Changes between Version 3 and Version 4 of u/EricasLibrary

Timestamp:

07/27/11 14:57:03 (14 years ago)

Author:

Erica Kaminski

Comment:

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u/EricasLibrary

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 [[CollapsibleStart(Summary)]]
-Develops methods for AMR, dynamic grids that allot finer resolution over many length scales that is imperative for studying problems of gravitational collapse. The criteria for refinement is crucial, and their’s is the jeans length. This sets the resolution smaller than the local Jean’s length, allowing new benchmarks in the probing of the dynamics. They find uniformly rotating spherical clouds to collapse along the equatorial plane. When perturbed, these form ‘filamentary singularties’ that don’t fragment when isothermal.
+Develops methods for AMR, dynamic grids that allot finer resolution over many length scales that is imperative for studying problems of gravitational collapse. The criteria for refinement is crucial, and it is the jeans condition. This sets the resolution smaller than the local Jean’s condition, allowing new benchmarks in the probing of the dynamics. They find uniformly rotating spherical clouds to collapse along the equatorial plane. When perturbed, these form ‘filamentary singularties’ that don’t fragment when isothermal.
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 [[CollapsibleStart(Methodology)]]
 This paper goes through in extensive detail on the 3 components of their code methodology: the hyperbolic solvers that employ the Gudonov method for solution of the hydro equations,  elliptic solvers that utilize AMR multigrid method to solve Poisson’s equation, and finally these two methods operation within an AMR framework. The use of stencils as different layers of cell-centered quantities used for averaging the node centered quantities (for self - gravity) is detailed. Paper refers to Almgren for discussion on AMR multigrid cycle procedures. 
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-[[CollapsibleStart(AMR)]]
+[[CollapsibleStart(AMR and refinement criteria)]]
 
 Paper refers to Pember et al. (‘98) for a summary of the procedure for advancing grids. Their methods are based on Berger and Oliger (‘84), Berger and Collela (‘89), and Bell et al. (‘94). 
 
-Truelove, Klein, McKee, et al. (‘97). The Jeans Condition: A new constraint on spatial resolution in simulations of isothermal self-gravitational hydrodynamics.
-http://adsabs.harvard.edu/abs/1997ApJ...489L.179T
+To trigger refinement from level 0 to level 1, the code employs a density criterion to cells that contain gas of the original cloud. Such cells are identified if they contain a density greater than or equal to 1/2 the original cloud density at the outer edge. This results in the level 0 cells effectively removing the boundary of the computational volume from the surface of the cloud. Jean's condition is than used for refinement to 2nd and higher levels (discussed below).
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+[[CollapsibleStart(The Jeans Condition)]]
+Jeans analysis of the linearized 1D gravitohydrodynamic equations of equations an infinite medium 
+[[CollapsibleEnd]]
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 [[CollapsibleStart(Poisson's boundary conditions)]]