Fluid Simulation on Compressible Flow Maps

Fig. 1. We present diverse phenomena simulated using our compressible flow map method. From small-scale water striders swimming on the surface of a pond, to large-scale ships on vast oceans, and a Dragon capsule landing on Mars, our simulator captures both compressible and weakly compressible dynamics spanning various scales of applications with a single unified framework.

This paper presents a unified compressible flow map framework designed to accommodate diverse compressible flow systems, including high-Machnumber 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.