Simulating Incompressible Fluid Flows with Uncertainty Using Lattice Boltzmann Methods

Uncertainty quantification (UQ) has become a critical component in computational fluid dynamics (CFD), particularly for assessing the reliability of simulation results in the presence of uncertain parameters such as inlet velocity, viscosity, or boundary conditions. The lattice Boltzmann method (LBM), a mesoscopic CFD technique known for its parallel scalability and flexibility with complex geometries, provides a promising platform for integrating UQ. However, systematic UQ capabilities remain underdeveloped in current LBM-based frameworks.

This dissertation develops a unified UQ framework for incompressible LBM simulations, combining both non-intrusive and intrusive approaches. The non-intrusive strategy is implemented by extending the open-source OpenLB library with a modular UQ module that supports Monte Carlo sampling, quasi-Monte Carlo methods, and stochastic collocation (SC) based on generalized polynomial chaos (gPC). The OpenLB-UQ module automates sampling, parallel execution, and statistical post-processing, enabling scalable UQ workflows. Validation on canonical benchmarks—such as the Taylor–Green vortex and flow past a cylinder—demonstrates accurate moment estimation and parallel performance gains.
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In parallel, the first fully coupled stochastic Galerkin (SG) LBM is proposed, which reformulates the LBM equations using polynomial chaos expansions.
The proposed intrusive SG LBM directly evolves the coefficients of the discrete-velocity distribution functions obtained via polynomial chaos expansion. Its algorithmic structure fully preserves the LBM streaming and collision processes, ensuring structural consistency with standard LBM frameworks.
The SG LBM achieves spectral convergence and reduces computational cost by a factor of five to six compared to Monte Carlo methods in representative cases.

To demonstrate real-world applicability, we applied an uncertain data assimilation workflow based on OpenLB-UQ to an urban wind simulation around an isolated building in Reutlingen (Germany).
Measurement uncertainty was directly injected into the inflow boundary data and propagated through a non-intrusive SC LBM pipeline, yielding spatio-temporal statistics of the velocity field across the domain.
The workflow enabled the computation of mean and standard deviation fields, the identification of flow-sensitive zones such as wakes and shear layers, and the derivation of confidence intervals at monitoring probes. This provided interpretable uncertainty maps that respect the statistical nature of measurement-driven inflow and highlighted their relevance for urban planning and wind engineering applications.

Together, these contributions provide a scalable and comprehensive, open-source UQ toolkit for LBM-based CFD. Conclusively, this work advances efficient uncertainty-aware simulations of incompressible flows across scientific and engineering domains.