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- 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.

- Several fluid-structure interaction examples are already available for the Clawpack-based patch solver.
- Recommendations for using the current implementation

Some brief concept papers in PDF format are available

- Overview of embedded boundary methods
- Constructing ghost cells values in Cartesian embedded boundary methods

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 |
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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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