A wide variety of plasma problems require both high resolution and large spatial domains that present a problem for existing models. Adaptive Mesh Refinement (AMR) provides an efficient method of obtaining both high resolution and a large spatial domain. AMR allows for the possibility of simultaneously achieving high resolution over part of a spatial domain, while maintaining a large computational domain. For structure AMR, this is achieved by providing different levels of refinement over different parts of the computational domain by dividing the domain into different patches and then providing refinement over part of those patches. To achieve these goals we are combining a MHD plasma model with structured adaptive mesh refinement through the SAMRAI framework [1]. This allows for the continued use of a relatively simple discretization of the spatial domain with the flexibility of a spatially and time-varying resolution. It also lends itself to large scale parallelism through splitting of the domain and spatial scales. The coupled model uses SAMRAI to provide a structured AMR hierarchy that maintains the global problem solution. For each patch, we apply the physics operators by using an existing magneto-hydrodynamic (MHD) model PIXIE3D [2]. PIXIE3D is a fully implicit, fully nonlinear finite-volume code that solves the extended MHD set of equations in generalized curvilinear geometry [2,3]. Its non-linearly stable collocated discretization, combined with its fully nonlinear character, lends it exceptional numerical robustness and conservation properties [2]. Algorithmically, PIXIE3D has demonstrated excellent scalability serially and in parallel with up to 4092 processors [4]. Global time integrators and implicit solvers over the entire AMR hierarchy are then applied to solve the resulting problem over the complete domain.
We test the algorithm using the island coalescence MHD problem [4]. The island coalescence is a self-contained, multiscale MHD driven reconnection problem in which two co-flowing current channels attract and reconnect. In the reconnection process, extremely thin current sheets of thickness sqrt(eta) (with eta the normalized resistivity) develop non-linearly. Capturing such nonlinear current sheet thinning behavior is essential for the accurate modeling of the macroscopic dynamics, and thus mesh adaptivity is of the essence. Furthermore, because the MHD system is a stiff hyperbolic system, finer meshes are accompanied by more stringent CFL time step stability constraints, and hence an implicit temporal scheme is desirable.
1. http://computation.llnl.gov/casc/SAMRAI/index.html
2. L. Chacón. Comput. Phys. Comm., 163, p. 143 (2004).
3. L. Chacón. Phys. Plasmas, 15, 056103 (2008).
4. J. Finn and P. Kaw, Phys. Fluids, Vol. 20, p. 72 (1977).