Sub-grid Scale Terms in Plasma TurbulenceDirect Numerical Simulations of Drift-Kinetic Turbulence in 4D

Ravi Samtaney

PSE and MCSE Divisions, KAUST

Motivation & Approach

• Goal: Develop “sub-grid-scale” models for kinetic and gyro-kinetic plasma turbulence simulations

• To compute edge turbulence at a coarse-grain resolution without sacrificing physics accuracy

• Fully resolved simulations are prohibitively expensive

Motivated by• Hydrodynamic turbulence simulations frequently employ “large eddy simulation (LES)” methodology to capture “sub-grid-scale (SGS)” physics

Science Question: In kinetic plasma turbulence, what are the mechanisms of energy cascade from large to small scales?

Approach: • Investigate numerical aspects of plasma turbulence simulations in the context of drift-kinetic turbulence in 4D (present work) and 5D and 6D (future work)•Developed an Eulerian drift-kinetic code

Investigate a variety of numerical algorithms

•Perform “Direct Numerical Simulations”, i.e., fully-resolved simulations

Role of collisions (models) and regularization of the equations

•Quantify the sub-grid scale terms to aid in development of SGS models

Main Contribution and Key Results

Contribution: Developed a high-order energy and mass conserving code to investigate ion-temperature gradient drift kinetic turbulence in a cylindrical geometry. Key Results: (1) A priori results of DNS of 4D kinetic turbulence indicates a substantial contribution is in the sub-grid-terms. (2) Without collision physics, the equations may be ill-posed

Reference: Samtaney, to be submitted to Computational Science & Discovery, 2011

Figure: Time sequence of distribution function on three orthogonal planes in cylindrical geometry at constant velocity. Mesh resolution: 256x256x32x256. The distribution function exhibits small scale features at late times. Simulation on IBM Blue-Gene P Shaheen on 512 processors

Figure:Weak scaling study on Shaheen. The x-axis is log2p so p ranges from 64 to 16,384.

Figure: Quantification of SGS terms indicates substantial contribution in the nonlinear regime. Results shown for 4-th and 7-order methods