Adaptive mesh techniques for fronts in star formation

Details Adaptive mesh techniques for fronts in star formation Adaptive mesh techniques for fronts in star formation

Jul 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984phyd...12..408w&link_type=abstract

Physica D: Nonlinear Phenomena, Volume 12, Issue 1-3, p. 408-425.

Computer Science

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6

Scientific paper

We present an implicit, adaptive-grid, finite-difference technique specifically designed to locate and track arbitrary fronts, interfaces and structures in a radiation hydro flow. The adaptive mesh is constructed in such a way that the ``average'' change of the flow-variables per grid zone is the same throughout the entire grid. A local grid refinement of up to a factor of 106 compared to an equidistant mesh has been obtained on a machine with 14 decimal digits per word. Crucial to this type of approach is the use of a stiffness operator, which prevents tangling of the mesh. The elliptic equation for the grid motion is solved implicitly coupled with the equations for the flow variables. Per timestep very steep and narrow flow features can travel many times their own width in true space. However, with respect to the adaptive mesh the motion of such flow features is always less than one zone. Thus, the Courant-Friedrichs-Lewy [1] (CFL)-condition's accuracy limitation is always fulfilled although its stability criterion does not pose any timestep limitations for our implicit numerical method. In fact, the choice of timesteps is based purely on physical and accuracy considerations. Typical applications run on Courant numbers ranging from 0.1 to 1012. The performance of this numerical scheme is demonstrated on a planar 1-D shocktube and the formation of a one solar mass protostar in spherical symmetry.
Visitor, Max-Planck-Institut für Astrophysik.

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