Montag, 30. Mai 2011 - 11:00
Mordecai Mac Low (American Museum of Natural History):
"A new Lagrangian, adaptive, high-order particle algorithm for gas dynamics and MHD."
Zusammenfassung. We develop an algorithm for simulating the equations of ideal magnetohydrodynamics with unstructured particles. The algorithm is Lagrangian in that particles move with the fluid, and hence the timestep is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Local third order least-squares polynomial fits are calculated around each point from the values of neighboring points to provide spatial derivatives. Simulated quantities and point positions are advanced in time with a second order predictor-corrector scheme. Phurbas is spatially adaptive. A target resolution can be specified for each point in space, with points being added and deleted as needed to meet this target. Point 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. A set of non-adaptive Lagrangian tracer particles may be used to follow fluid elements. Globally conserved quantities are maintained constant by differentially correcting regions of large change. We have parallelized the code by modifying the framework provided by GADGET-2 (Springel 2005). A set of standard test problems, including 1e-6 amplitude linear MHD waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities is run. The results demonstrate that the algorithm can simulate magnetized, subsonic and supersonic flows with the wavenumber resolution of a third order grid code of equivalent resolution. Finally we demonstrate agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry, as well as following its non-linear