SPH vs Lattice-Boltzmann: Two Fundamentally Different Ways to Simulate Fluids
Smoothed Particle Hydrodynamics (SPH) tracks fluid as moving particles, while the Lattice-Boltzmann Method (LBM) tracks fluid as particle distributions flowing across a fixed grid. Compare both fluid-simulation approaches live.
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⚡ Quick answer
SPH (Smoothed Particle Hydrodynamics) is a mesh-free method: fluid is represented by particles that carry mass and move freely through space, with density and pressure computed by smoothing over nearby particles. The Lattice-Boltzmann Method (LBM) instead uses a fixed grid, where each cell tracks probability distributions of particles moving in a small set of directions — fluid properties like velocity and density emerge from streaming and colliding these distributions between neighbouring cells.
📊 SPH Fluid vs Lattice-Boltzmann Flow
| SPH Fluid | Lattice-Boltzmann Flow | |
|---|---|---|
| Representation | Discrete particles carrying mass, moving freely in continuous space | Fixed regular grid (lattice); each cell holds particle-distribution values, not physical particles |
| Underlying model | Discretised Navier-Stokes via smoothed kernel interpolation between particles | Discretised Boltzmann transport equation (D2Q9 velocity set in the 2D case) |
| Best suited for | Free surfaces, splashes, droplets — anywhere the fluid boundary moves and deforms a lot | Flow around fixed or drawn obstacles, vortex shedding, boundary-layer effects at set Reynolds numbers |
| Boundary handling | Naturally handles free surfaces and splash impulses (no fixed domain shape) | Naturally handles solid obstacles and no-slip walls with simple bounce-back rules |
| Computational pattern | Neighbour search around each moving particle every step | Simple local streaming + collision per fixed grid cell, easy to parallelize |
| Visual signature on this site | Splashing droplets and instanced-mesh particles reacting to gravity, viscosity and walls | Colour-coded velocity/vorticity/density fields flowing smoothly around obstacles you draw |
| Best for learning | How particle-based (Lagrangian) methods model deformable fluid surfaces | How grid-based (Eulerian-ish) kinetic methods recover Navier-Stokes flow from simple local rules |
Smoothed Particle Hydrodynamics (SPH) and the Lattice-Boltzmann Method (LBM) both simulate the same underlying physics — viscous, pressure-driven fluid flow — but they discretise the world in opposite ways. SPH is a "Lagrangian" method: it drops a cloud of particles into the domain and lets them carry mass and momentum wherever the flow takes them, computing pressure and viscosity by smoothing over each particle’s nearby neighbours. That makes it a natural fit for splashes, droplets and any situation where the fluid’s outer boundary itself is moving — exactly what this site’s SPH Fluid simulation demonstrates when you click and drag to make a splash.
Lattice-Boltzmann instead keeps a fixed grid of cells and, in each one, tracks how much "fluid" is moving in a handful of fixed directions (nine, in the D2Q9 scheme used here). Every step, these directional packets stream to neighbouring cells and then "collide" locally according to simple rules — and remarkably, averaging this microscopic bookkeeping recovers the same macroscopic Navier-Stokes behaviour that SPH targets directly. That grid-based structure makes LBM especially good at flow-around-obstacles problems: this site’s simulation lets you draw walls with the mouse and immediately see vortices shed downstream, with switchable velocity, vorticity and density colour fields.
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