An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods

A Cartesian grid method with adaptive mesh refinement and multigrid acceleration is presented for the compressible Navier–Stokes equations. Cut cells are used to represent boundaries on the Cartesian grid, while ghost cells are introduced to facilitate the implementation of boundary conditions. A ce...

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Vydané v:Computers & fluids Ročník 37; číslo 9; s. 1103 - 1125
Hlavní autori: Hartmann, Daniel, Meinke, Matthias, Schröder, Wolfgang
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Elsevier Ltd 01.10.2008
Elsevier Science
Predmet:
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Physics
Compressible fluid
Multiple deck method
Computational fluid dynamics
Convergence acceleration
Refinement method
Digital simulation
Boundary conditions
Adaptive method
Hierarchized structure
Laminar flow
Multigrid
Modelling
Mesh generation
Cartesian coordinates
Navier-Stokes equations
ISSN:0045-7930, 1879-0747
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Shrnutí:A Cartesian grid method with adaptive mesh refinement and multigrid acceleration is presented for the compressible Navier–Stokes equations. Cut cells are used to represent boundaries on the Cartesian grid, while ghost cells are introduced to facilitate the implementation of boundary conditions. A cell-tree data structure is used to organize the grid cells in a hierarchical manner. Cells of all refinement levels are present in this data structure such that grid level changes as they are required in a multigrid context do not have to be carried out explicitly. Adaptive mesh refinement is introduced using phenomenon-based sensors. The application of the multilevel method in conjunction with the Cartesian cut-cell method to problems with curved boundaries is described in detail. A 5-step Runge–Kutta multigrid scheme with local time stepping is used for steady problems and also for the inner integration within a dual time-stepping method for unsteady problems. The inefficiency of customary multigrid methods on Cartesian grids with embedded boundaries requires a new multilevel concept for this application, which is introduced in this paper. This new concept is based on the following novelties: a formulation of a multigrid method for Cartesian hierarchical grid methods, the concept of averaged control volumes, and a mesh adaptation strategy allowing to directly control the number of refined and coarsened cells.
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ISSN:0045-7930
1879-0747
DOI:10.1016/j.compfluid.2007.06.007