Fast Subspace Fluid Simulation with a Temporally-Aware Basis

TL;DR

This paper introduces a fast, memory-efficient fluid simulation method using Dynamic Mode Decomposition that allows real-time control and high fidelity in graphics applications, outperforming traditional reduced-order models.

Contribution

The novel integration of DMD with control and optimization techniques enables real-time, user-controllable fluid simulations with improved performance and fidelity over existing methods.

Findings

Robust performance across diverse scenarios including vortex rings and plumes.

Significantly fewer basis functions needed compared to traditional spatial ROMs.

Enables time-reversible and super-resolution fluid simulations.

Abstract

We present a novel reduced-order fluid simulation technique leveraging Dynamic Mode Decomposition (DMD) to achieve fast, memory-efficient, and user-controllable subspace simulation. We demonstrate that our approach combines the strengths of both spatial reduced order models (ROMs) as well as spectral decompositions. By optimizing for the operator that evolves a system state from one timestep to the next, rather than the system state itself, we gain both the compressive power of spatial ROMs as well as the intuitive physical dynamics of spectral methods. The latter property is of particular interest in graphics applications, where user control of fluid phenomena is of high demand. We demonstrate this in various applications including spatial and temporal modulation tools and fluid upscaling with added turbulence. We adapt DMD for graphics applications by reducing computational overhead, incorporating user-defined force inputs, and optimizing memory usage with randomized SVD. The integration of OptDMD and DMD with Control (DMDc) facilitates noise-robust reconstruction and real-time user interaction. We demonstrate the technique's robustness across diverse simulation scenarios, including artistic editing, time-reversal, and super-resolution. Through experimental validation on challenging scenarios, such as colliding vortex rings and boundary-interacting plumes, our method also exhibits superior performance and fidelity with significantly fewer basis functions compared to existing spatial ROMs. The inherent linearity of the DMD operator enables unique application modes, such as time-reversible fluid simulation. This work establishes another avenue for developing real-time, high-quality fluid simulations, enriching the space of fluid simulation techniques in interactive graphics and animation.