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Author: Christopher Flint
Requested Type: Poster
Submitted: 2016-02-15 13:47:07

Co-authors: G. Vahala, L. Vahala, M. Soe

Contact Info:
College of William & Mary
Department of Physics
Williamsburg, VA   23185

Abstract Text:
While the Kelvin-Helmholtz instability can be stabilized by a uniform magnetic field aligned to the velocity shear, here we examine the interplay between the tearing and Kelvin-Helmholtz instabilities using lattice Boltzmann (LB). The initial profiles have both magnetic and velocity shear with the corresponding profiles being anti-parallel. While the LB algorithm yields an exceptionally well parallelized code, its stability puts limitations on MHD parameters. However Karlin et. al. have introduced an entropic lattice Boltzmann scheme for Navier-Stokes turbulence in which the relaxation distribution function and collision operator obeys an entropic H-theorem. While this permits turbulence simulations to be performed at arbitrary Reynolds numbers (subject to grid resolution), the determination of the entropy stabilizer parameter is numerically expensive. In particular, it must be determined (numerically) at each grid point at every time step, from a Newton-Raphson iterative procedure. For 3D simulations this becomes quite prohibitive. However, recently, the Karlin group has introduced an analytic approximation for this parameter that guarantees positive definiteness of the distribution function for Navier-Stokes turbulence. Here we extend these results to 2D MHD turbulence. A 9-bit model is proposed for both the velocity and magnetic distribution functions. By identifying the zeroth moment of the vector magnetic distributions to be the magnetic field, div B is still identically zero. The analytical entropy stabilizer is applied only to the scalar (velocity) distribution function. The sub- and super-Alfvenic regimes are examined.