arXiv subjects

Luc Mieussens

Publications and source records attributed to Luc Mieussens.

17 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° 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

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

An ES-BGK model for vibrational polyatomic gases

We propose an extension of the Ellipsoidal-Statistical BGK model to account for discrete levels of vibrational energy in a rarefied polyatomic gas. This model satisfies an H-theorem and contains parameters that allow to fit almost arbitrary values for the Prandtl number and the relaxation times of rotational and vibrational energies. With the reduced distribution technique , this model can be reduced to a three distribution system that could be used to simulate polyatomic gases with rotational and vibrational energy for a computational cost close to that of a simple monoatomic gas.

cond-mat.stat-mech↗

arXiv2020

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↗

arXiv2020

BGK and Fokker-Planck models of the Boltzmann equation for gases with discrete levels of vibrational energy

We propose two models of the Boltzmann equation (BGK and Fokker-Planck models) for rarefied flows of diatomic gases in vibrational non-equilibrium. These models take into account the discrete repartition of vibration energy modes, which is required for high temperature flows, like for atmospheric re-entry problems. We prove that these models satisfy conservation and entropy properties (H-theorem), and we derive their corresponding compressible Navier-Stokes asymptotics.

physics.class-ph↗

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↗

arXiv2020

An Eulerian model for sea spray transport and evaporation

Reliable estimates of the fluxes of momentum, heat, and moisture at the air-sea interface are essential for accurate long term climate projections, as well as the prediction of short term weather events such as tropical cyclones. In recent years, it has been suggested that these estimates need to incorporate an accurate description of the transport of sea spray within the atmospheric boundary layer and the drop-induced fluxes of moisture, momentum, and heat, so that the resulting effects on the atmospheric flow can be evaluated. In this paper we propose a model based on a theoretical and mathematical framework inspired from kinetic gas theory. This approach reconciles the Lagrangian nature of the spray transport with the Eulerian description of the atmosphere. In turn, this enables a relatively straightforward inclusion of the spray fluxes and the resulting spray effects on the atmospheric flow. A comprehensive dimensional analysis has led us to identify the spray effects that are most likely to influence the temperature, moisture, and speed of the airflow. We also provide an example application to illustrate the capabilities of the model in specific environmental conditions. Finally, suggestions for future work are offered.

physics.flu-dyn↗

arXiv2020

BGK and Fokker Planck Models for thermally perfect gases

We propose two models of the Boltzmann equation (BGK and Fokker-Planck models) for rarefied flows of thermally perfect gases. These models take into account various models of energy, which are required for high temperature flows, like for atmospheric re-entry problems. We prove that these models satisfy conservation and entropy properties (H-theorem), and we derive their corresponding compressible Navier-Stokes asymptotics.

math-ph↗

arXiv2015

A Cartesian Cut Cell Method for Rarefied Flow Simulations around Moving Obstacles

For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian cells and various kind of cut cells by the same algorithm, with no need to identify the specific shape of each cut cell. This makes the implementation quite simple, and allows a direct extension to 3D problems. Such simulations are also made possible by using an adaptive mesh refinement technique and a hybrid parallel implementation. This is illustrated by several test cases, including a 3D unsteady simulation of the Crookes radiometer.

math.NA↗

arXiv2014

Local discrete velocity grids for deterministic rarefied flow simulations

Most of numerical methods for deterministic simulations of rarefied gas flows use the discrete velocity (or discrete ordinate) approximation. In this approach, the kinetic equation is approximated with a global velocity grid. The grid must be large and fine enough to capture all the distribution functions, which is very expensive for high speed flows (like in hypersonic aerodynamics). In this article, we propose to use instead different velocity grids that are local in time and space: these grids dynamically adapt to the width of the distribution functions. The advantages and drawbacks of the method are illustrated in several 1D test cases.

math.NA↗

arXiv2013

Locally refined discrete velocity grids for stationary rarefied flow simulations

Most of deterministic solvers for rarefied gas dynamics use discrete velocity (or discrete ordinate) approximations of the distribution function on a Cartesian grid. This grid must be sufficiently large and fine to describe the distribution functions at every space position in the computational domain. For 3-dimensional hypersonic flows, like in re-entry problems, this induces much too dense velocity grids that cannot be practically used, for memory storage requirements. In this article, we present an approach to generate automatically a locally refined velocity grid adapted to a given simulation. This grid contains much less points than a standard Cartesian grid and allows us to make realistic 3-dimensional simulations at a reduced cost, with a comparable accuracy.

math.NA↗

arXiv2013

Gas-surface interaction and boundary conditions for the Boltzmann equation

In this paper we revisit the derivation of boundary conditions for the Boltzmann Equation. The interaction between the wall atoms and the gas molecules within a thin surface layer is described by a kinetic equation introduced in [9] and used in [1]. This equation includes a Vlasov term and a linear molecule-phonon collision term and is coupled with the Boltzmann equation describing the evolution of the gas in the bulk flow. Boundary conditions are formally derived from this model by using classical tools of kinetic theory such as scaling and systematic asymptotic expansion. In a first step this method is applied to the simplified case of a flat wall. Then it is extented to walls with nanoscale roughness allowing to obtain more complex scattering patterns related to the morphology of the wall. It is proved that the obtained scattering kernels satisfy the classical imposed properties of non-negativeness, normalization and reciprocity introduced by Cercignani [11].

math.AP↗

arXiv2013

On the Asymptotic Preserving property of the Unified Gas Kinetic Scheme for the diffusion limit of linear kinetic models

The unified gas kinetic scheme (UGKS) of K. Xu et al. [K. Xu and J.-C. Huang, J. Comput. Phys., 229, pp. 7747--7764, 2010], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free transport regime as well. Moreover, this scheme is modified to include a time implicit discretization of the limit diffusion equation, and to correctly capture the solution in case of boundary layers. Contrary to many AP schemes, this method is based on a standard finite volume approach, it does neither use any decomposition of the solution, nor staggered grids. Several numerical tests demonstrate the properties of the scheme.

math.NA↗

arXiv2009

Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31, pp. 334-368, 2008] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths, and is close to a convection CFL condition for large mean free paths. Ou r analysis is based on very simple energy estimates.

math.NA↗

arXiv2009

A Multiscale Kinetic-Fluid Solver with Dynamic Localization of Kinetic Effects

This paper collects the efforts done in our previous works [P. Degond, S. Jin, L. Mieussens, A Smooth Transition Between Kinetic and Hydrodynamic Equations, J. Comp. Phys., 209 (2005) 665--694.],[P.Degond, G. Dimarco, L. Mieussens, A Moving Interface Method for Dynamic Kinetic-fluid Coupling, J. Comp. Phys., Vol. 227, pp. 1176-1208, (2007).],[P. Degond, J.G. Liu, L. Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi. Model. Sim. 5(3), 940--979 (2006)] to build a robust multiscale kinetic-fluid solver. Our scope is to efficiently solve fluid dynamic problems which present non equilibrium localized regions that can move, merge, appear or disappear in time. The main ingredients of the present work are the followings ones: a fluid model is solved in the whole domain together with a localized kinetic upscaling term that corrects the fluid model wherever it is necessary; this multiscale description of the flow is obtained by using a micro-macro decomposition of the distribution function [P. Degond, J.G. Liu, L. Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi. Model. Sim. 5(3), 940--979 (2006)]; the dynamic transition between fluid and kinetic descriptions is obtained by using a time and space dependent transition function; to efficiently define the breakdown conditions of fluid models we propose a new criterion based on the distribution function itself. Several numerical examples are presented to validate the method and measure its computational efficiency.

math-ph↗