Covector Fluids (SIGGRAPH 2022)

We simulate Euler equations for inviscid fluids by using a novel formulation based on covectors. This new formulation is an entirely velocity-based method in the vein of advection-projection methods while emulating vortex methods. This allows for capturing more intricate vortex dynamics and reducing dissipation of energy with low computational overhead.

Publication:
Mohammad Sina Nabizadeh, Stephanie Wang, Ravi Ramamoorthi and Albert Chern. (2022) Covector Fluids. ACM Transactions on Graphics (TOG), Vol. 41, Issue 4, Article 113.

Paper and code are available on the project page:

Abstract:
The animation of delicate vortical structures of gas and liquids has been of great interest in computer graphics. However, common velocity-based fluid solvers can damp the vortical flow, while vorticity-based fluid solvers suffer from performance drawbacks. We propose a new velocity-based fluid solver derived from a reformulated Euler equation using covectors. Our method generates rich vortex dynamics by an advection process that respects the Kelvin circulation theorem. The numerical algorithm requires only a small local adjustment to existing advection-projection methods and can easily leverage recent advances therein. The resulting solver emulates a vortex method without the expensive conversion between vortical variables and velocities. We demonstrate that our method preserves vorticity in both vortex filament dynamics and turbulent flows significantly better than previous methods, while also improving preservation of energy.

Music in the video:

[TeeTeeNet]

What happened to the Von Karman Cortex Street, was that a sensible result? What Reynolds number were you simulating and was non-periodic/chaotic shedding expected?

[programing]

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