Upwind schemes for the Euler and Navier-Stokes equations may be broadly classified into two distinct classes: those based directly on the macroscopic Navier-Stokes equations and those based indirectly on the Navier-Stokes equations via the Boltzmann equation. The former, conventional approach represents the majority of current research. However, recently gas-kinetic methods have gained attentio...

Starting from the BGK model of the Boltzmann equation, we develop a robust and accurate finite volume gas kinetic scheme on unstructured triangular meshes. The proposed numerical approach is composed of two steps—an initial reconstruction step and a gas evolution step. In the initial reconstruction step, an unstructured version of the local extremum diminishing interpolation is applied to the c...

Landau damping and Bernstein-Greene-Kruskal BGK modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase mixing of ...

We establish forward and backward relations between entropy satisfying BGK relaxation models such as those introduced previously by the author and the rst order ux vector splitting numerical methods for general systems of conservation laws. Classically, to a kinetic BGK model that is compatible with some family of entropies we can associate an entropy ux vector splitting. We prove that the conv...

In this paper, a 3D double-population thermal lattice Boltzmann BGK scheme is applied to solve three-dimensional, incompressible thermal fluid flow problem. The simplest lattice BGK D3Q6 model, developed based on passive-scalar approach, is proposed to represent the energy distribution function. While the D3Q19 lattice model is chosen to represent density distribution function in order to calcu...

With the aim of better understanding numerical properties lattice Boltzmann method (LBM), a general methodology is proposed to derive its hydrodynamic limits in discrete setting. It relies on Taylor expansion limit low Knudsen numbers. single asymptotic analysis, two kinds deviations with Navier-Stokes (NS) equations are explicitly evidenced: consistency errors, inherited from kinetic descripti...

The excitation of synchronized Bernstein, Greene, and Kruskal (BGK) modes in a pure electron plasma confined in Malmberg–Penning trap is studied. The modes are excited by controlling the frequency of an oscillating external potential. Initially, the drive resonates with, and phase-locks to, a group of axially bouncing electrons in the trap. These initially phase-locked electrons remain phase-lo...