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

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 ^[2]; ^[2]

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

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Institute 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, Journal Name: Journal of Computational Physics Vol. 494; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (50)

An immersed boundary vector potential‐vorticity meshless solver of the incompressible Navier–Stokes equation Bourantas, George C.; Zwick, Benjamin F.; Lavier, Theo Philippe International Journal for Numerical Methods in Fluids, Vol. 95, Issue 1 https://doi.org/10.1002/fld.5146	journal	September 2022
Computation of Solid–Liquid Phase Fronts in the Sharp Interface Limit on Fixed Grids Udaykumar, H. S.; Mittal, R.; Shyy, Wei Journal of Computational Physics, Vol. 153, Issue 2 https://doi.org/10.1006/jcph.1999.6294	journal	August 1999
A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries Udaykumar, H. S.; Mittal, R.; Rampunggoon, P. Journal of Computational Physics, Vol. 174, Issue 1 https://doi.org/10.1006/jcph.2001.6916	journal	November 2001
A Cartesian Grid Method for Solving the Two-Dimensional Streamfunction-Vorticity Equations in Irregular Regions Calhoun, Donna Journal of Computational Physics, Vol. 176, Issue 2 https://doi.org/10.1006/jcph.2001.6970	journal	March 2002
A Numerical Simulation of Vortex Shedding from an Oscillating Circular Cylinder Guilmineau, E.; Queutey, P. Journal of Fluids and Structures, Vol. 16, Issue 6 https://doi.org/10.1006/jfls.2002.0449	journal	August 2002
A penalization method to take into account obstacles in incompressible viscous flows Angot, Philippe; Bruneau, Charles-Henri; Fabrie, Pierre Numerische Mathematik, Vol. 81, Issue 4 https://doi.org/10.1007/s002110050401	journal	February 1999
Large Eddy Simulation of Wind Turbine Wakes Chatelain, Philippe; Backaert, Stéphane; Winckelmans, Grégoire Flow, Turbulence and Combustion, Vol. 91, Issue 3 https://doi.org/10.1007/s10494-013-9474-8	journal	June 2013
Low-storage Runge-Kutta schemes Williamson, J. H. Journal of Computational Physics, Vol. 35, Issue 1 https://doi.org/10.1016/0021-9991(80)90033-9	journal	March 1980
A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow Russell, David; Jane Wang, Z. Journal of Computational Physics, Vol. 191, Issue 1 https://doi.org/10.1016/S0021-9991(03)00310-3	journal	October 2003
Calculation of hydrodynamic forces acting on a submerged moving object using immersed boundary method Shen, Linwei; Chan, Eng-Soon; Lin, Pengzhi Computers & Fluids, Vol. 38, Issue 3 https://doi.org/10.1016/j.compfluid.2008.07.002	journal	March 2009
A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains Linnick, Mark N.; Fasel, Hermann F. Journal of Computational Physics, Vol. 204, Issue 1 https://doi.org/10.1016/j.jcp.2004.09.017	journal	March 2005
An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries Yang, Jianming; Balaras, Elias Journal of Computational Physics, Vol. 215, Issue 1 https://doi.org/10.1016/j.jcp.2005.10.035	journal	June 2006
An immersed interface method for simulating the interaction of a fluid with moving boundaries Xu, Sheng; Wang, Z. Jane Journal of Computational Physics, Vol. 216, Issue 2 https://doi.org/10.1016/j.jcp.2005.12.016	journal	August 2006
Strongly coupled flow/structure interactions with a geometrically conservative ALE scheme on general hybrid meshes Ahn, Hyung Taek; Kallinderis, Yannis Journal of Computational Physics, Vol. 219, Issue 2 https://doi.org/10.1016/j.jcp.2006.04.011	journal	December 2006
Numerical simulation of the fluid dynamics of 2D rigid body motion with the vortex particle method Eldredge, Jeff D. Journal of Computational Physics, Vol. 221, Issue 2 https://doi.org/10.1016/j.jcp.2006.06.038	journal	February 2007
