What is the difference between SPH and Euler fluid?

SPH (Smoothed Particle Hydrodynamics) is a Lagrangian method: fluid is represented by moving particles that carry mass, velocity, and pressure. Eulerian methods use a fixed grid and compute fluxes between cells. SPH handles splashing and free surfaces better; Eulerian grids handle large smooth flows more efficiently.

What causes the Kármán vortex street?

At Reynolds numbers between ~50 and ~200 000, flow past a cylinder becomes unstable. Vortices shed alternately from the upper and lower sides of the obstacle, creating a periodic street of counter-rotating vortices. This phenomenon causes the singing of telephone wires and structural resonance in chimneys.

How is the Navier-Stokes equation solved in real time?

The simulation uses Jos Stam's stable fluids method: advection (semi-Lagrangian backtracking), diffusion (implicit Gauss-Seidel), and pressure projection (Helmholtz decomposition) ensure unconditional stability at interactive frame rates, at the cost of some numerical dissipation.

What is the Reynolds number and why does it matter for fluid simulations?

The Reynolds number Re = ρvL/μ is the ratio of inertial to viscous forces in a flow. At low Re (< ~2300 in a pipe) the flow is laminar and predictable; at high Re the flow becomes turbulent with chaotic mixing. The Lattice-Boltzmann and Kármán vortex simulations let you dial Re directly to explore the laminar-to-turbulent transition.

Fluid Dynamics & Aerodynamics

Category Simulations

From laminar to turbulent — fluids in motion

Fluid simulation is one of the hardest problems in real-time graphics. The Navier-Stokes equations are non-linear PDEs with no closed-form general solution. Modern methods — SPH particles, lattice-Boltzmann cells, height-field approximations — trade physical exactness for interactive framerates.

🌊

★★★ Advanced New

Ripple Tank

A 2D ripple tank solving ∂²h/∂t²=c²∇²h: point and plane sources, reflection off barriers, diffraction through slits, and refraction over a sloping bottom where waves bend toward the shallows.

Wave Equation Interference Diffraction Canvas 2D

💧

★★★ Advanced

Capillary Action — Jurin's Law

Surface tension pulls liquid up narrow tubes by h = 2γcosθ/(ρgr). Watch the meniscus curve, compare tube radii (rise ∝ 1/r), and switch liquids — including mercury, which is pushed down.

Canvas 2D Surface Tension Jurin's Law Meniscus

🪂

★★★ Advanced

Drag Coefficient — Shape & Wake

How a body's shape and Reynolds number set aerodynamic drag: watch flow separate behind bluff bodies, compare textbook C_d values, and find the drag crisis on the live C_d–Re curve.

Canvas 2D Aerodynamics Reynolds Wake

🌊

★★★ Advanced

Stokes Flow — Low Reynolds Number

Creeping flow where viscosity dominates inertia: streamlines past a sphere, the striking reversibility that re-forms a smeared dye blob, and the scallop theorem for microswimmers.

Canvas 2D Low Reynolds Reversibility Microswimmer

💧

★★★ Advanced

SPH Fluid Simulation

Smoothed Particle Hydrodynamics in WebGL. Thousands of particles interact via Lennard-Jones-like pressure and viscosity forces. Adjustable surface tension, gravity and density. Marching-squares surface extraction optional.

WebGL SPH Navier-Stokes Density

🌊

★★☆ Moderate

Ocean Waves

Gerstner wave superposition on a Three.js mesh with per-vertex displacement and foam accumulation. Tune amplitude, wavelength, phase speed and wind direction in real time.

Three.js Gerstner Waves GLSL FFT

〰️

★★☆ Moderate

Wave Equation

2D wave equation solved on a grid using finite differences. Click to place sources; tune wave speed and damping. Interference patterns, standing waves, and boundary reflections emerge naturally.

Canvas 2D Finite Differences PDE Interference

🌧️

★☆☆ Beginner

Rain & Puddles

Falling raindrops with realistic splatter physics; ripple rings expand on the puddle surface with physically motivated decay. Wind angle and rain intensity sliders included.

Canvas 2D Ripples Surface Tension Particles

🫧

★☆☆ Beginner

Soap Bubbles

Pressure-driven bubbles rising through a fluid column. Surface tension drives the spherical shape; coalescence and film thinning produce the Plateau–Rayleigh instability when bubbles meet.

Canvas 2D Surface Tension Pressure Buoyancy

🌀

★★★ Advanced New

Kármán Vortex Street

2D Lattice Boltzmann (D2Q9, BGK) simulation of vortex shedding behind a cylinder. Adjust Reynolds number in real time. Color by velocity, vorticity or density. Click to add obstacles.

