A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations

Ji, Xinjie; Gabbard, James; van Rees, Wim M.

doi:10.1016/j.jcp.2023.112513

Title: A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations

Journal Article · Wed Sep 27 00:00:00 EDT 2023 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2023.112513· OSTI ID:2203189

Ji, Xinjie ^[1]; Gabbard, James ^[1];

^[1]

Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)

Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. Here, this makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by hydrodynamic forces. However, for the vorticity-velocity form of the Navier-Stokes equations, existing immersed geometry discretizations for two-way coupled problems only achieve first order spatial accuracy near solid boundaries. Here we introduce a sharp-interface approach based on the immersed interface method to handle the one- and two-way coupling between an incompressible flow and one or more rigid bodies using the 2D vorticity-velocity Navier-Stokes equations. Our main contributions are three-fold. First, we develop and analyze a moving boundary treatment for sharp immersed methods that can be applied to PDEs with implicitly defined boundary conditions, such as those commonly imposed on the vorticity field. Second, we develop a two-way coupling methodology for the vorticity-velocity Navier-Stokes equations based on control-volume momentum balance that does not require the pressure field. Third, we show through extensive testing and validation that our resulting flow-body solver reaches second-order accuracy for most practical scenarios, and provides significant efficiency benefits compared to a representative first-order approach.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0020998

OSTI ID:: 2203189

Alternate ID(s):: OSTI ID: 2202523

Journal Information:: Journal of Computational Physics, Vol. 494; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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