Gaussian Fluids: A Grid-Free Fluid Solver based on Gaussian Spatial Representation

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Official implementation for the paper:

Gaussian Fluids: A Grid-Free Fluid Solver based on Gaussian Spatial Representation
Jingrui Xing¹, Bin Wang², Mengyu Chu¹, Baoquan Chen^1
1Peking University, ²Independent Researcher
SIGGRAPH 2025

Installation

Prerequisites:

• python 3.9+
• An NVIDIA GPU with CUDA 11+

Firstly, install dependencies in requirements.txt:

pip install -r requirements.txt

Next, install PyTorch with a compatible version for your CUDA. Please check https://pytorch.org/ for details.

Finally, install Taichi language:

pip install taichi

Running

2D Examples

To run 2D examples, go into directory 2D first:

cd 2D

Next, run the initial fitting process (take Leapfrog 2D as an example):

python initialize.py --init_cond leapfrog --dir output_2d_leapfrog

The visualization results can then be found in directory output_2d_leapfrog.

Finally, run the simulation:

python advance.py --init_cond leapfrog --dt .025 --last_time 40. --dir output_2d_leapfrog > output_2d_leapfrog/log.txt

This command will run silently as its outputs are redirect into output_2d_leapfrog/log.txt. The visualizations of each frame will also be stored in output_2d_leapfrog.

Similar steps can be done to reproduce other examples in the paper.

Taylor-Green:

python initialize.py --init_cond taylor_green --dir output_2d_taylor_green
python advance.py --init_cond taylor_green --dt .001 --last_time .2 --dir output_2d_taylor_green > output_2d_taylor_green/log.txt

Taylor vortex:

python initialize.py --init_cond taylor_vortex --dir output_2d_taylor_vortex
python advance.py --init_cond taylor_vortex --dt .01 --last_time 4. --dir output_2d_taylor_vortex > output_2d_taylor_vortex/log.txt

Vortices pass:

python initialize.py --init_cond vortices_pass_particles --dir output_2d_vortices_pass
python advance.py --init_cond vortices_pass_particles --dt .01 --last_time 5. --dir output_2d_vortices_pass > output_2d_vortices_pass/log.txt

Karman vortex street:

python initialize.py --init_cond karman --dir output_2d_karman
python advance.py --init_cond karman --dt .05 --last_time 10. --dir output_2d_karman > output_2d_karman/log.txt

3D Examples

To run 3D examples, go into directory 3D first:

cd 3D

Then follow the same steps as in 2D examples. The following shows the command lines for all the 3D examples.

Leapfrog 3D:

python initialize.py --init_cond leapfrog --dir output_3d_leapfrog
python advance.py --init_cond leapfrog --dir output_3d_leapfrog > output_3d_leapfrog/log.txt

Ring collide:

python initialize.py --init_cond ring_collide --dir output_3d_ring_collide
python advance.py --init_cond ring_collide --dir output_3d_ring_collide > output_3d_ring_collide/log.txt

Smoking bunny:

python initialize.py --init_cond ring_with_obstacle --dir output_3d_ring_with_obstacle
python advance.py --init_cond ring_with_obstacle --dir output_3d_ring_with_obstacle > output_3d_ring_with_obstacle/log.txt

More Options

You can assign both processes (initialization.py and advance.py) to any GPU by specifying --device option. For example, you can run simulation of the Leapfrog 2D example on GPU 2 with the following command line:

python advance.py --device 2 --init_cond leapfrog --dt .025 --last_time 40. --dir output_2d_leapfrog > output_2d_leapfrog/log.txt

You can start simulation from a certain frame specified with --start_frame option. For example, start simulation of the Leapfrog 2D example from frame $100$ by (please make sure file gaussian_velocity_100.pt exists in output_2d_leapfrog):

python advance.py --start_frame 100 --init_cond leapfrog --dt .025 --last_time 40. --dir output_2d_leapfrog > output_2d_leapfrog/log_from_100.txt

Citation

@inproceedings{xing2025gaussian-fluids,
	author = {Xing, Jingrui and Wang, Bin and Chu, Mengyu and Chen, Baoquan},
	title = {Gaussian Fluids: A Grid-Free Fluid Solver based on Gaussian Spatial Representation},
	year = {2025},
	isbn = {9798400715402},
	publisher = {Association for Computing Machinery},
	address = {New York, NY, USA},
	url = {https://doi.org/10.1145/3721238.3730620},
	doi = {10.1145/3721238.3730620},
	abstract = {We present a grid-free fluid solver featuring a novel Gaussian representation. Drawing inspiration from the expressive capabilities of 3D Gaussian Splatting in multi-view image reconstruction, we model the continuous flow velocity as a weighted sum of multiple Gaussian functions. This representation is continuously differentiable, which enables us to derive spatial differentials directly and solve the time-dependent PDE via a custom first‑order optimization tailored to fluid dynamics. Compared to traditional discretizations, which typically adopt Eulerian, Lagrangian, or hybrid perspectives, our approach is inherently memory-efficient and spatially adaptive, enabling it to preserve fine-scale structures and vortices with high fidelity. While these advantages are also sought by implicit neural representations, GSR offers enhanced robustness, accuracy, and generality across diverse fluid phenomena, with improved computational efficiency during temporal evolution. Though our first‑order solver does not yet match the speed of fluid solvers using explicit representations, its continuous nature substantially reduces spatial discretization error and opens a new avenue for high‑fidelity simulation. We evaluate the proposed solver across a broad range of 2D and 3D fluid phenomena, demonstrating its ability to preserve intricate vortex dynamics, accurately capture boundary-induced effects such as Kármán vortex streets, and remain robust across long time horizons—all without additional parameter tuning. Our results suggest that GSR offers a compelling direction for future research in fluid simulation.},
	booktitle = {ACM SIGGRAPH 2025 Conference Papers},
	articleno = {31},
	numpages = {11},
	keywords = {Fluid Simulation, Gaussian Spatial Representation},
	location = {Vancouver, BC, Canada},
	series = {SIGGRAPH '25}
}