Abstract
The Multi-Level Multi-Domain (MLMD) method is a semi-implicit adaptive method for Particle-In-Cell plasma simulations. It has been demonstrated in the past in simulations of Maxwellian plasmas, electrostatic and electromagnetic instabilities, plasma expansion in vacuum, magnetic reconnection [1, 2, 3]. In multiple occasions, it has been commented on the coupling between the coarse and the refined grid solutions. The coupling mechanism itself, however, has never been explored in depth. Here, we investigate the theoretical bases of grid coupling in the MLMD system. We obtain an evolution law for the electric field solution in the overlap area of the MLMD system which highlights a dependance on the densities and currents from both the coarse and the refined grid, rather than from the coarse grid alone: grid coupling is obtained via densities and currents.
Highlights
Kinetic simulations of space plasmas have greatly benefitted, over the last decades, of the almost predictable technological improvements commonly known as Moore’s law: semiconductor technology doubles the number of transistors per unit area every 18 months [4]
It is demonstrated that the projection operation implemented in the Multi-Level Multi-Domain (MLMD) method (Equation 32-33 in [1]) results into grid coupling because it introduces a dependancy of the mixed grid electric field solution on the refined grid density and currents
The MLMD method, a semi-implicit adaptive method for fully kinetic plasma simulations, relies on two pillars: the capability of the Coarse Grid (CG) to drive Refined Grid (RG) evolution through CG-to-RG boundary conditions and good RG-CG coupling in the overlap area. The latter property is achieved through electric field projection from the refined to the coarse grid
Summary
Kinetic simulations of space plasmas have greatly benefitted, over the last decades, of the almost predictable technological improvements commonly known as Moore’s law: semiconductor technology doubles the number of transistors per unit area every 18 months [4]. It is demonstrated that the projection (restriction) operation implemented in the MLMD method (Equation 32-33 in [1]) results into grid coupling because it introduces a dependancy of the mixed grid electric field solution on the refined grid density and currents. They are reproduced without approximation (i.e., at the appropriate resolution) by the RG They are simulated in an approximated way by the Coarse Grid where, as typical of semi-implicit methods, selective damping and spatial compression affect the under-resolved scales [25].
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