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

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

doi:10.1016/j.jcp.2024.113095

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

Journal Article · 09 May 2024 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2024.113095 · OSTI ID:2550713

Xu, Danjie ^[1]; Colomés, Oriol ^[2]; Main, Alex ^[3]; Li, Kangan ^[4]; Atallah, Nabil M. ^[5]; Abboud, Nabil ^[6];

^[1]

Duke Univ., Durham, NC (United States)
Duke Univ., Durham, NC (United States); Delft Univ. of Technology (Netherlands)
Duke Univ., Durham, NC (United States); Ansys, Canonsburg, PA (United States)
Duke Univ., Durham, NC (United States); Pennsylvania State Univ., University Park, PA (United States)
Duke Univ., Durham, NC (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Ansys, Atlanta, GA (United States)

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. Here, 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.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2550713

Report Number(s):: LLNL-JRNL-854220; 1082518

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 510; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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

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