Up to an arbitrary order of the Chapman–Enskog expansion of the kinetic Bhatnagar– Gross–Krook (BGK) equation, a corresponding analytic solution can be obtained. Based on such a compact exact solution, a new gas-kinetic scheme is constructed for the compressible Navier–Stokes equations. Instead of using a discontinuous initial condition in the gas-kinetic BGK–NS method Xu [K. Xu, A gas-kinetic ...

A gas-kinetic model with multiple translational temperature for the continuum and near continuum flow simulations is proposed. The main purpose for this work is to derive the generalized Navier-Stokes equations with multiple temperature. It is well recognized that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier-Stokes equations lose accuracy....

Understanding and predicting turbulent transport in the edge scrape-off-layer (SOL) of magnetic confinement fusion devices is crucial for developing feasible power plants. In this work, we present latest improvements to gyrokinetic turbulence code GENE-X validate extended model against experimental results TCV tokamak (“TCV-X21”). features a full-f electromagnetic specifically targeted SOL simu...

We study the design of a general, fully explicit numerical method for simulating kinetic equations with an extended BGK collision model allowing for multiple relaxation times. In that case, the problem is stiff and we show that its spectrum consists of multiple separated eigenvalue clusters. Projective integration methods are explicit integration schemes that first take a few small (inner) step...

In this paper we prove the convergence of a suitable particle system towards BGK model. More precisely, consider an interacting stochastic in which each can instantaneously thermalize locally. We show that, under scaling limit, propagation chaos does hold and that one-particle distribution function converges to solution equation.

An analytical version of the discrete-ordinates method is used here in the field of rarefied-gas dynamics to solve a version of the temperature-jump problem that is based on a linearized, variable collision frequency model of the Boltzmann equation. In addition to a complete development of the discrete-ordinates method for the application considered, the computational algorithm is implemented t...

We consider isentropic gas dynamics equations with unilateral constraint on the density and mass loss. The and pressureless pressure laws are considered. We propose an entropy weak formulation of the system that incorporates the constraint and Lagrange multiplier, for which we prove weak stability and existence of solutions. The nonzero pressure model is approximated by a kinetic BGK relaxation...

– A previously proposed thermohydrodynamic lattice BGK scheme using nonperturbative, or non-polynomial, equilibria is found to simulate continuum equations that differ from the Euler equations of gas dynamics at leading order. Shock tube simulations with this BGK scheme coincide with solutions obtained by solving these different continuum equations with conventional methods. Both sets of soluti...