Novel immersed interface method based on local stability conditions

C. Brehm, H. F. Fasel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

A novel immersed interface method is presented which is based on a local Taylor series expansion at irregular grid points whereby numerical stability is enforced through a local stability condition. In the past, various immersed interface/boundary methods were developed by solely considering the order of the local truncation error at the irregular grid points. The numerical stability of these schemes was demonstrated in a global sense by applying either a matrix stability analysis or considering a number of different test cases. None of these schemes used a concrete local stability condition to derive the stencils at irregular grid points for advection-diffusion type equations. This paper will show the derivation of stencil coefficients at irregular grid points for the one dimensional advection-diffusion equation. The advection-diffusion equation may be viewed as a simple model equation for the incompressible Navier-Stokes equations. This paper will demonstrate that the local stability constraints can be justified in a global setting as long as the DFL-number stability limit is not reached. This paper will also present an extension of the one-dimensional immersed interface method to the two-dimensional case. In addition, the novel immersed interface method will be extended with a capability which allows for moving boundaries. Finally, several numerical sample problems as well as numerical matrix stability analysis for advection-diffusion type equations will prove the full operability of this novel immersed interface method.

Original languageEnglish (US)
Title of host publication40th AIAA Fluid Dynamics Conference
PublisherAmerican Institute of Aeronautics and Astronautics Inc.
ISBN (Print)9781617389221
DOIs
StatePublished - Jan 1 2010

Publication series

Name40th AIAA Fluid Dynamics Conference
Volume1

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

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    Brehm, C., & Fasel, H. F. (2010). Novel immersed interface method based on local stability conditions. In 40th AIAA Fluid Dynamics Conference [2010-4432] (40th AIAA Fluid Dynamics Conference; Vol. 1). American Institute of Aeronautics and Astronautics Inc.. https://doi.org/10.2514/6.2010-4432