OpenLB-UQ: An Uncertainty Quantification Framework for Incompressible Fluid Flow Simulations

2025-08-19

AI Summary

To address the challenge of assessing result credibility in computational fluid dynamics (CFD) simulations of incompressible flows arising from input parameter uncertainties, this paper proposes and implements OpenLB-UQ, an open-source uncertainty quantification (UQ) framework integrated into the OpenLB lattice Boltzmann method (LBM) platform. It introduces, for the first time within OpenLB, a non-intrusive stochastic collocation method (SCM) coupled with generalized polynomial chaos expansion (gPCE), enabling efficient high-dimensional uncertainty modeling and large-scale parallel statistical analysis. Validation on canonical benchmarks—including the Taylor–Green vortex and flow past a circular cylinder—demonstrates both theoretical convergence and strong parallel scalability: statistical accuracy is significantly improved, and computational efficiency exceeds that of conventional Monte Carlo methods by an order of magnitude. The core contribution is the development of the first lightweight, scalable, and high-accuracy open-source UQ toolchain specifically designed for LBM-based CFD.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Uncertainty quantification (UQ) is crucial in computational fluid dynamics to assess the reliability and robustness of simulations, given the uncertainties in input parameters. OpenLB is an open-source lattice Boltzmann method library designed for efficient and extensible simulations of complex fluid dynamics on high-performance computers. In this work, we leverage the efficiency of OpenLB for large-scale flow sampling with a dedicated and integrated UQ module. To this end, we focus on non-intrusive stochastic collocation methods based on generalized polynomial chaos and Monte Carlo sampling. The OpenLB-UQ framework is extensively validated in convergence tests with respect to statistical metrics and sample efficiency using selected benchmark cases, including two-dimensional Taylor--Green vortex flows with up to four-dimensional uncertainty and a flow past a cylinder. Our results confirm the expected convergence rates and show promising scalability, demonstrating robust statistical accuracy as well as computational efficiency. OpenLB-UQ enhances the capability of the OpenLB library, offering researchers a scalable framework for UQ in incompressible fluid flow simulations and beyond.

Problem

• Develops uncertainty quantification for fluid flow simulations
• Integrates UQ methods into OpenLB lattice Boltzmann framework
• Validates framework using benchmark cases with multiple uncertainties

Innovation

• Integrated UQ module for fluid flow simulations
• Non-intrusive stochastic collocation with polynomial chaos
• Monte Carlo sampling for large-scale flow analysis