A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a ma...

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Vydáno v:Journal of computational physics Ročník 352; s. 463 - 497
Hlavní autoři: Feng, Wenqiang, Guo, Zhenlin, Lowengrub, John S., Wise, Steven M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge Elsevier Inc 01.01.2018
Elsevier Science Ltd
Témata:
Adaptive algorithms
Algorithms
Approximation
Block-structured
Cell-centered finite differences
Computational physics
Computer simulation
Conservation
Convergence
Finite difference method
Full approximation storage scheme
Geometry
Grid refinement (mathematics)
Interpolation
Locally-cartesian adaptive meshes
Multigrid
Multigrid methods
Prolongation
Time dependence
Variables
Full approximation storage scheme
Cell-centered finite differences
Multigrid
Locally-cartesian adaptive meshes
Block-structured
ISSN:0021-9991, 1090-2716
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Shrnutí:We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h→0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term. •We present a new conservative FAS multigrid solver for finite difference methods on AMR grids.•The method can be applied in any number of dimensions and can be easily modified for nonlinear, time-dependent, and coupled systems of equations.•The smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions.•We demonstrate that the solver has optimal, or nearly optimal, complexity.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2017.09.065