FlowBench: A Large Scale Benchmark for Flow Simulation over Complex Geometries

TL;DR

FlowBench addresses the need for rigorous benchmarks of neural PDE solvers in complex-flow geometries by providing a large-scale, multiphysics dataset with 2D and 3D simulations of NS and NS-HT across diverse geometries. It combines DNS-quality velocity, pressure, and temperature fields at three resolutions with geometry masks, signed distance fields, and engineering summaries (e.g., $C_L$, $C_D$, Nu), along with a structured evaluation framework and baseline results for multiple neural operators and foundation models. The contributions include a principled dataset design, detailed metadata and formats, and a multi-metric evaluation protocol (global, boundary, properties, and residuals) to probe accuracy and physical consistency. This benchmark enables robust assessment, generalization studies, and acceleration of SciML solvers for coupled flow–thermal problems in engineering and beyond.

Abstract

Simulating fluid flow around arbitrary shapes is key to solving various engineering problems. However, simulating flow physics across complex geometries remains numerically challenging and computationally resource-intensive, particularly when using conventional PDE solvers. Machine learning methods offer attractive opportunities to create fast and adaptable PDE solvers. However, benchmark datasets to measure the performance of such methods are scarce, especially for flow physics across complex geometries. We introduce FlowBench, a dataset for neural simulators with over 10K samples, which is currently larger than any publicly available flow physics dataset. FlowBench contains flow simulation data across complex geometries (\textit{parametric vs. non-parametric}), spanning a range of flow conditions (\textit{Reynolds number and Grashoff number}), capturing a diverse array of flow phenomena (\textit{steady vs. transient; forced vs. free convection}), and for both 2D and 3D. FlowBench contains over 10K data samples, with each sample the outcome of a fully resolved, direct numerical simulation using a well-validated simulator framework designed for modeling transport phenomena in complex geometries. For each sample, we include velocity, pressure, and temperature field data at 3 different resolutions and several summary statistics features of engineering relevance (such as coefficients of lift and drag, and Nusselt numbers). %Additionally, we include masks and signed distance fields for each shape. We envision that FlowBench will enable evaluating the interplay between complex geometry, coupled flow phenomena, and data sufficiency on the performance of current, and future, neural PDE solvers. We enumerate several evaluation metrics to help rank order the performance of neural PDE solvers. We benchmark the performance of several baseline methods including FNO, CNO, WNO, and DeepONet.

Figures (14)

• Figure 1: https://baskargroup.bitbucket.io/ offers comprehensive datasets and metrics for assessing neural PDE solvers designed to model flow phenomena around complex objects. It includes three sets of application-relevant geometries with varying complexities and high-fidelity flow simulation data under different forcing conditions. The left panel in the figure above showcases 30 randomly selected shapes from each geometry group. The middle panel provides a close-up of one geometry within the computational domain, highlighting the boundary conditions. The right panel displays the simulation outputs, including velocity results for three samples.
• Figure 2: Examples of the diverse and complex geometries in https://baskargroup.bitbucket.io/ using 9 samples from each of the three groups. The first row corresponds to geometries from the nurbs group G1, the second row to the spherical harmonics group G2, and the third row to the skelneton group G3.
• Figure 3: Drag coefficients ($C_D$), and lift coefficients ($C_L$) for different shapes and different Reynolds numbers in pure-NS LDC simulations.
• Figure 4: Drag coefficients ($C_D$), lift coefficients ($C_L$), and Nusselt numbers (Nu) for different shapes and different Richardson numbers in NSHT LDC simulations (fixed Re = 100).
• Figure 5: Drag coefficients ($C_D$), lift coefficients ($C_L$), and Nusselt numbers (Nu) for different shapes and different Richardson numbers in NSHT LDC simulations (random Reynolds number).