Above:
An efficient subspace re-simulation of novel fluid dynamics. This scene was generated an order of magnitude faster than the original. The solver itself, without velocity reconstruction, runs three orders of magnitude faster.

Abstract

We present a new subspace integration method that is capable of efficiently adding and subtracting dynamics from an existing high-resolution fluid simulation.
We show how to analyze the results of an existing high-resolution simulation, discover an efficient reduced approximation, and use it to quickly "re-simulate"
novel variations of the original dynamics. Prior subspace methods have had difficulty re-simulating the original input dynamics because they lack efficient
means of handling semi-Lagrangian advection methods. We show that multi-dimensional cubature schemes can be applied to this and other advection methods,
such as MacCormack advection. The remaining pressure and diffusion stages can be written as a single matrix-vector multiply, so as with previous subspace
methods, no matrix inversion is needed at runtime. We additionally propose a novel importance sampling-based fitting algorithm that asymptotically accelerates
the precomputation stage, and show that the Iterated Orthogonal Projection method can be used to elegantly incorporate moving internal boundaries into a
subspace simulation. In addition to efficiently producing variations of the original input, our method can produce novel, abstract fluid motions that we have
not seen from any other solver.

This material is based upon work supported by a National Science Foundation CAREER award (IIS-1253948). We acknowledge rendering support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC (DMR-1121053), Hewlett-Packard, and NSF CNS-0960316. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.