Conservative fourth-order finite-volume Vlasov-Poisson solver for axisymmetric plasmas in cylindrical (r, vr, vθ) phase space coordinates

JOURNAL OF COMPUTATIONAL PHYSICS

卷:373

Article

Vogman, G. V.¹  Shumlak, U.²  Colella, P.³ 

[1] Lawrence Livermore Natl Lab, Ctr High Energy Dens Sci, Livermore, CA 94550 USA

[2] Univ Washington, Aerosp & Energet Res Program, Seattle, WA 98195 USA

[3] Lawrence Berkeley Natl Lab, Computat Res Div, Berkeley, CA 94720 USA

关键词: Vlasov-Poisson;    Cylindrical coordinates;    Axisymmetric plasma;    Fourth-order;    Finite-volume;    Conservation-law form;   

DOI  :  10.1016/j.jcp.2018.07.029

来源: Elsevier

【 摘 要 】

A fourth-order finite-volume Vlasov-Poisson algorithm is developed for simulating axisymmetric plasma configurations in (r, v(r), v(theta)) phase space coordinates. The Vlasov equation for cylindrical phase space coordinates is cast into conservation-law form and is discretized on a structured grid. The conservative finite-volume discretization is based on fifth-order up-wind reconstructions of the distribution function and a fourth-order quadrature rule that accounts for transverse variations of fluxes along control volume surfaces. High-order specular reflection boundary conditions enable high-fidelity treatment of plasma distribution functions at the axis and at wall boundaries. The numerical method is applied to simulate a confined uniform neutral gas to assess convergence properties for an equilibrium system in which effects of finite-temperature and acceleration due to centrifugal and Coriolis forces are present. The discretization is also applied to a Z-pinch configuration to study electrostatic ion confinement and the dynamics of the associated breathing mode. Simulations show that the ion distribution function exhibits non-Maxwellian features and that a temperature anisotropy develops and is sustained. The finite-volume implementation is demonstrated to converge at fourth-order for both applications. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free