CADES — Computational Aerodynamics Display & Evaluation System

A high-performance, interactive 2D aerodynamics simulator built with the Lattice Boltzmann Method (LBM) and D2Q9 lattice. Visualize airflow around a NACA 0012 airfoil in real-time with live pressure coefficient distributions, stall detection, and interactive particle tracing.

Features

Core Simulation

• Lattice Boltzmann D2Q9 Solver: Accurate incompressible fluid dynamics on a 150×75 grid
• NACA 0012 Airfoil: Parametric geometry with variable angle of attack (±25°)
• Smagorinsky Subgrid Turbulence Closure: Dynamic relaxation time for stable, realistic turbulence modeling
• Boundary Conditions:
  • Zou-He velocity inlet (left wall)
  • Extrapolation outlet (right wall)
  • Periodic boundaries (top/bottom)
  • No-slip bounce-back on airfoil surface

Aerodynamic Analysis

• Lift Coefficient (Cl) Calculation: Real-time computation from integrated surface pressure
• Pressure Coefficient (Cp) Distribution Plot: Live chordwise pressure curves for upper and lower surfaces
• Stall Detection: Automatic warning at angles of attack ≥12°
• Comprehensive Visualization:
  • Velocity field heatmap
  • Pressure field diverging colormap
  • Vorticity magnitude field
  • Static streamlines or particle tracing

Interactive Controls

• Angle of Attack Slider: -25° to +25°
• Reynolds Number Control: 50 to 300 (influences viscosity and relaxation)
• Inlet Velocity Adjustment: Fine-tune flow dynamics
• Particle Count: 0 to 2500 tracing particles
• Field Visualization: Switch between velocity, pressure, vorticity, or blank background
• Overlay Modes: Streamlines, particles, or none
• Theme Support: Light and dark canvas themes
• Interactive Ink Spraying: Click or touch to inject particles and visualize flow patterns
• Playback Controls: Play/pause, manual stepping, reset

Technical Details

Solver Architecture

Distribution Functions (D2Q9)

The simulation maintains 9 distribution functions per grid cell representing discrete velocity directions:

Direction indices:     Velocity vectors:
    6 2 5                (-1,+1) (0,+1) (+1,+1)
    3 0 1                (-1, 0) (0, 0) (+1, 0)
    7 4 8                (-1,-1) (0,-1) (+1,-1)

LBM Algorithm Steps

1. Collision: BGK operator with Smagorinsky turbulence correction
2. Streaming: Advection with bounce-back boundary handling
3. Inlet BC: Zou-He scheme for prescribed velocity
4. Outlet BC: Extrapolation from upstream cell
5. Macroscopic Recovery: Compute density and velocity from distributions

Aerodynamic Calculations

Pressure Sampling: Surface pressure is sampled perpendicular to the airfoil surface at each chordwise position.

Lift Coefficient:

Cl = Fy / (0.5 × ρ × u₀² × chord)

where Fy is the integrated vertical pressure force.

Pressure Coefficient:

Cp = (p - p∞) / (0.5 × ρ × u₀²)

Grid & Parameters

• Grid Size: 150 × 75 cells (lattice units)
• Chord Length: 40 lattice units
• Max Particles: 2,500 tracer particles
• Max Velocity: ±0.25 lattice units/step (Mach number control)
• Density Range: 0.2 to 2.0 (compressibility control)

File Structure

├── index.html              # Main HTML structure
├── main.js                 # Render loop & entry point
├── solver.js               # LBM D2Q9 engine with SGS turbulence
├── aerodynamics.js         # Cl, Cp, stall detection
├── renderer.js             # Field visualization & canvas DPI scaling
├── particles.js            # Particle advection & lifecycle
├── airfoil.js              # NACA 0012 geometry & solid mask
├── colormap.js             # Color lookup tables for all fields
├── ui.js                   # Event listeners & user controls
├── state.js                # Simulation state & parameters
├── constants.js            # Grid dimensions & D2Q9 lattice
├── cpplot.js               # Pressure coefficient plot renderer
├── cades.jsx               # React wrapper (if used in React environment)
└── aerodynamics.js         # Aerodynamic forces module

