Fluid Simulation with Smoothed Particle Hydrodynamics (SPH)

TL;DR

I implemented a particle-based fluid simulator using Smoothed Particle Hydrodynamics (SPH) to model incompressible fluid behavior.
The system computes density, pressure, and viscosity forces from local neighborhoods and integrates them in real time, producing visually convincing fluid motion with collision handling and tunable physical parameters.

Overview

This project implements Smoothed Particle Hydrodynamics (SPH), a mesh-free Lagrangian approach to fluid simulation. Instead of solving fluid quantities on a grid (Eulerian), SPH represents the fluid as particles and computes density/pressure/forces using local neighborhood smoothing kernels.

Why SPH?

• Mesh-free and flexible for complex motion
• Naturally handles free surfaces and splashes
• Intuitive particle viewpoint for interactive demos

Purpose

Realistic fluid motion is difficult because the system involves:

• many interacting elements (particles)
• forces that depend on local neighborhoods
• stability constraints (time step, pressure stiffness)

Goal: reproduce visually convincing fluid behavior by building a particle simulator with:

• density estimation
• pressure forces
• viscosity forces
• external forces (gravity)
• collision handling against obstacles

Methodology

1) Eulerian vs Lagrangian framing

• Eulerian: sample velocity/pressure on a grid.
• Lagrangian (SPH): follow moving particles and compute fields from them.

2) Core SPH idea: smoothing kernel + neighborhood

Each particle contributes to nearby particles through a kernel function. The kernel is used for:

• density estimation
• gradients (pressure direction)
• Laplacians (viscosity diffusion)

3) Pipeline per simulation step

At each time step:

A) Density estimation

Compute each particle’s density from nearby particle masses.

Why this matters:

• density drives pressure
• pressure drives incompressibility-like behavior

B) Pressure computation

Use a state relation (often inspired by ideal gas law forms) to convert density error into pressure.

C) Internal forces

Compute forces from neighbors:

• Pressure force: pushes particles from high pressure to low pressure
• Viscosity force: resists relative motion, smoothing velocity differences

D) External forces

• Gravity (baseline external acceleration)
• (Optional extensions: buoyancy, surface tension)

E) Integrate

Update velocity and position using the net force.

4) Collision handling

The simulator resolves particle-obstacle interaction using:

• contact point
• penetration depth
• surface normal at contact point

This prevents particles from tunneling through obstacles and produces believable boundary behavior.

Results

What works (demo outcomes)

• Particle-based fluid motion with pressure-driven expansion/compression
• Visible viscosity effects (thicker vs runnier behavior)
• Stable gravity-driven flow under collisions

Parameters you can tune

SPH is very sensitive to physical parameters. The most important ones you can expose in UI:

• rest density
• stiffness (pressure coefficient)
• viscosity coefficient
• smoothing radius (kernel radius)
• time step

Limitations

The primary limitation is computational cost, especially as particle count increases. SPH requires neighborhood queries and pairwise interactions, which scale poorly without acceleration structures. :contentReference[oaicite:10]{index=10}

Other common practical issues:

• stability constraints requiring small time steps
• clumping / jitter if parameters are poorly tuned
• boundary handling quality depends on collision model

Future work

Concrete extensions that make this feel like a real graphics portfolio project:

• Obstacle variety: sphere, terrain, complex colliders
• Free surface rendering: smoother surface extraction/meshing for visuals
• Erosion / interaction: fluid affecting terrain over time
• Acceleration: spatial hashing / uniform grid neighbor search
• GPU path: compute shader implementation for higher particle counts