Lattice kinetic schemes in fusion plasmas

Abstract

Lattice Boltzmann Methods (LBM) are an established alternative approach for numerical simulations of a large spectrum of physical processes. They are based on a mesoscopic analysis of the underlying physics through a velocity distribution function f(x,ξ,t) which obeys the Boltzmann Equation (BE). Furthermore, it has been argued that a number of macroscopic processes can be modeled through a mesoscopic evolution equation similar to BE appropriately tuned to recover the desired macroscopic behavior while retaining the multi-scale characteristics of LBM. Such an approach can be utilized to analyze a magnetohydrodynamic (MHD) system via lattice kinetic schemes [1,2]. All macroscopic quantities are given as moments of f and the algorithm is seen to solve consistently the hydrodynamic and magnetic induction dissipative equations in generalized 3D geometry [3]. We examine the potential of such an algorithm for large-scale fusion simulations. Initial conditions may be provided by the Integrated Tokamak Modelling (ITM) mdsplus server in ENEA frascati, Rome, for ITER related scenarios [4]. The case considered is the evolution of continuous shear Alfvén waves in a plasma [5].