A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries Mittal, R.; Dong, H.; Bozkurttas, M. Journal of Computational Physics, Vol. 227, Issue 10 https://doi.org/10.1016/j.jcp.2008.01.028	journal	May 2008
Dynamically coupled fluid–body interactions in vorticity-based numerical simulations Eldredge, Jeff D. Journal of Computational Physics, Vol. 227, Issue 21 https://doi.org/10.1016/j.jcp.2008.03.033	journal	November 2008
A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies Coquerelle, M.; Cottet, G. -H. Journal of Computational Physics, Vol. 227, Issue 21 https://doi.org/10.1016/j.jcp.2008.03.041	journal	November 2008
Finite difference methods for approximating Heaviside functions Towers, John D. Journal of Computational Physics, Vol. 228, Issue 9 https://doi.org/10.1016/j.jcp.2009.01.026	journal	May 2009
Analysis of an immersed boundary method for three-dimensional flows in vorticity formulation Poncet, Philippe Journal of Computational Physics, Vol. 228, Issue 19 https://doi.org/10.1016/j.jcp.2009.06.023	journal	October 2009
A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations Yang, Xiaolei; Zhang, Xing; Li, Zhilin Journal of Computational Physics, Vol. 228, Issue 20 https://doi.org/10.1016/j.jcp.2009.07.023	journal	November 2009
GPU accelerated simulations of bluff body flows using vortex particle methods Rossinelli, Diego; Bergdorf, Michael; Cottet, Georges-Henri Journal of Computational Physics, Vol. 229, Issue 9 https://doi.org/10.1016/j.jcp.2010.01.004	journal	May 2010
Simulations of single and multiple swimmers with non-divergence free deforming geometries Gazzola, Mattia; Chatelain, Philippe; van Rees, Wim M. Journal of Computational Physics, Vol. 230, Issue 19 https://doi.org/10.1016/j.jcp.2011.04.025	journal	August 2011
A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations Seo, Jung Hee; Mittal, Rajat Journal of Computational Physics, Vol. 230, Issue 19 https://doi.org/10.1016/j.jcp.2011.06.003	journal	August 2011
An accurate moving boundary formulation in cut-cell methods Schneiders, Lennart; Hartmann, Daniel; Meinke, Matthias Journal of Computational Physics, Vol. 235 https://doi.org/10.1016/j.jcp.2012.09.038	journal	February 2013
Numerical simulation of fluid–structure interaction with the volume penalization method Engels, Thomas; Kolomenskiy, Dmitry; Schneider, Kai Journal of Computational Physics, Vol. 281 https://doi.org/10.1016/j.jcp.2014.10.005	journal	January 2015
MRAG-I2D: Multi-resolution adapted grids for remeshed vortex methods on multicore architectures Rossinelli, Diego; Hejazialhosseini, Babak; van Rees, Wim Journal of Computational Physics, Vol. 288 https://doi.org/10.1016/j.jcp.2015.01.035	journal	May 2015
Strongly coupled dynamics of fluids and rigid-body systems with the immersed boundary projection method Wang, Chengjie; Eldredge, Jeff D. Journal of Computational Physics, Vol. 295 https://doi.org/10.1016/j.jcp.2015.04.005	journal	August 2015
Bioinspired swimming simulations Bergmann, Michel; Iollo, Angelo Journal of Computational Physics, Vol. 323 https://doi.org/10.1016/j.jcp.2016.07.022	journal	October 2016
Immersed interface interpolation schemes for particle–mesh methods Marichal, Yves; Chatelain, Philippe; Winckelmans, Grégoire Journal of Computational Physics, Vol. 326 https://doi.org/10.1016/j.jcp.2016.09.027	journal	December 2016
A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies Nangia, Nishant; Johansen, Hans; Patankar, Neelesh A. Journal of Computational Physics, Vol. 347 https://doi.org/10.1016/j.jcp.2017.06.047	journal	October 2017
Fast immersed interface Poisson solver for 3D unbounded problems around arbitrary geometries Gillis, T.; Winckelmans, G.; Chatelain, P. Journal of Computational Physics, Vol. 354 https://doi.org/10.1016/j.jcp.2017.10.042	journal	February 2018
Development of immersed boundary computational aeroacoustic prediction capabilities for open-rotor noise Brehm, C.; Barad, M. F.; Kiris, C. C. Journal of Computational Physics, Vol. 388 https://doi.org/10.1016/j.jcp.2019.02.011	journal	July 2019
