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An accurate moving boundary formulation in cut-cell methods

Schneiders, Lennart and Hartmann, Daniel and Meinke, Matthias and Schröder, Wolfgang (2013) An accurate moving boundary formulation in cut-cell methods. Journal of Computational Physics, 235 . pp. 786-809. ISSN 0021-9991. http://resolver.caltech.edu/CaltechAUTHORS:20130308-104647884

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Abstract

A cut-cell method for Cartesian meshes to simulate viscous compressible flows with moving boundaries is presented. We focus on eliminating unphysical oscillations occurring in Cartesian grid methods extended to moving-boundary problems. In these methods, cells either lie completely in the fluid or solid region or are intersected by the boundary. For the latter cells, the time dependent volume fraction lying in the fluid region can be so small that explicit time-integration schemes become unstable and a special treatment of these cells is necessary. When the boundary moves, a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level. This causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme. This temporally discontinuous alteration is shown to act like an unphysical source term, which deteriorates the numerical solution, i.e., it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary. We develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut-cell method which avoids these discontinuities. Results for canonical two- and three-dimensional test cases evidence the accuracy and robustness of the newly developed scheme.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jcp.2012.09.038DOIUNSPECIFIED
http://www.sciencedirect.com/science/article/pii/S0021999112005839PublisherUNSPECIFIED
Additional Information:© 2012 Elsevier Inc. Received 10 September 2011; Received in revised form 6 August 2012; Accepted 20 September 2012; Available online 13 October 2012. D. Hartmann is sponsored by the German Research Association (Deutsche Forschungsgemeinschaft (DFG)) under grant HA 5535/2-1. The support is gratefully acknowledged. Furthermore, we do thank the NRW research program "Brennstoffgewinnung aus nachwachsenden Rohstoffen" (BrenaRo) and the DFG funded cluster of Excellence "Tailor-Made Fuels from Biomass" for their financial support.
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG) (Germany)HA 5535/2-1
NRW research programUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG) (Germany)UNSPECIFIED
Subject Keywords:Cut-cell method; Immersed boundary method; Moving boundary; Spurious force oscillations; Oscillating cylinder; Compressible Navier-Stokes
Record Number:CaltechAUTHORS:20130308-104647884
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130308-104647884
Official Citation:Lennart Schneiders, Daniel Hartmann, Matthias Meinke, Wolfgang Schröder, An accurate moving boundary formulation in cut-cell methods, Journal of Computational Physics, Volume 235, 15 February 2013, Pages 786-809, ISSN 0021-9991, 10.1016/j.jcp.2012.09.038.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37418
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 Apr 2013 23:53
Last Modified:04 Apr 2013 23:53

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