Uncertainty Quantification for the BGK Model of the Boltzmann Equation Using Multilevel Variance Reduced Monte Carlo Methods

DOI10.1137/20M1331846zbMath1473.35389arXiv2004.07638OpenAlexW3162270989MaRDI QIDQ4995118

Jingwei Hu, Yu-Bo Wang, Lorenzo Pareschi

Publication date: 23 June 2021

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07638

zbMATH Keywords

kinetic equationBGK modeluncertainty quantificationmultilevel Monte Carlo methodrandom inputscontrol variate method

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Asymptotic behavior of solutions to PDEs (35B40) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Boltzmann equations (35Q20)

Related Items (4)

Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties ⋮ A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs ⋮ Stochastic Galerkin particle methods for kinetic equations of plasmas with uncertainties ⋮ Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport

Cites Work

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• Global existence to the BGK model of Boltzmann equation
• Weighted \(L^ \infty\) bounds and uniqueness for the Boltzmann BGK model
• The mathematical theory of dilute gases
• Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries
• Uncertainty quantification for kinetic equations
• Uncertainty quantification for hyperbolic and kinetic equations
• A generalized approximate control variate framework for multifidelity uncertainty quantification
• Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertainties: space-homogeneous case
• Quantifying uncertain system outputs via the multilevel Monte Carlo method. I: Central moment estimation
• Multi-scale control variate methods for uncertainty quantification in kinetic equations
• A bi-fidelity method for the multiscale Boltzmann equation with random parameters
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• Implicit-explicit schemes for BGK kinetic equations
• Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations
• Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method
• Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws
• Multilevel Monte Carlo Path Simulation
• Relaxation Schemes for Nonlinear Kinetic Equations
• Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
• Asymptotic-Preserving and Positivity-Preserving Implicit-Explicit Schemes for the Stiff BGK Equation
• Numerical methods for kinetic equations
• Multiscale Variance Reduction Methods Based on Multiple Control Variates for Kinetic Equations with Uncertainties
• Numerical Solution of Scalar Conservation Laws with Random Flux Functions
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems

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