arXiv subjects

Julien Mathiaud

Publications and source records attributed to Julien Mathiaud.

7 recordsLinked to original sources

arXiv2026

A Multispecies ESBGK Model for Gas Mixtures with Variable Hard Sphere Transport: Theory and Verification

A multi-species Bhatnagar-Gross-Krook (BGK) model for gas mixtures is presented that achieves the correct species-wise relaxation of velocities, temperatures, and pressure tensors according to the Boltzmann collision integral, as well as the correct mixture Prandtl number, while retaining a single relaxation term per species. The model extends the ellipsoidal statistical BGK (ESBGK) model by introducing relative relaxation targets for each species, derived from the Variable Hard Sphere (VHS) production rates of the Grad 13 approximation. Three approaches for the species relaxation frequency are proposed and analyzed: a Grad 13-based per-species frequency, a mixture-averaged frequency, and an empirical harmonic mean of the two. The model is implemented in the particle-based code PICLas and verified against Direct Simulation Monte Carlo (DSMC) results for a range of test cases, including 0D reservoir relaxation, mass diffusion, supersonic Couette flow, and hypersonic flow around a 70{\deg} blunted cone for binary and ternary gas mixtures. Across all test cases, the proposed model reproduces the correct Prandtl number, species temperature, velocity relaxation rates and pressure tensor relaxation, with the empirical relaxation frequency consistently yielding the best agreement with DSMC.

physics.flu-dyn↗

arXiv2025

Generalized UGK scheme in the diffusive

The unified gas kinetic scheme (UGKS) was initially designed to address multiscale challenges in rarefied gas dynamics and then extended to radiative transfert theory, as described by BGK like relaxation models. In this work, we extend its application to linear kinetic models with non isotropic scattering collision operators, as well as Fokker-Planck models . These problems typically exhibit a fully diffusive nature in the optically thick limit (corresponding to a small Knudsen number). It still leads to an asymptotic preserving (AP) property not only in this diffusive regime but also in the free transport limit. A series of numerical experiments confirm the effectiveness of the approach.

math.NA↗

arXiv2025

A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes

In this article, we extend the Boltzmann framework for polyatomic gases by introducing quasi-resonant kernels, which relax resonant interactions, for which kinetic and internal energies are separately conserved and lead to equilibrium states with two temperatures. We establish an H-theorem and analyze the quasi-resonant model's asymptotic behaviour, demonstrating a two-phase relaxation process: an initial convergence towards a two-temperature Maxwellian state followed by gradual relaxation of the two temperatures towards each other. Numerical simulations validate our theoretical predictions. The notion of quasi-resonance provides the first rigorous framework of a Boltzmann dynamics for which the distribution is at all times close to a multi-temperature Maxwellian, relaxing towards a one-temperature Maxwellian.

math.AP↗

arXiv2025

An asymptotic preserving scheme for the M1model of non-local thermal transport for two-dimensional structured and unstructured meshes

The M1 moment model for electronic transport is commonly used to describe non-local thermal transport effects in laser-plasma simulations. In this article, we propose a new asymptotic-preserving scheme based on the Unified Gas Kinetic Scheme (UGKS) for this model in two-dimensional space. This finite volume kinetic scheme follows the same approach as in our previous article and relies on a moment closure, at the numerical scale, of the microscopic flux of UGKS. The method is developed for both structured and unstructured meshes, and several techniques are introduced to ensure accurate fluxes in the diffusion limit. A second-order extension is also proposed. Several test cases validate the different aspects of the scheme and demonstrate its efficiency in multiscale simulations. In particular, the results demonstrate that this method accurately captures non-local thermal effects.

math.NA↗

arXiv2022

An ES-BGK model for diatomic gases with correct relaxation rates for internal energies

We propose a new ES-BGK model for diatomic gases which allows for translational-rotational and translational-vibrational energy exchanges, as given by Landau-Teller and Jeans relaxation equations. This model is consistent with the general definition of the vibrational and rotational collision numbers that are also commonly used in DSMC solvers. It is proved to satisfy the H-theorem and to give the correct transport coefficients, up to the volume viscosity.

physics.flu-dyn↗

arXiv2020

Numerical boundary conditions in Finite Volume and Discontinuous Galerkin schemes for the simulation of rarefied flows along solid boundaries

We present a numerical comparison between two standard finite volume schemes and a discontinuous Galerkin method applied to the BGK equation of rarefied gas dynamics. We pay a particular attention to the numerical boundary conditions in order to preserve the rate of convergence of the method. Most of our analysis relies on a 1D problem (Couette flow), but we also present some results for a 2D aerodynamical flow.

math.NA↗

arXiv2018

A BGK model for high temperature rarefied gas flows

High temperature gases, for instance in hypersonic reentry flows, show complex phenomena like excitation of rotational and vibrational energy modes, and even chemical reactions. For flows in the continuous regime, simulation codes use analytic or tabulated constitutive laws for pressure and temperature. In this paper, we propose a BGK model which is consistent with any arbitrary constitutive laws, and which is designed to make high temperature gas flow simulations in the rarefied regime. A Chapman-Enskog analysis gives the corresponding transport coefficients. Our approach is illustrated by a numerical comparison with a compressible Navier-Stokes solver with rotational and vibrational non equilibrium. The BGK approach gives a deterministic solver with a computational cost which is close to that of a simple monoatomic gas.

physics.comp-ph↗