Introduction of temporal sub-stepping in the Multi-Level Multi-Domain semi-implicit Particle-In-Cell code Parsek2D-MLMD

In this paper, the introduction of temporal sub-stepping in Multi-Level Multi-Domain (MLMD) simulations of plasmas is discussed. The MLMD method addresses the multi-scale nature of space plasmas by simulating a problem at different levels of resolution. A large-domain "coarse grid" is simulated with low resolution to capture large-scale, slow processes. Smaller scale, local processes are obtained through a "refined grid" which uses higher resolution. Very high jumps in the resolution used at the different levels can be achieved thanks to the Implicit Moment Method and appropriate grid interlocking operations. Up to now, the same time step was used at all the levels. Now, with temporal sub-stepping, the different levels can also benefit from the use of different temporal resolutions. This saves further resources with respect to "traditional" simulations done using the same spatial and temporal stepping on the entire domain. It also prevents the levels from working at the limits of the stability condition of the Implicit Moment Method. The temporal sub-stepping is tested with simulations of magnetic reconnection in space. It is shown that, thanks to the reduced costs of MLMD simulations with respect to single-level simulations, it becomes possible to verify with realistic mass ratios scaling laws previously verified only for reduced mass ratios. Performance considerations are also provided. (C) 2014 Elsevier B.V. All rights reserved.