An Efficient Dynamical Low-Rank Algorithm for the Boltzmann-BGK Equation Close to the Compressible Viscous Flow Regime

DOI10.1137/21M1392772zbMath1486.35322arXiv2101.07104OpenAlexW3199064861MaRDI QIDQ3382797

Lexing Ying, Jingwei Hu, Lukas Einkemmer

Publication date: 22 September 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.07104

zbMATH Keywords

convolutionChapman-Enskog expansioncompressible Navier-Stokes equationsFourier spectral methodsdynamical low-rank integratorBoltzmann-BGK mode

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Numerical methods for stiff equations (65L04) Boltzmann equations (35Q20) Compressible Navier-Stokes equations (76N06)

Related Items (12)

On the Stability of Robust Dynamical Low-Rank Approximations for Hyperbolic Problems ⋮ A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps ⋮ An adaptive dynamical low rank method for the nonlinear Boltzmann equation ⋮ A robust collision source method for rank adaptive dynamical low-rank approximation in radiation therapy ⋮ Efficient 6D Vlasov simulation using the dynamical low-rank framework \texttt{Ensign} ⋮ A dynamical low-rank approach to solve the chemical master equation for biological reaction networks ⋮ A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations ⋮ Accelerating the simulation of kinetic shear Alfvén waves with a dynamical low-rank approximation ⋮ Accelerated Simulation of Boltzmann-BGK Equations near the Diffusive Limit with Asymptotic-Preserving Multilevel Monte Carlo ⋮ A low-rank power iteration scheme for neutron transport criticality problems ⋮ Efficient dynamical low-rank approximation for the Vlasov-Ampère-Fokker-Planck system ⋮ A rank-adaptive robust integrator for dynamical low-rank approximation

Cites Work

• Unnamed Item
• A conservative discontinuous Galerkin scheme for the 2D incompressible Navier-Stokes equations
• On the approximation of high-dimensional differential equations in the hierarchical Tucker format
• Macroscopic transport equations for rarefied gas flows. Approximation methods in kinetic theory.
• Non-oscillatory central differencing for hyperbolic conservation laws
• From quantum to classical molecular dynamics: Reduced models and numerical analysis.
• The Boltzmann equation and its applications
• A high-order discontinuous Galerkin method for 2D incompressible flows
• A hybrid kinetic--fluid model for solving the Vlasov--BGK equation
• A second-order projection method for the incompressible Navier-Stokes equations
• A low-rank method for two-dimensional time-dependent radiation transport calculations
• An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation
• A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction
• A projector-splitting integrator for dynamical low-rank approximation
• Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values
• Sparse Grids for the Vlasov–Poisson Equation
• Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors
• Asymptotic-Preserving Schemes for Multiscale Hyperbolic and Kinetic Equations
• Dynamical Tensor Approximation
• Time Integration in the Multiconfiguration Time-Dependent Hartree Method of Molecular Quantum Dynamics
• An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics
• Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
• Numerical methods for kinetic equations
• A Low-Rank Projector-Splitting Integrator for the Vlasov--Poisson Equation
• Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit
• A Low-Rank Algorithm for Weakly Compressible Flow
• A Quasi-Conservative Dynamical Low-Rank Algorithm for the Vlasov Equation
• A Hierarchy of Hybrid Numerical Methods for Multiscale Kinetic Equations
• Dynamical Low‐Rank Approximation
• A Semi-Lagrangian Vlasov Solver in Tensor Train Format
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
• The Gaussian-BGK model of Boltzmann equation with small Prandtl number

This page was built for publication: An Efficient Dynamical Low-Rank Algorithm for the Boltzmann-BGK Equation Close to the Compressible Viscous Flow Regime