Fluid Simulation on Compressible Flow Maps

*Joint First Author
ACM Transactions on Graphics (SIGGRAPH 2025), Vol. 44(4), to appear
Poster Dataset Distillation (PoDD)

Abstract

This paper presents a unified compressible flow map framework designed to accommodate diverse compressible flow systems, including high-Mach-number flows (e.g., shock waves and supersonic aircraft), weakly compressible systems (e.g., smoke plumes and ink diffusion), and incompressible systems evolving through compressible acoustic quantities (e.g., free-surface shallow water). At the core of our approach is a theoretical foundation for compressible flow maps based on Lagrangian path integrals, a novel advection scheme for the conservative transport of density and energy, and a unified numerical framework for solving compressible flows with varying pressure treatments. We validate our method across three representative compressible flow systems, characterized by varying fluid morphologies, governing equations, and compressibility levels, demonstrating its ability to preserve and evolve spatiotemporal features such as vortical structures and wave interactions governed by different flow physics. Our results highlight a wide range of novel phenomena, from ink torus breakup to delta wing tail vortices and vortex shedding on free surfaces, significantly expanding the range of fluid systems that flow-map methods can handle.

Shock Wave Simulation

Bullets

Dragon Capsule

Rocket

Jet

Mach Diamond

Piston Leapfrog (Comparison & Validation)

Shallow Water Simulation

Three Ships on the Sea

Water Strider

Static Karman Vortex Street

Two-way Coupled Karman Vortex Street

Ship in Tank

Pillar

Swimming Board

Shallow Water Leapfrog (Comparison & Validation)

Shallow Water Two Vortices (Comparison & Validation)

Shallow Water Three Vortices (Comparison & Validation)

Weakly Compressible Flow Simulation

Delta Wing

Ink Drop

Trefoil

Video

BibTeX

@article{chen2025compressible,
        title={Fluid Simulation on Compressible Flow Maps},
        author={Chen, Duowen and Li, Zhiqi and Zhang, Taiyuan and He, Jinjin and Zhou, Junwei and van Bloemen Waanders, Bart and Zhu, Bo},
        journal={ACM Transactions on Graphics},
        year={2025},
        volume={44},
        number={4},
        note={to appear},
        publisher={ACM New York, NY}
      }