LBM D2Q9 Reynolds Number

🌪️

★★★ Advanced

Tornado

Rotating convective vortex: pressure gradient drives inflow, updraft sustains the funnel. Adjust wind speed and humidity to see formation and dissipation dynamics.

Vortex Convection Particles

🌍

★★☆ Moderate

Planetary Atmosphere

Simplified GCM: Hadley cells, Coriolis deflection and jet streams on a rotating sphere. See how latitude and rotation rate shape global circulation patterns.

GCM Coriolis Three.js

🌀

New★★★ Advanced

Lattice-Boltzmann Flow

D2Q9 Lattice-Boltzmann fluid simulator. Draw obstacles, watch vortices form, visualise velocity, vorticity and density fields. Adjust viscosity and Reynolds number in real time.

Canvas 2D LBM Vorticity

✈️

★★★ Advanced

Aerofoil & Lift

NACA 4-digit profile with streamlines and pressure distribution. Adjust angle of attack and watch Cl/Cd coefficients and stall onset update in real time.

Canvas 2D NACA Lift Bernoulli

🔵

★☆☆ Beginner

Bernoulli's Principle

Fluid through a Venturi tube: particles speed up in the constriction as pressure drops. P + ½ρv² = const and A₁v₁ = A₂v₂ shown with live pressure gauges. Choose Water, Air, Oil or Mercury.

Bernoulli Continuity Canvas 2D

🌊

★★☆ Moderate New

Shallow Water Equations

1D Saint-Venant equations solved with the Lax-Friedrichs scheme. Dam-break, sloshing, tidal wave, and hydraulic step scenarios. Live Froude number, wave speed, Manning friction and mass conservation tracking.

Saint-Venant Lax-Friedrichs Froude Number Canvas 2D

✈️

★☆☆ Beginner

Bernoulli's Principle — Airfoil Lift & Flow

Visualise Bernoulli's principle with interactive streamlines around an airfoil. Adjust angle of attack and airspeed to see how pressure differential generates lift.

Bernoulli Airfoil Lift Streamlines

Fluid Lattice-Boltzmann

Lattice Boltzmann method (D2Q9) simulating Karman vortex street and computational fluid dynamics.

Lattice Boltzmann LBM D2Q9

🚰

★★☆ Moderate New

Pipe Flow Profiles

Visualise laminar Poiseuille flow and turbulent velocity profiles in a pipe. Explore the Reynolds number transition at Re ≈ 2300 with the 1/7 power law and cross-section heatmap.

Poiseuille Reynolds Number Power Law Canvas 2D

💨

★★★ Advanced New

Vortex Ring Dynamics

Watch a vortex ring self-propel through fluid. Biot-Savart law governs the induced velocity field. A...

Biot-Savart Vortex Canvas 2D

🌊

★★★ Advanced New

Taylor-Green Vortex Decay

Simulate the Taylor-Green vortex — a canonical turbulence benchmark. Watch the initial sinusoidal ve...

Turbulence Taylor-Green Canvas 2D

🫧

★★☆ Moderate New

Rising Bubble in Viscous Fluid

A gas bubble rises through a viscous liquid driven by buoyancy. Stokes drag, Morton number, and Eötv...

Buoyancy Morton Number Canvas 2D

Fluid Pressure — Pascal's Law & Hydrostatics

Visualise pressure variation with depth (P = ρgh), Pascal's law hydraulic press and Archimedes' buoyancy principle. Adjust fluid density and container geometry.

Pascal's Law Hydrostatics Buoyancy Archimedes

Key Concepts

The equations behind fluid motion

Navier-Stokes

∂u/∂t + (u·∇)u = −∇p/ρ + ν∇²u + f. The left-hand non-linear convection term is what makes turbulence so hard. Incompressibility adds ∇·u = 0. No general closed-form solution exists for 3D — one of the Millennium Prize Problems.

Smoothed Particle Hydrodynamics

Lagrangian method: fluid is N particles. Each carries mass, velocity and pressure. Quantities at any point are a kernel-weighted sum over neighbours within radius h. Pressure from density via equation of state. No mesh — handles free surfaces naturally.

Gerstner Waves

Surface particles move on circles: x = x₀ − (A/kh)sin(kx−ωt), y = A cos(kx−ωt). Superpose multiple components with different wavelengths via a Phillipps spectrum for photorealistic ocean. Velocity is analytic — no PDE solve needed.

Lattice-Boltzmann Method

Mesoscopic approach: instead of tracking particles or solving Navier-Stokes directly, evolve a particle distribution function on a fixed lattice. Streaming + collision → BGK operator. Recovers incompressible NS in the low-Mach limit. GPU-friendly — each cell updates independently.

