[SIGGRAPH 1999] Stable fluids. Jos Stam.
Modern C++ 23 / CUDA Implementation with C ABI of the paper Stable fluids by Jos Stam.
1. Algorithm Pipeline
Fields
-
$\mathbf{w}$: velocity field
-
$\mathbf{\rho}$: density field
1.1 Velocity Pipeline
$$
\mathbf{w}^n_0
\xrightarrow{\text{add force}} \mathbf{w}^n_1
\xrightarrow{\text{advect}} \mathbf{w}^n_2
\xrightarrow{\text{diffuse}} \mathbf{w}^n_3
\xrightarrow{\text{project}} \mathbf{w}^n_4
\Rightarrow{} \mathbf{w}^{n+1}_0.
$$
add force
$$
\mathbf{w}_1(\mathbf{x}) = \mathbf{w}_0(\mathbf{x}) + \Delta t, f(\mathbf{x}, t)
$$
advect (semi-Lagrangian method)
$$
\mathbf{w}_2(\mathbf{x}) = \mathbf{w}_1(\mathbf{p}(\mathbf{x}, -\Delta t)).
$$
diffuse
$$
(I - \nu \Delta t \nabla^2) \mathbf{w}_3(\mathbf{x}) = \mathbf{w}_2(\mathbf{x})
$$
where $\nu$ is the viscosity coefficient.
project
$$
\nabla^2 q = \nabla \cdot \mathbf{w}_3
\qquad
\mathbf{w}_4 = \mathbf{w}_3 - \nabla q
$$
1.2 Density Pipeline
$$
\mathbf{\rho}^n_0 \xrightarrow{\text{add source}}
\mathbf{\rho}^n_1 \xrightarrow{\text{advect}}
\mathbf{\rho}^n_2 \xrightarrow{\text{diffuse}}
\mathbf{\rho}^n_3 \Rightarrow{}
\mathbf{\rho}^{n+1}_0.
$$
add source
$$
\mathbf{\rho}_1(\mathbf{x}) = \mathbf{\rho}_0(\mathbf{x}) + \Delta t S(\mathbf{x}, t)
$$
where $S(\mathbf{x}, t)$ is the scalar source term (e.g., injected smoke or dye).
advect (semi-Lagrangian method)
$$
\mathbf{\rho}_2(\mathbf{x}) = \mathbf{\rho}_1(\mathbf{p}(\mathbf{x}, -\Delta t))
$$
diffuse
$$
(I - \kappa \Delta t \nabla^2) \mathbf{\rho}_3(\mathbf{x}) = \mathbf{\rho}_2(\mathbf{x})
$$
where $\kappa$ is the diffusion coefficient (similar to viscosity for density dissipation).
2. Build Instruction
Build C ABI library
- CMake 4.3.0 or higher
- Ninja build system (for CXX std module support)
- A C++23 compliant compiler (tested on Arch Linux with gcc/g++ 15.2.1, Windows with MSVC 17.14.29)
- NVIDIA CUDA 13.2 or higher
cmake -B build -S . -G Ninja
cmake --build build --parallel
Build with Vulkan visualizer
A built-in Vulkan visualizer is provided. To enable it, you need to install latest Vulkan SDK.
- Vulkan SDK 1.4 or higher.
cmake -B build -S . -G Ninja -DSTABLE_FLUIDS_BUILD_VULKAN_APP=ON
cmake --build build --parallel
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