[P-EM17] Space Plasma Science

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

*Jonna Marie Wehmeyer¹, Takahiro Miyoshi² (1.The Graduate University for Advanced Studies, 2.Graduate School of Advanced Science and Engineering, Hiroshima University)

Keywords:full two-fluid plasma model, discrete Gauss’s laws, staggered grid, implicit-explicit Runge-Kutta

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.