2D Navier–Stokes Fluid Simulation

A DFOC Solo Computational Physics Project (Java)

Overview

This project is a simplified educational implementation of a 2D incompressible fluid simulator in Java.
It numerically models how velocity, pressure, viscosity, and external forces interact on a 2D grid.

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Physical Parameters Used in the Simulation

Velocity Field

• u(x, y, t): Horizontal and vertical velocity components at each grid cell
• Units: arbitrary (simulation units)

Pressure Field

• p(x, y, t): Scalar pressure value at each grid cell
• Used to enforce incompressibility

Density

• rho: Fluid density
• Assumed constant (typically set to 1.0 for simulation)

Viscosity

• nu: Kinematic viscosity
• Controls how quickly the fluid diffuses and smooths out
• Typical simulation range: 0.0001 – 0.1

External Forces

• F: External forces applied to the fluid
• Examples: user dragging mouse, injected momentum, gravity-like effects

Time Step

• dt: Size of each simulation step
• Smaller dt gives more accurate results
• Typical values: 0.01 – 0.1

Grid Resolution

• N: Number of cells along each axis (NxN grid)
• Higher N = more accuracy, slower simulation
• Typical beginner value: 64 or 128

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Numerical Components Used

• Advection: Moving velocity/dye along the flow
• Diffusion: Smoothing due to viscosity
• Projection: Adjusting the velocity field to make divergence = 0
• Boundary Conditions: No-slip or reflective walls
• Gauss–Seidel iteration: For solving diffusion and pressure steps

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Requirements

• Java 17+
• Optional: JavaFX or Swing for animation and visualization

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References

• Jos Stam — “Stable Fluids” (1999)
• Bridson — Fluid Simulation for Computer Graphics

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License

MIT License