2:45 PM - 3:00 PM
[PEM17-10] Development of a numerical scheme strictly satisfying Gauss's laws for the full two-fluid plasma model
Keywords:full two-fluid plasma model, discrete Gauss’s laws, staggered grid
The full two-fluid plasma model approximates electrons and ions as two different compressible fluids and reflects microscopic effects such as charge separation in the macroscopic plasma dynamics. Hitherto proposed numerical schemes for the full two-fluid plasma model employ the perfectly hyperbolic Maxwell’s equations [1] to disperse divergence errors from Gauss’s laws via advection and diffusion, and thereby approximately satisfy divergence constraints. However, small fluctuations of the actual electromagnetic field are being dispersed likewise and their effect on the macroscopic plasma dynamics might not be reproduced accurately. In this study, we developed a new numerical scheme that strictly satisfies Gauss’s Laws and thus is able to reproduce even the effect of small electromagnetic fields that charge separation can cause.
The numerical scheme developed in this study strictly satisfies Gauss’s laws by discretizing Maxwell’s equations, that are used to evolve the electromagnetic fields, differently from the fluid equations. The two sets of Euler equations, describing the ion and electron fluid respectively, are solved with the HLLC approximate Riemann solver [2], while the electric and magnetic fields are arranged in a staggered grid [3] and calculated with a central differencing scheme. This method preserves Gauss’s laws and therefore the divergence constraints will be satisfied permanently, given that the initial conditions do so. We performed standard numerical experiments such as plasma oscillations and ion acoustic solitons to validate our numerical scheme. Furthermore, we analyzed the Kelvin-Helmholtz instability in the full two-fluid plasma model, which is affected by the electromagnetic fields autonomously emerging from charge separation.
References
[1] Munz et al.: J. Comput. Phys. 161 (2000) 484-511
[2] Batten et al.: SIAM J. Sci. Statist. Comput. 18 (1997) 1553-1570
[3] Yee: IEEE Trans. Antennas Propag. 14 (1966) 302-307
The numerical scheme developed in this study strictly satisfies Gauss’s laws by discretizing Maxwell’s equations, that are used to evolve the electromagnetic fields, differently from the fluid equations. The two sets of Euler equations, describing the ion and electron fluid respectively, are solved with the HLLC approximate Riemann solver [2], while the electric and magnetic fields are arranged in a staggered grid [3] and calculated with a central differencing scheme. This method preserves Gauss’s laws and therefore the divergence constraints will be satisfied permanently, given that the initial conditions do so. We performed standard numerical experiments such as plasma oscillations and ion acoustic solitons to validate our numerical scheme. Furthermore, we analyzed the Kelvin-Helmholtz instability in the full two-fluid plasma model, which is affected by the electromagnetic fields autonomously emerging from charge separation.
References
[1] Munz et al.: J. Comput. Phys. 161 (2000) 484-511
[2] Batten et al.: SIAM J. Sci. Statist. Comput. 18 (1997) 1553-1570
[3] Yee: IEEE Trans. Antennas Propag. 14 (1966) 302-307