| Adaptive Mesh Refinement |
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The advantages of a dynamic gridding scheme are: #Increased computational savings over a static grid approach. #Increased storage savings over a static grid approach. #Complete control of grid resolution, compared to the fixed resolution of a static grid approach, or the Lagrangian-based adaptivity of Smoothed Particle Hydrodynamics . INTRODUCTION TO ADAPTIVE MESH REFINEMENT In a series of Papers , Marsha Berger , John Oliger , and Phillip Colella developed an Algorithm for dynamic gridding called ''local adaptive mesh refinement''. The algorithm begins with the entire computational Domain covered with a coarsely resolved base-level regular Cartesian Grid . As the calculation progresses, individual grid cells are tagged for refinement, using a criterion that can either be user-supplied (for example Mass per cell remains constant, hence higher Density regions are more highly resolved) or based on Richardson Extrapolation . All tagged cells are then refined, meaning that a finer grid is overlayed on the coarse one. After refinement, individual grid patches on a single fixed level of refinement are passed off to an Integrator which advances those cells in Time . Finally, a correction procedure is implemented to correct the transfer along coarse-fine grid interfaces, to insure that the amount of any conserved quantity leaving one cells exactly balances the amount enter the bordering cell. If at some point the level of refinement in a cell is greater than required, the high resolution grid may be removed and replaced with a coarser one. This allows the user to solve problems that are completely intractable on a uniform grid; for example, Astrophysicists have used AMR to model a collapsing Giant Molecular Cloud core down to an effective resolution of 131,072 cells per initial cloud Radius , corresponding to a Resolution of 1015 cells on a uniform grid. |
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