Related papers: Crank-Nicolson BGK Integrator for Multi-Scale Part…
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 generalization of the lattice Bhatnagar-Gross-Krook (LBGK) model for the simulation of hydrodynamics is presented, which takes into account the difference and the frame-independence of the relaxation of non-hydrodynamic modes. The present…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
In this paper, we are concerned with the local-in-time well-posedness of a fluid-kinetic model in which the BGK model with density dependent collision frequency is coupled with the inhomogeneous Navier-Stokes equation through drag forces.…
The multi-scale flow mechanism is crucial for force and heat loaded on near-space and reentry vehicles, the control of spacecraft by thrusters, the propelling and cooling of MEMS, etc. Since the continuum flow and rarefied flow often exist…
Ideal gases can be modeled by the Boltzmann equation from statistical physics. Instead of trying to track the position and velocity of a large number of gas molecules, it is possible to describe the particles with a particle distribution…
Bhatnagar-Gross-Krook (BGK) equation is a relaxation model of the Boltzmann equation which is widely used in place of the Boltzmann equation for the simulation of various kinetic flow problems. In this work, we study the asymptotic…
The Boltzmann equation describes the detailed microscopic behaviour of a dilute gas, and represents the basis of the kinetic theory of gases. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a…
This paper extends the second-order accurate BGK finite volume schemes for the ultra-relativistic flow simulations [5] to the 1D and 2D special relativistic hydrodynamics with the Synge equation of state. It is shown that such 2D schemes…
It has recently been demonstrated that dynamical low-rank algorithms can provide robust and efficient approximation to a range of kinetic equations. This is true especially if the solution is close to some asymptotic limit where it is known…
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…
This article extends a recently introduced kinetic closure of turbulence by developing its theoretical framework, operational realizations, and validation. In contrast with filtered Navier--Stokes formulations, filtering the Boltzmann…
The implementation of the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) method in the open-source particle code PICLas is extended for multi-species modeling of polyatomic molecules, including internal energies with multiple…
Gaseous thermal transpiration flows through a rectangular micro-channel are simulated by the direct simulation BGK (DSBGK) method. These flows are rarefied, within the slip and transitional flow regimes, which are beyond many traditional…
We apply the collision-based hybrid introduced in \cite{hauck} to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator.…
Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches…
Multi-species modeling is implemented for the particle-based ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) for monatomic species in the open-source plasma simulation suite PICLas. After a literature review on available multi-species…
This work explores the feasibility of performing three-dimensional molecular gas dynamics simulations of hypersonic flows such as re-entry vehicles through directly solving the six-dimensional nonlinear Boltzmann equation closed with the…
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,…
Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study…