A weighted shifted boundary method for immersed moving boundary simulations of Stokes' flow

Danjie Xu, Oriol Colomés, Alex Main, Kangan Li, Nabil M. Atallah, Nabil Abboud, Guglielmo Scovazzi*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests.

Original languageEnglish
Article number113095
Number of pages30
JournalJournal of Computational Physics
Volume510
DOIs
Publication statusPublished - 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
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Keywords

  • Approximate boundary
  • Computational fluid dynamics
  • Immersed boundary method
  • Moving boundaries
  • Shifted boundary method
  • Unfitted finite element method

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