Reduction of nonlinear embedded boundary models for problems with evolving interfaces

Maciej Balajewicz, Charbel Farhat

Research output: Contribution to journalArticlepeer-review

Abstract

Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational frameworks based on such methods seems however to be challenging. Indeed, most popular model reduction techniques are projection-based, and rely on basis functions obtained from the compression of simulation snapshots. In a traditional interface-fitted computational framework, the computation of such basis functions is straightforward, primarily because the computational domain does not contain in this case a fictitious region. This is not the case however for an embedded computational framework because the computational domain typically contains in this case both real and ghost regions whose definitions complicate the collection and compression of simulation snapshots. The problem is exacerbated when the interface separating both regions evolves in time. This paper addresses this issue by formulating the snapshot compression problem as a weighted low-rank approximation problem where the binary weighting identifies the evolving component of the individual simulation snapshots. The proposed approach is application independent and therefore comprehensive. It is successfully demonstrated for the model reduction of several two-dimensional, vortex-dominated, fluid-structure interaction problems.

Original languageEnglish (US)
Pages (from-to)489-504
Number of pages16
JournalJournal of Computational Physics
Volume274
DOIs
StatePublished - Oct 1 2014
Externally publishedYes

Keywords

  • Data compression
  • Embedded boundary method
  • Evolving domains
  • Immersed boundary method
  • Interfaces
  • Model reduction
  • Singular value decomposition

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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