Abstract
AbstractThe fast adaptive composite grid method (FAC) is a discretization and solution method design to achieve efficient local resolution by constructing the discretization based on various regular grids and using these grids as a basis for fast solution. FAC is designed so as to share all of the attributes of the composite grid and multigrid methods. As is the case for most mesh refinement schemes, it is advantageous to optimally choose the grids so as to save both storage and computational costs. The FAC method has previously been shown to be an effective tool in obtaining numerical solutions of many types of steady problems. In addition time‐dependent problems with stationary fronts or singularities have also been resolved efficiently with FAC. An adaptive scheme has been developed and implemented that, based on given error tolerances, calculates the optimal time discretization and locates the spatial regions where more resolution is needed. Patches are set up to be used by the various FAC algorithms. The spatial refinement scheme is able to track areas of resolution which move across the domain, allowing for small composite grids at each time step.
Published Version
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