement?No, not yet. Grid cell size is the same everywhere in the simulation box.

• Can FluidX3D model both water and air at the same time?No. FluidX3D can model either water or air, but not both at the same time. For free surface simulations with the SURFACE extension, I went with a volume-of-fluid/PLIC modeling approach as that provides a sharp water-air interface, so individual droplets can be resolved as small as 3 grid cells in diameter. However this model ignores the gas phase completely, and only models the fluid phase with LBM as well as the surface tension. An alternative I had explored years ago was the phase-field models (simplest of them is Shan-Chen model) - they model both fluid and gas phases, but struggle with the 1:1000 density contrast of air:water, and the modeled interface is diffuse over ~5 grid cells. So the smallest resolved droplets are ~10 grid cells in diameter, meaning for the same resolution you need ~37x the memory footprint - infeasible on GPUs. Coming back to VoF model, it is possible to extend it with a model for the gas phase, but one has to manually track bubble split/merge events, which makes this approach very painful in implementation and poorly performing on the hardware.

• Can FluidX3D compute lift/drag forces?Yes. See the lift/drag forces section in the FluidX3D Documentation!

• Can FluidX3D simulate transsonic/supersonic flows?No. The LBM model in FluidX3D works only in the weakly compressible regime at Mach numbers < 0.3.

• How to simulate moving/rotating geometry?See the section about .stl voxelization in the FluidX3D Documentation.

• Can FluidX3D model thermal convection?Yes. See the TEMPERATURE extension section in the FluidX3D Documentation!

• Can FluidX3D model chemical reactions?No.

• Can FluidX3D model particles?Yes, either as passive tracer particles or with 2-way coupling (buoyancy). See the PARTICLES extension section in the FluidX3D Documentation!

• I see white lines or everything disappeared. Why?This indicates that the simulation has become unstable. See the the section on parametrization and instability in the FluidX3D Documentation!

• The density and/or velocity field are oscillatory. Why?

  Either this is acoustic (standing) waves, or non-physical artifacts. Play around with SI-LBM unit conversion, and reduce time step size in SI units by reducing lbm_u.

• 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 Copy Section

• 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 overlaid 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 AMD+Intel+Nvidia 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.

• Can I run FluidX3D on the CPU?Yes, and this is especially useful when you need more memory than a GPU can offer. You only need to install the Intel CPU Runtime for OpenCL.

• 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 and not CUDA, so it runs on any GPU from any vendor since around 2009.

• 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.

• In the benchmarks you list some very expensive hardware. How do you get access to that?As a PhD candidate in computational physics, I used FluidX3D for my research, so I had access to BZHPC, SuperMUC-NG, JSC JURECA-DC, and Leonardo supercomputers.

Graphics Copy Section

• 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 [email protected]:"~/path/to/images/folder" ..

• Graphics support on Apple macOS?

  On macOS and Android, INTERACTIVE_GRAPHICS mode is not supported, as no X11 is available. You can still use INTERACTIVE_GRAPHICS_ASCII though, or render video to the hard drive with regular GRAPHICS mode.

Licensing Copy Section

• 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 Copy Chapter

• OpenCL-Headers and C++ Wrapper 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 Copy Chapter

• Lehmann, M.: Computational study of microplastic transport at the water-air interface with a memory-optimized lattice Boltzmann method. PhD thesis, (2023)
• 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 Copy Chapter

• FluidX3D is solo-developed and maintained by Dr. Moritz Lehmann.
• For any questions, feedback or other inquiries, contact me at [email protected].
• Updates are posted on Mastodon via @ProjectPhysX/#FluidX3D and on YouTube.

Support Copy Chapter

I'm developing FluidX3D in my spare time, to make computational fluid dynamics lightning fast, accessible on all hardware, and free for everyone.

• You can support FluidX3D by reporting any bugs or things that don't work in the issues. I'm welcoming feedback!
• If you like FluidX3D, share it with friends and colleagues. Spread the word that CFD is now lightning fast, accessible and free.
• If you want to support FluidX3D financially, you can sponsor me on GitHub or buy me a coffee. Thank you!