SPH Fluid Simulator - Constraint Theory

Simulation Parameters

Particle Count 300

Smoothing Radius (h) 16

Rest Density (ρ₀) 1000

Pressure Stiffness (k) 2000

Viscosity (μ) 2500

Gravity (g) 980

Time Step (dt) 0.008

Preset Configurations

Boundary Conditions

Enable Walls Enable Floor Enable Obstacles

Visualization Mode

Velocity Field Pressure Field Density Field

Show Velocity Vectors Show Field Background

Mouse Interaction

Push Fluid Add Fluid Place Obstacle

Interaction Radius 50

Force Strength 5000

About SPH

Smoothed Particle Hydrodynamics is a mesh-free computational method for simulating fluid dynamics.

Key Concepts:

Density Constraint: Particles maintain target density through pressure forces
Kernel Functions: Smooth interpolation weights for neighbor contributions
Pressure Force: Pushes particles apart when density exceeds rest density
Viscosity Force: Smooths velocity differences between neighbors

Constraint Theory Connection:

This simulator demonstrates how fluid dynamics can be expressed through geometric constraints on particle distributions. The density constraint ρ(x) → ρ₀ creates emergent fluid behavior.