43 / 2025-04-17 15:51:32

Non-Intrusive and Intrusive Uncertainty Quantification for Lattice Boltzmann Method

lattice Boltzmann method,uncertainty quantification,generalized polynomial chaos

Efficiently accounting for uncertainties in computational fluid dynamics (CFD) models remains a crucial challenge. For computing statistical solutions of partial differential equations in fluid flow models, combining scalable deterministic solvers based on lattice Boltzmann methods (LBMs), such as OpenLB, with uncertainty quantification (UQ) techniques is highly beneficial. In this talk, we present a comprehensive introduction to both intrusive and non-intrusive UQ methods. Specifically, we highlight our robust and flexible non-intrusive implementations of Monte Carlo (MC) and stochastic collocation (SC) methods within OpenLB, as well as our prior work on the intrusive stochastic Galerkin lattice Boltzmann method (SGLBM). Non-intrusive methods facilitate efficient implementations without altering the deterministic solver, promoting ease of use and broad applicability. Intrusive methods, such as SGLBM, integrate uncertainty directly into the solver structure, often offering enhanced computational efficiency. We demonstrate and compare these approaches through simulations of the Taylor–Green vortex flow problem. Numerical results indicate that the stochastic collocation method achieves accuracy comparable to Monte Carlo simulations but at substantially reduced computational cost, while the SGLBM serves as a complementary efficient alternative. Finally, we discuss the application of MC and SC LBMs in urban wind flow simulations with OpenLB. Thus, our comprehensive UQ framework effectively balances accuracy and computational efficiency, offering a powerful and versatile platform for uncertainty quantification in lattice Boltzmann-based CFD simulations.