A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations
Name
2309.08479v1.pdf
Description
Accepted version
Size
2.75 MB
Format
Adobe PDF
Checksum (MD5)
a69c78e9baec3bcaa719bc9f5c487d23
Author(s)
Ji, Xinjie
Gabbard, James
van Rees, Wim M.
Date Issued
December 2023
Journal
Journal of Computational Physics
Publisher
Elsevier BV
Citation
Ji, Xinjie, Gabbard, James and van Rees, Wim M. 2023. "A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations." Journal of Computational Physics, 494.
Version
Author's final manuscript
Abstract
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. 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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-ShareAlike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jcp.2023.112513
