Statistics – Methodology
Scientific paper
Jan 2012
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012aas...21910406m&link_type=abstract
American Astronomical Society, AAS Meeting #219, #104.06
Statistics
Methodology
Scientific paper
We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial fits are calculated from the field values of neighboring particles to derive field values and spatial derivatives at the particle position. Field values and particle positions are advanced in time with a second order predictor-corrector scheme. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is required for stability, and gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. Particle addition and deletion is based on a local void and clump detection algorithm. Novel stabilization operators are used to filter high-frequency modes and provide diffusion in shocks. Globally conserved quantities are maintained constant by differentially adjusting regions of large change. We describe the parallel implmentation and show a suite of tests, including linear amplitude waves, shock tubes, and magnetrotational instability. We discuss the novel ways magnetic divergence errors can be controlled in a point collocation method and the control of such errors is demonstrated. We also describe a rigorous methodology for showing
the correctness of numerical solutions to a well posed Kelvin-Helmholtz (KH) problem including demonstrations in several codes. This methodology clarifies the ongoing controversy about the differences seen in KH instability grid codes, moving mesh codes, and in particular highlights the consequences of the zeroth order inconsistency in Smoothed Particle Hydrodynamics.
Mac Low Mordecai-Mar
Maron Jason L.
McNally Colin
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