Real-Time Inviscid Fluid Dynamics and Aero-acoustics on a Sphere

Abstract: Real-time fluid and aeroacoustic simulation on complex surfaces can have interactive applications - from globe-based weather visualizations to immersive computer games with physically accurate wind and sound. However, conventional grid-based solvers struggle with numerical instability near surface singularities, and mesh-based approaches lack a straightforward path to solving partial differential equations (PDEs) with stable, high-order accuracy. Our model presents a unified framework for real-time inviscid fluid simulation and aeroacoustics on spherical surfaces with embedded obstacles, combining the Closest Point Method (CPM), projection-based Navier-Stokes solvers, and the Ffowcs Williams-Hawkings (FWH) analogy. CPM enables surface PDEs to be solved in a Cartesian embedding without parametrization by restricting computation to a narrow band around the sphere. Each band point is mapped to its nearest surface location, where band operators project results onto the local tangent space. Surface obstacles are modelled with signed distance functions (SDFs), enforcing no-slip velocity constraints and Bernoulli-based pressure adjustments for consistent real-world boundary interactions. Aeroacoustic sources are computed directly from surface pressure force derivatives and mapped to real-time audio via frequency and amplitude modulation with artifact-suppressing hysteresis smoothing. Our findings from this model simulate the behaviour of inviscid fluid on spherical surfaces while generating sound using the pressure of the fluid flowing on the surface. This approach gives results that offer stability, geometric consistency, and support applications in scientific visualization, virtual reality, and educational tools.