Related papers: A Numerical method for coupling the BGK model and …
A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to…
Kinetic models based on the Bhatnagar-Gross-Krook (BGK) framework provide an efficient alternative to the Boltzmann equation for rarefied gas flows; however, existing formulations for gas mixtures remain limited in representing…
A new method for the computation of flows at the micrometer scale is presented. It is based on the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the…
In this article we focus on kinetic equations for gas mixtures since in applications one often has to deal with mixtures instead of a single gas. In particular we consider an approximation of the Boltzmann equation, the…
In this paper, we propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source)…
With the aim of better understanding the numerical properties of the lattice Boltzmann method (LBM), a general methodology is proposed to derive its hydrodynamic limits in the discrete setting. It relies on a Taylor expansion in the limit…
The numerical method of dynamical low-rank approximation (DLRA) has recently been applied to various kinetic equations showing a significant reduction of the computational effort. In this paper, we apply this concept to the linear…
Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision term. A class of asymptotic preserving schemes was introduced in [6] to handle this kind of problems. The…
In this paper we present a new ultra efficient numerical method for solving kinetic equations. In this preliminary work, we present the scheme in the case of the BGK relaxation operator. The scheme, being based on a splitting technique…
A novel hybrid algorithm is presented for the Boltzmann-BGK equation, in which a low-rank decomposition is applied solely in the velocity subspace, while a full-rank representation is maintained in the physical (position) space. This…
In this paper we present a novel technique for the simulation of moving boundaries and moving rigid bodies immersed in a rarefied gas using an Eulerian-Lagrangian formulation based on least square method. The rarefied gas is simulated by…
We propose a numerical approach, of the BGK kinetic type, that is able to approximate with a given, but arbitrary, order of accuracy the solution of linear and non-linear convection-diffusion type problems: scalar advection-diffusion,…
Partial differential equations (p.d.e) equipped of spatial derivatives of fractional order capture anomalous transport behaviors observed in diverse fields of Science. A number of numerical methods approximate their solutions in dimension…
The stochastic particle method based on Bhatnagar-Gross-Krook (BGK) or ellipsoidal statistical BGK (ESBGK) model approximates the pairwise collisions in the Boltzmann equation using a relaxation process. Therefore, it is more efficient to…
Simulations of the discrete Boltzmann Bhatnagar-Gross-Krook (BGK) equation are an important tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a discontinuous Galerkin finite element method (DG-FEM) for…
This paper presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of…
Bhatnagar-Gross-Krook (BGK) collision kernel is employed in the Boltzmann equation to formulate relativistic dissipative hydrodynamics. In this formulation, we find that there remains freedom of choosing a matching condition that affects…
BGK (Bhatnagar-Gross-Krook) model is a relaxation-type model of the Boltzmann equation, which is popularly used in place of the Boltzmann equation in physics and engineering. In this paper, we address the ill-posedness problem for the BGK…
We consider the neural representation to solve the Boltzmann-BGK equation, especially focusing on the application in microscopic flow problems. A new dimension reduction model of the BGK equation with the flexible auxiliary distribution…
In a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the Boltzmann type (G. Dimarco, R. Loubere, Towards an ultra efficient kinetic scheme. Part I: basics on the 689 BGK equation, J. Comp.…