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3D AMR simulation (using BATS-R-US) of the May 2, 1998 coronal mass ejection. The background solar wind was obtained using solar magnetogram observations and the CME was initiated by rotating and converging flows inside an active region. The 3D image shows the CME 1 hour after eruption.

Solid lines are magnetic field lines; the false color code shows the magnitude of the current density. The magnitude of the flow velocity is shown on a translucent plane given by y=0. Values in excess of 1,000 km/s are blanked and shown in light grey. The inner sphere corresponds to R=1 Rs; the color code shows the distribution of radial magnetic field. Regions with radial field strength greater than 3 Gauss are blanked and appear in grey. The AMR grid is shown by thin black lines on the plane.


The University of Michigan magnetohydrodynamic (MHD) code BATS-R-US solves the MHD equations on a block-adaptive grid. The code is based on a finite volume approach with self-similar blocks. The parallel AMR solver was designed from the ground up with a view to achieving very high performance on massively parallel architectures. The hierarchical data structure and self-similar blocks make domain decomposition easy and readily enable good load-balancing, a crucial element for truly scalable computing. The computational cells are embedded in regular structured blocks. Starting with an initial mesh, adaptation is accomplished by the dividing and refining of appropriate solution blocks or the converse. Other features of the parallel implementation include the use of FORTRAN 90 as the programming language and the message passing interface (MPI) library for performing the interprocessor communication. Use of these standards greatly enhances the portability of the code and leads to very good serial and parallel performance. The message passing is performed in an asynchronous fashion with gathered wait states and message consolidation. BATS-R-US nearly perfectly scales to 1,500 processors.

The present implementation of BATS-R-US supports Cartesian (x,y,z), cylindrical (r,φ,z), or spherical (R or log(R),φ,θ) coordinate systems. Both the cylindrical and spherical grids are applicable for simulating toroidal plasma configurations. Cylindrical grids one better suited for configurations in which the axis of symmetry (or pole) is isolated from the simulation domain (such as tokamak, stellarator, FRS). On the other hand, spherical coordinates are favorable for spheromak-like configurations. The use of classical toroidal coordinates for a simulation is challenging due to the strongly stretched control volumes near the toroidal pole, but such toroidal grids will be available at least for presenting and visualizing the simulation results. A powerful parallel "coupling toolkit" has been recently developed at Michigan that can efficiently interpolate from one type of grid to another (like cylindrical-to-toroidal).

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