Christopher Flint

Magnetic field stabilization of a two-dimensional fluid jet: a multiple relaxation Lattice Boltzmann simulation

The stabilization of a two-dimensional fluid jet from the Kelvin–Helmholtz (KH) instability by an external parallel magnetic field is examined by lattice Boltzmann techniques. For sufficiently strong magnetic fields, the jet does not break up into large-scale vortices but retains the major features of the jet, albeit somewhat expanded. There are time-dependent striations within the expanded jet.

A 9-bit multiple relaxation Lattice Boltzmann magnetohydrodynamic algorithm for 2D turbulence

While a minimalist representation of 2D Magnetohydrodynamics (MHD) on a square lattice is a 9-bit scalar and 5-bit vector distribution functions, here we examine the effect of using the 9-bit vector distribution function on the effect of a magnetic field on the Kelvin-Helmholtz instability. While there is little difference in the simulation results between the 5-bit and the 9-bit vector distribution models in the vorticity, energy spectra, etc., the 9-bit model permits simulations with mean magnetic field a factor of approximately 2 greater than those attainable in the standard 5-bit model. Indeed a 9-bit single-relaxation model can attain such success over a 5-bit multiple-relaxation model at the same computational expense.

Lattice Boltzmann large eddy simulation model of MHD

ABSTRACT The work of Ansumali et al. [Phys. A: Stat. Mech. Appl. 2004, 338(3), 379–394] is extended to two-dimensional magnetohydrodynamic (MHD) turbulence in which energy is cascaded to small spatial scales and thus requires subgrid modeling. Applying large eddy simulation (LES) modeling of the macroscopic fluid equations results in the need to apply ad hoc closure schemes. LES is applied to a suitable mesoscopic lattice Boltzmann representation from which one can recover the MHD equations in the long-wavelength, long-time scale Chapman–Enskog limit (i.e. the Knudsen limit). Thus on first performing filter width expansions on the lattice Boltzmann equations followed by the standard small Knudsen expansion on the filtered lattice Boltzmann system results in a closed set of MHD turbulence equations provided we enforce the physical constraint that the subgrid effects first enter the dynamics at the transport time scales. In particular, a multi-time relaxation collision operator is considered for the density distribution function and a single-relaxation collision operator for the vector magnetic distribution function. The LES does not destroy the property that automatically without the need for divergence cleaning.

A partial entropic lattice Boltzmann MHD simulation of the Orszag–Tang vortex

ABSTRACT Karlin has introduced an analytically determined entropic lattice Boltzmann (LB) algorithm for Navier-Stokes turbulence. Here, this is partially extended to an LB model of magnetohydrodynamics, on using the vector distribution function approach of Dellar for the magnetic field (which is permitted to have field reversal). The partial entropic algorithm is benchmarked successfully against standard simulations of the Orszag–Tang vortex [Orszag, S.A.; Tang, C.M. J. Fluid Mech. 1979, 90 (1), 129–143].

A large eddy lattice Boltzmann simulation of magnetohydrodynamic turbulence

Abstract Large eddy simulations (LES) of a lattice Boltzmann magnetohydrodynamic (LB-MHD) model are performed for the unstable magnetized Kelvin–Helmholtz jet instability. This algorithm is an extension of Ansumali et al. [1] to MHD in which one performs first an expansion in the filter width on the kinetic equations followed by the usual low Knudsen number expansion. These two perturbation operations do not commute. Closure is achieved by invoking the physical constraint that subgrid effects occur at transport time scales. The simulations are in very good agreement with direct numerical simulations.

Lattice algorithms for nonlinear physics

Simple LB suffers fromnumerical instabilities when the collisional relaxation rate is reduced to model high Reynolds number turbulence (1). Various groups (2, 3) then introduced systematic entropic representationswhich satisfiedadiscreteH-theoremand thus led to stable numerical algorithms for Navier-Stokes (NS) turbulence. However, twomajor drawbacksbecame clear (4): (1) a Newton–Raphson iterative solver must be applied at every lattice node and at every time step in order to determine the entropy function isosurface; and (2) the entropic stabilizing factor directly effects the transport coefficient, leading to a time–space varying eddy transport coefficient. Recently, the Karlin group (3, 5) has developed an analytic entropy algorithm that leaves the viscosity ν invariant. It is based on a multiple relaxation LB model and the splitting of the distribution function fi into a moment-conserving ki set, a shear/stress si set and the remaining higher order set of moments hi. (There is a 1-1 onto map between the number of velocities and the number of moments). Thus the standard LB algorithm

Imaginary time integration method using a quantum lattice gas approach

By modifying the collision operator in the quantum lattice gas (QLG) algorithm one can develop an imaginary time (IT) integration to determine the ground state solutions of the Schrödinger equation and its variants. These solutions are compared to those found by other methods (in particular the backward-Euler finite-difference scheme and the quantum lattice Boltzmann). In particular, the ground state of the quantum harmonic oscillator is considered as well as bright solitons in the one-dimensional (1D) non-linear Schrödinger equation. The dark solitons in an external potential are then determined. An advantage of the QLG IT algorithm is the avoidance of any real/complex matrix inversion and that its extension to arbitrary dimensions is straightforward.