Related papers: A Numerical method for coupling the BGK model and …
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two and three dimensions. In the spatial discretization, we use piecewise polynomials of degrees $ k \ (k…
We study a two phase flow with interactions of liquid and rarefied gas inside the gas phase. The gas phase is modeled by the BGK model of the Boltzmann equation. The liquid phase is modeled by the incompressible Navier-Stokes equations. In…
We study the stability and sensitivity of an absorbing layer for the Boltzmann equation by examining the Bhatnagar-Gross-Krook (BGK) approximation and using the perfectly matched layer (PML) technique. To ensure stability, we discard some…
We introduce a hyperbolic closure for the Grad moment expansion of the Bhatnagar-Gross-Krook's (BGK) kinetic model using a neural network (NN) trained on BGK's moment data. This closure is motivated by the exact closure for the free…
Numerical simulations of turbulent flows are well known to pose extreme computational challenges due to the huge number of dynamical degrees of freedom required to correctly describe the complex multi-scale statistical correlations of the…
Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…
We give an explicit description of the spectral closure for the three-dimensional linear Boltzmann-BGK equation in terms of the macroscopic fields, density, flow velocity and temperature. This results in a new linear fluid dynamics model…
Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be…
We apply the projection operator formalism to the problem of determining the asymptotic behavior of the lattice BGK equation in the hydrodynamic limit. As an alternative to the more usual Chapman-Enskog expansion, this approach offers many…
In this work, a novel synthetic iteration scheme (SIS) is developed for the LBE to find solutions to Kramer's problem accurately and efficiently: the velocity distribution function is first solved by the conventional iterative scheme, then…
We present a new method in order to get variable slip coefficient in binary lattice Boltzmann models to simulate gaseous flows. Boundary layer theory is presented. We study both the single- and multi-fluid BGK-type models as well. The…
To simulate non-equilibrium compressible flows, a new discrete Boltzmann model, discrete Ellipsoidal Statistical(ES)-BGK model, is proposed. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number.…
Wave disturbances of a stratified gas are studied. The description is built on a basis of the Bhatnagar -- Gross -- Krook (BGK) kinetic equation which is reduced down the level of fluid mechanics. The double momenta set is introduced inside…
In this paper we have applied a Semi-Lagrangian schemes with meshfree interpolation, based on a Moving Least Squares (MLS) method, to solve the BGK model for rarefied gas dynamics. Sod's shock tube problems are presented for a large range…
The classical problem of steady rarefied gas flow past an infinitely thin circular disk is revisited, with particular emphasis on the gas behavior near the disk edge. The uniform flow is assumed to be perpendicular to the disk surface. An…
We prove the existence of non-hydrodynamic solutions to the linear density-dependent BGK equation in $d$ dimensions. Specifically, we show the existence of an initial condition for any Knudsen number $\tau$ for which the dissipation rate of…
We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…
For the one-dimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and…
We propose a new randomized method for solving systems of nonlinear equations, which can find sparse solutions or solutions under certain simple constraints. The scheme only takes gradients of component functions and uses Bregman…