A weighted Shifted Boundary Method for free surface flow problems

Colomés, Oriol; Main, Alex; Nouveau, Léo; Scovazzi, Guglielmo

doi:10.1016/j.jcp.2020.109837

Title: A weighted Shifted Boundary Method for free surface flow problems

Journal Article · Fri Sep 10 00:00:00 EDT 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109837· OSTI ID:1851595

^[1]; Main, Alex ^[1]; Nouveau, Léo ^[1];

^[1]

Duke Univ., Durham, NC (United States). Dept. of Civil and Environmental Engineering

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods and was recently introduced for the Poisson, linear advection/diffusion, Stokes, Navier-Stokes, acoustics, and shallow-water equations. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. 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 Navier-Stokes flows with moving free-surfaces, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach prevents spurious pressure oscillations in time, which would otherwise be produced if the total active fluid volume were to change abruptly over a time step. In fact, the proposed weighted SBM method induces small mass (i.e., volume) conservation errors, which converge quadratically in the case of piecewise-linear finite element interpolations, as the grid is refined. Finally, we present an extensive set of two- and three-dimensional tests to demonstrate the robustness and accuracy of the method.

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Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Office of Naval Research (ONR)

Grant/Contract Number:: SC0012169; N00014-14-1-0311

OSTI ID:: 1851595

Alternate ID(s):: OSTI ID: 1671850

Journal Information:: Journal of Computational Physics, Vol. 424, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Title: A weighted Shifted Boundary Method for free surface flow problems

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