Approximation of mono-dimensional hyperbolic systems: a lattice Boltzmann scheme as a relaxation method

DOI10.1016/j.jcp.2014.02.017zbMath1310.76145OpenAlexW4327842141MaRDI QIDQ398038

Benjamin Graille

Publication date: 12 August 2014

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2014.02.017

zbMATH Keywords

relaxation methodhyperbolic systemlattice Boltzmann scheme

Mathematics Subject Classification ID

Particle methods and lattice-gas methods (76M28)

Related Items (15)

Nonlinear fourth order Taylor expansion of lattice Boltzmann schemes ⋮ Finite difference formulation of any lattice Boltzmann scheme ⋮ Multiresolution-Based Mesh Adaptation and Error Control for Lattice Boltzmann Methods with Applications to Hyperbolic Conservation Laws ⋮ Parallel kinetic scheme for transport equations in complex toroidal geometry ⋮ Method of relaxed streamline upwinding for hyperbolic conservation laws ⋮ Structure-preserving discretizations for nonlinear systems of hyperbolic, involution-constrained partial differential equations on manifolds. Abstracts from the workshop held April 10--16, 2022 ⋮ Task-Based Parallelization of an Implicit Kinetic Scheme ⋮ On relaxation systems and their relation to discrete velocity Boltzmann models for scalar advection–diffusion equations ⋮ Vectorial Kinetic Relaxation Model with Central Velocity. ApplicationtoImplicitRelaxationsSchemes ⋮ Implicit time schemes for compressible fluid models based on relaxation methods ⋮ High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation ⋮ Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis ⋮ High accuracy analysis of adaptive multiresolution-based lattice Boltzmann schemes via the equivalent equations ⋮ A robust and efficient solver based on kinetic schemes for magnetohydrodynamics (MHD) equations ⋮ Palindromic Discontinuous Galerkin Method

Cites Work

• Lattice Boltzmann simulations of thermal convective flows in two dimensions
• Finite element methods for linear hyperbolic problems
• Probabilistic analysis of the upwind scheme for transport equations
• Two routes from the Boltzmann equation to compressible flow of polyatomic gases
• Equivalent partial differential equations of a lattice Boltzmann scheme
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Weakly coupled systems of quasilinear boundary value problem with applications to semilinear elliptic equations
• Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy
• A finite difference interpretation of the lattice Boltzmann method
• Momentum transfer of a Boltzmann-lattice fluid with boundaries
• The Optimal Convergence Rate of Monotone Finite Difference Methods for Hyperbolic Conservation Laws
• The relaxation schemes for systems of conservation laws in arbitrary space dimensions
• Une introduction au schéma de Boltzmann sur réseau
• BOUNDARY VALUE PROBLEMS FOR DEGENERATE SECOND ORDER ELLIPTIC EQUATIONS
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