An analysis of over-relaxation in kinetic approximation

2018/07/16 by Florence Drui, Drui, Florence, Emmanuel Franck +5
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.1807.05695

openalex publication_date 2018/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The over-relaxation approach is an alternative to the Jin-Xin relaxation method (Jin and Xin [1]) in order to apply the equilibrium source term in a more precise way (Coulette et al. [2, 3]). This is also a key ingredient of the Lattice-Boltzmann method for achieving second order accuracy (Dellar [4]). In this work we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.

Related

• Accelerated kinetic over-relaxation for dynamic energy minimization in lattice many-body problems
• Convergence of a two-relaxation-times kinetic approximation towards the solution of a scalar conservation law
• Lattice Boltzmann schemes with relative velocities
• Connecting lattice Boltzmann methods to physical reality by coarse-graining Molecular Dynamics simulations
• Weak and strong coupling limits of the Boltzmann equation in the relaxation-time approximation