Simulations of propelling and energy harvesting articulated bodies via vortex particle-mesh methods Bernier, Caroline; Gazzola, Mattia; Ronsse, Renaud Journal of Computational Physics, Vol. 392 https://doi.org/10.1016/j.jcp.2019.04.036	journal	September 2019
A 2D immersed interface Vortex Particle-Mesh method Gillis, T.; Marichal, Y.; Winckelmans, G. Journal of Computational Physics, Vol. 394 https://doi.org/10.1016/j.jcp.2019.05.033	journal	October 2019
An immersed boundary fluid–structure interaction method for thin, highly compliant shell structures Boustani, Jonathan; Barad, Michael F.; Kiris, Cetin C. Journal of Computational Physics, Vol. 438 https://doi.org/10.1016/j.jcp.2021.110369	journal	August 2021
A remeshed vortex method for mixed rigid/soft body fluid–structure interaction Bhosale, Yashraj; Parthasarathy, Tejaswin; Gazzola, Mattia Journal of Computational Physics, Vol. 444 https://doi.org/10.1016/j.jcp.2021.110577	journal	November 2021
An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies Gabbard, James; Gillis, Thomas; Chatelain, Philippe Journal of Computational Physics, Vol. 464 https://doi.org/10.1016/j.jcp.2022.111339	journal	September 2022
Two-degree-of-freedom flow-induced vibrations on isolated and tandem cylinders with varying natural frequency ratios Bao, Yan; Huang, Cheng; Zhou, Dai Journal of Fluids and Structures, Vol. 35 https://doi.org/10.1016/j.jfluidstructs.2012.08.002	journal	November 2012
Numerical analysis of two-dimensional motion of a freely falling circular cylinder in an infinite fluid Namkoong, Kak; Yoo, Jung Yul; Choi, Hyoung G. Journal of Fluid Mechanics, Vol. 604 https://doi.org/10.1017/S0022112008001304	journal	May 2008
Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity–wake interference region Borazjani, Iman; Sotiropoulos, Fotis Journal of Fluid Mechanics, Vol. 621 https://doi.org/10.1017/S0022112008004850	journal	February 2009
High-resolution simulations of the flow around an impulsively started cylinder using vortex methods Koumoutsakos, P.; Leonard, A. Journal of Fluid Mechanics, Vol. 296 https://doi.org/10.1017/S0022112095002059	journal	August 1995
Immersed interface methods for moving interface problems Li, Zhilin Numerical Algorithms, Vol. 14, Issue 4, p. 269-293 https://doi.org/10.1023/A:1019173215885	journal	January 1997
An efficient explicit jump high-order compact immersed interface approach for transient incompressible viscous flows Singhal, Raghav; Kalita, Jiten C. Physics of Fluids, Vol. 34, Issue 10 https://doi.org/10.1063/5.0107308	journal	October 2022
Immersed boundary method for the simulation of heat transfer and fluid flow based on vorticity–velocity formulation Soltani, Elshan; Ghomizad, Mehdi Badri Numerical Heat Transfer, Part B: Fundamentals, Vol. 70, Issue 1 https://doi.org/10.1080/10407790.2016.1173463	journal	June 2016
MURPHY---A Scalable Multiresolution Framework for Scientific Computing on 3D Block-Structured Collocated Grids Gillis, Thomas; van Rees, Wim M. SIAM Journal on Scientific Computing, Vol. 44, Issue 5 https://doi.org/10.1137/21M141676X	journal	September 2022
Immersed Methods for Fluid–Structure Interaction Griffith, Boyce E.; Patankar, Neelesh A. Annual Review of Fluid Mechanics, Vol. 52, Issue 1 https://doi.org/10.1146/annurev-fluid-010719-060228	journal	January 2020
Wake-Induced Oscillatory Paths of Bodies Freely Rising or Falling in Fluids Ern, Patricia; Risso, Frédéric; Fabre, David Annual Review of Fluid Mechanics, Vol. 44, Issue 1 https://doi.org/10.1146/annurev-fluid-120710-101250	journal	January 2012
Immersed Boundary Methods Mittal, Rajat; Iaccarino, Gianluca Annual Review of Fluid Mechanics, Vol. 37, Issue 1 https://doi.org/10.1146/annurev.fluid.37.061903.175743	journal	January 2005
A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains Li, Zhilin; