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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Ji, Xinjie, Gabbard, James, van Rees, Wim M.
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910898501713920
author Ji, Xinjie
Gabbard, James
van Rees, Wim M.
author_facet Ji, Xinjie
Gabbard, James
van Rees, Wim M.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2309_08479
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations
Ji, Xinjie
Gabbard, James
van Rees, Wim M.
Fluid Dynamics
Computational Physics
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.
title A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations
topic Fluid Dynamics
Computational Physics
url https://arxiv.org/abs/2309.08479