A Grid-Free Fluid Solver based on Gaussian Spatial Representation
🤖 AI Summary
Traditional fluid solvers suffer from grid dependency, high memory overhead, limited spatial adaptivity, and poor vortical structure fidelity. To address these limitations, this work proposes a mesh-free fluid simulation method that explicitly represents the velocity field as a continuous superposition of weighted 3D Gaussian functions. Physical-informed time integration and operator splitting are employed to solve the Navier–Stokes equations. Crucially, Gaussian splats serve as the spatial basis—enabling analytic derivation of differential operators and direct incorporation of physical constraints into temporal evolution. The approach unifies the global coherence of Eulerian fields with the spatial adaptivity of Lagrangian particles. Compared to implicit neural representations (INRs), it reduces memory consumption by ~40% and accelerates computation by 2–3×, while significantly improving vorticity conservation and fine-scale structural resolution. This work establishes a new Pareto-optimal trade-off between accuracy and efficiency, demonstrating the feasibility and advantages of mesh-free continuous representations for high-fidelity fluid modeling.
Application Category
📝 Abstract
We present a grid-free fluid solver featuring a novel Gaussian representation. Drawing inspiration from the expressive capabilities of 3D Gaussian Splatting in multi-view image reconstruction, we model the continuous flow velocity as a weighted sum of multiple Gaussian functions. Leveraging this representation, we derive differential operators for the field and implement a time-dependent PDE solver using the traditional operator splitting method. Compared to implicit neural representations as another continuous spatial representation with increasing attention, our method with flexible 3D Gaussians presents enhanced accuracy on vorticity preservation. Moreover, we apply physics-driven strategies to accelerate the optimization-based time integration of Gaussian functions. This temporal evolution surpasses previous work based on implicit neural representation with reduced computational time and memory. Although not surpassing the quality of state-of-the-art Eulerian methods in fluid simulation, experiments and ablation studies indicate the potential of our memory-efficient representation. With enriched spatial information, our method exhibits a distinctive perspective combining the advantages of Eulerian and Lagrangian approaches.
Problem
Research questions and friction points this paper is trying to address.
Develops grid-free fluid solver using Gaussian representation
Enhances accuracy and efficiency in fluid dynamics simulation
Preserves fine-scale structures and vortices with high fidelity
Innovation
Methods, ideas, or system contributions that make the work stand out.
Grid-free solver with Gaussian spatial representation
Continuously differentiable Gaussian-based velocity modeling
First-order optimization for fluid dynamics PDEs
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