[P-EM17] 宇宙プラズマ科学

[PEM17-P07] An implicit-explicit Runge-Kutta scheme strictly satisfying Gauss’s Laws for the full two-fluid plasma model

*エマヤ ヨナ¹、三好 隆博² (1.総合研究大学院大学、2.広島大学大学院先進理工系科学研究科)

キーワード：完全二流体プラズマモデル、離散的ガウスの法則、スタッガード格子、陰陽的ルンゲ＝クッタ法

We present a new numerical scheme for the full-two fluid plasma model, which couples the Euler Equations for ion and electron fluids with Maxwell’s Equations to account for electromagnetic interactions. The fluid equations are solved with the HLLC approximate Riemann solver [1], while the electric and magnetic fields are arranged in a staggered grid [2] and calculated with a central differencing scheme. By using different spatial discretization, we ensure that the discrete Gauss’s laws are conserved over time and therefore the divergence constraints of the Maxwell equations will be satisfied permanently, given that the initial conditions do so. Therefore, our model can calculate even very small polarization electric fields with high accuracy. We present algorithms for both explicit and implicit-explicit temporal integration using Runge-Kutta methods [3]. By calculating the stiff source term implicitly, we aim to exclude rapid oscillations, that happen on a time scale irrelevant to the problem which is to be solved. The implicit-explicit scheme does not require iteration to converge and is significantly more robust than the solely explicit scheme. Finally, we validate our scheme by performing several standard numerical experiments, such as the electron plasma oscillation and the Brio-Wu shock tube.

References
[1] Batten et al., SIAM J. Sci. Statist. Comput. 18, 1553-1570, 1997.
[2] Yee, IEEE Trans. Antennas Propag. 14, 302-307, 1966.
[3] Ascher, Ruuth, and Spiteri, Appl. Numer. Math., 25 (2–3), 151–167, 1997.