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# Ghost-fluid Method in AMROC

The ghost-fluid method (GFM) [1,2] is a simple lumped boundary treatment that allows the incorporation of imbedded moving boundaries into every Cartesian patch solver. The boundary is represented implicitly with level set functions. Currently, the method is only used for Euler equations, but extensions to other hyperbolic equations would be straightforward. In principle, the method just constructs internal ghost cell values before the application of the underlying Cartesian scheme. Like closely related approaches [3,4] this technique diffuses the imbedded boundary and results in a non-conservative method. The ghost-fluid implementation in AMROC therefore has to be used with care:

• GFM calculations usually require higher resolution at the imbedded boundary than a standard first-order unstructured scheme, especially on non-uniform shear flow problems.
• Problems sensitive to boundary interaction require thorough convergence studies. This is especially true for
• instabilities arising from the boundary and
• strong discontinuous reflection phenomena.
• In such cases the length scale of the boundary flow problem should be significantly above the resolution for GFM. Appropriate level set-based refinement criteria have been implemented.
• A detailed two-dimensional accuracy study and a more realistic two-dimensional Mach reflection calculation are available to illustrate some of the deficiencies of GFM.

Nevertheless, flow problems that allow the application of a lumped bounday method can be simulated successfully.

Some brief concept papers in PDF format are available

The relation of the ghost-fluid or ghost-cell approach to various other (partially lumped, patially accurate) embedded or immersed boundary methods is described nicely in the following recent overview article:
R. Mittal, G. Iaccarino. Annual Review of Fluid Mechanics. Volume 37, Page 239-261, 21 January 2005.

[1] M. Arienti et al., A level set approach to Eulerian-Lagrangian coupling, J. Comput. Phys., 185 (2003) 213.

[2] R.P. Fedkiw et al., A non-oscillatory Eulerian approach to interfaces in multimaterial flow, J. Comput. Phys., 152 (1999) 457.

[3] J. Falcovitz et al., A two-dimensional conservation laws scheme for compressible flows with moving boundaries, J. Comput. Phys., 138 (1997) 83.

[4] H. Forrer, M. Berger, Flow simulations on Cartesian grids involving complex moving geometries flows, Int. Ser. Num. Math. 129, Birkhaeuser, Basel 1 (1998) 315.

I Attachment Size Date Who Comment
ghostfluid.pdf 89.1 K 01 Mar 2005 - 19:21 RalfDeiterding Concept paper embedded boundary methods
ghostcells.pdf 101.0 K 01 Mar 2005 - 19:22 RalfDeiterding Concept paper on constructing ghost cells values

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