Usage

Basic Workflow

1. Load the simulator in a modern web browser (Chrome, Firefox, Safari, Edge)
2. Adjust Parameters:
   • Use sliders for angle of attack, Reynolds number, velocity
   • Select visualization fields and overlay types
   • Choose light or dark theme
3. Observe Flow:
   • Watch velocity/pressure/vorticity fields update in real-time
   • Monitor Cl value and stall warning
   • Check Cp plot for pressure distribution
4. Interactive Drawing:
   • Click/drag or touch the canvas to inject tracer particles
   • Visualize flow patterns around the airfoil

Control Reference

Control	Range	Effect
Angle of Attack	-25° to +25°	Airfoil orientation; triggers stall warning at ≥12°
Reynolds Number	50–300	Affects viscosity and turbulent behavior
Inlet Velocity	0.01–0.15	Flow speed; influences Cl and separation
Particle Count	0–2,500	Tracer particle density for visualization
Background Field	velocity / pressure / vorticity / none	Main visualization layer
Overlay Type	particles / streamlines / none	Secondary flow visualization
Theme	light / dark	Canvas background and color palette

Performance Tips

• For smoother animation on slower devices, reduce particle count
• Increasing Reynolds number may require longer settling time (more iterations)
• 3 solver steps per frame is default; adjust stepsPerFrame in main.js for speed/accuracy trade-off

Physical Parameters

Reynolds Number Relationship

Re = (u₀ × chord) / ν
ν = (u₀ × chord) / Re
τ = 3ν + 0.5

Higher Re → thinner boundary layers, more complex separation; requires finer grid or higher relaxation time.

Stall Behavior

NACA 0012 typically stalls around 8–10° in real experiments. This simulator triggers a warning at ≥12° due to grid coarseness and lattice Mach number limitations.

Pressure Scaling

• Reference pressure: p∞ = 1/3 (lattice units)
• Density range: [0.93, 1.07] in steady-state flow
• Velocity clamps: ±0.25 (prevents numerical instability)

Color Schemes

Light Theme

• Velocity: Cool (light grey) → Hot (warm tones)
• Pressure: Deep blue (low) → Neutral grey → Deep red (high)
• Vorticity: Cyan/blue (negative/clockwise) → Neutral → Orange/red (positive/counterclockwise)
• Airfoil: Slate fill with dark border

Dark Theme

• Velocity: Dark blue → Cyan → Green → Yellow → Red
• Pressure: Dark blue → Red with higher contrast
• Vorticity: Blue/cyan → Orange/red with inverted scale
• Airfoil: Slate fill with white border

Numerical Stability & Limitations

Clamping & Safety

• Density is clamped to [0.2, 2.0] to prevent divergence
• Velocity is clamped to [−0.25, 0.25] to maintain low Mach number
• Auto-reset triggers if NaN is detected

Known Limitations

1. Coarse Grid: 150×75 resolution limits boundary layer detail
2. Lattice Mach Constraint: Ma = u₀/c_s < 0.3 restricts flow speeds
3. Symmetric Airfoil: NACA 0012 only; no cambered profiles
4. 2D Only: No spanwise variations or 3D effects
5. Inviscid Limit: Very low Re (<50) may show artificial behavior

Building & Extending

Browser Compatibility

• Requires ES5+ (modern JavaScript engines)
• Uses Uint8Array, Float32Array for efficient memory
• Canvas 2D API with high-DPI support

Adding Custom Airfoils

Replace the NACA 0012 equation in airfoil.js and renderer.js:

var yt = chord * (yourAirfoilFunction(xNorm));

Modifying Solver

• Change stepsPerFrame in main.js for speed/accuracy
• Adjust Smagorinsky constant Cs = 0.15 in solver.js
• Modify relaxation time bounds in state.js

React Integration

Use cades.jsx as a wrapper component for integration into React applications.

Performance Metrics

Typical Performance (Desktop)

• Frame Rate: 50–60 FPS (with 3 solver steps/frame, 1200 particles)
• Update Time: ~15–30ms per frame
• Memory: ~5–8 MB (grid + buffers + particles)

References

• Lattice Boltzmann Method: Succi, S. (2001). The Lattice Boltzmann Equation
• D2Q9 Lattice: Bhatnagar, Gross, and Krook (BGK) collision operator
• Smagorinsky SGS: Pope, S.B. (2000). Turbulent Flows
• NACA 0012: Abbott & Von Doenhoff (1959). Theory of Wing Sections
• Boundary Conditions: Zou & He (1997); Latt et al. (2008)