Learning Resources

Deep dives into fluid simulation techniques

Article Navier-Stokes Fluid Simulation From scratch: pressure projection, velocity advection, Poisson solver. Full JS implementation with canvas rendering. → Article SPH Fluid — How It Works Particle kernels, density estimation, pressure forces and viscosity — step by step with JavaScript code samples. → Article Lattice-Boltzmann in 200 Lines of JS D2Q9 streaming and BGK collision, boundary conditions, velocity field visualisation. → Article Gerstner Waves & Ocean Rendering Closed-form trochoidal waves, Phillipps spectrum superposition and foam accumulation in Three.js. →

All articles →

About Fluid Dynamics Simulations

SPH, Navier–Stokes, Kármán vortex streets, and ocean waves — live

Fluid dynamics simulations model the motion of liquids and gases governed by the Navier–Stokes equations. Smoothed-Particle Hydrodynamics (SPH) represents fluid as interacting particles that compute pressure and viscosity from kernel-weighted neighbourhood sums. The Kármán vortex street simulation solves a simplified 2D grid model to reproduce the alternating vortex shedding behind a cylinder — a pattern visible in cloud formations and studied in aerodynamics and civil engineering.

Ocean wave simulations implement Gerstner's trochoidal wave equations on a GPU vertex shader for tens of thousands of vertices at interactive frame rates. By adjusting Reynolds number, particle density, viscosity, or wave steepness you transition between laminar flow and turbulence, observe wave breaking, and watch surface tension create capillary ripples. These are the same mathematical frameworks used in CFD software, weather models, and animated film pipelines.

Fluid dynamics is among the most computationally demanding fields in science. Weather forecasting, aircraft design, cardiovascular medicine, and offshore engineering all depend on solving the Navier-Stokes equations. The Clay Mathematics Institute has offered a $1 million prize for a rigorous mathematical proof of whether smooth solutions always exist — one of the seven Millennium Prize Problems. These browser simulations give an intuitive feel for turbulence, vortex dynamics, and the transition from laminar to chaotic flow.

Key Concepts

Topics and algorithms you'll explore in this category

Navier-StokesMomentum and continuity equations for viscous flow

SPHSmoothed Particle Hydrodynamics for Lagrangian fluid

Eulerian GridFixed-grid finite-difference fluid solver

Reynolds NumberRatio of inertial to viscous forces: Re = ρvL/μ

Kármán Vortex StreetPeriodic vortex shedding behind a bluff body

LBMLattice Boltzmann Method — mesoscopic fluid simulation

🌊 Test Your Fluid Dynamics Knowledge

5 questions — Reynolds number, Bernoulli, viscosity and more

Frequently Asked Questions

Common questions about this simulation category

What is the difference between SPH and Euler fluid?: SPH (Smoothed Particle Hydrodynamics) is a Lagrangian method: fluid is represented by moving particles that carry mass, velocity, and pressure. Eulerian methods use a fixed grid and compute fluxes between cells. SPH handles splashing and free surfaces better; Eulerian grids handle large smooth flows more efficiently.
What causes the Kármán vortex street?: At Reynolds numbers between ~50 and ~200 000, flow past a cylinder becomes unstable. Vortices shed alternately from the upper and lower sides of the obstacle, creating a periodic street of counter-rotating vortices. This phenomenon causes the singing of telephone wires and structural resonance in chimneys.
How is the Navier-Stokes equation solved in real time?: The simulation uses Jos Stam's stable fluids method: advection (semi-Lagrangian backtracking), diffusion (implicit Gauss-Seidel), and pressure projection (Helmholtz decomposition) ensure unconditional stability at interactive frame rates, at the cost of some numerical dissipation.
What is the Reynolds number and why does it matter?: The Reynolds number Re = ρvL/μ is the ratio of inertial to viscous forces in a flow. At low Re (< ~2300 in a pipe) the flow is laminar and predictable; at high Re it becomes turbulent with chaotic mixing. The Lattice-Boltzmann and Kármán vortex simulations let you adjust Re directly to explore the laminar-to-turbulent transition.

Other Categories

Explore Fluid Dynamics with Interactive Simulations

Every Fluid Dynamics simulation on this page is a hands-on laboratory: load an interactive Fluid Dynamics model, adjust the governing parameters, and watch laminar streamlines dissolve into turbulent vortices in real time. Whether you are a student, an engineer or simply curious, you can learn Fluid Dynamics online here without any software, plug-ins or maths prerequisites — just open a simulation and experiment. The same principles you observe drive real-world applications such as aircraft wing design, where Bernoulli pressure differences and boundary-layer behaviour decide whether a wing generates lift or stalls.