A Gallery of Interactive Fluid Simulations
Henrik Peegel, Jaakob-Jaan Avvo, Ander Pavlov
Repo link: https://github.com/vapsik/Interactive_Fluid_Simulations
The goal of this project is to create a gallery of interactive 2D fluid simulations that enact the Navier-Stokes equations for incompressible fluids. The algorithm used to simulate the fluids is *Stable Fluids* based on the Jos Stam's seminal work, a 2001 article (link: https://pages.cs.wisc.edu/~chaol/data/cs777/stam-stable_fluids.pdf) in the field of real-time fluid simulation that has been extensively used in video games since its inception. In this algorithm, a simple incompressible (constant density) fluid is represented in a rectangular grid as a field coupled velocity vectors and pressure scalars that will dictate the movement of the fluid. The method relies on implicit diffusion, semi-Lagrangian advection and Gauss-Seidel projection, which all allow for stable, large time-step simulation without numerical divergence, combined with a projection step that enforces incompressibility, which makes the velocity field divergence-free using the Helmholtz decomposition theorem (https://en.wikipedia.org/wiki/Helmholtz_decomposition). Diffusion, external forces, and boundary interactions are incorporated in a computationally efficient time evolution scheme such that larger time steps can be used without losing physical accuracy or stability.
The first proof-of-concept non-interactive prototypes of the simulations will be created using Python in Jupyter notebook. Prototypes will lay the groundwork for visually enhanced and interactive simulations created with the Unity game engine, where computations will be parallelized via compute shaders for better real-time performance.
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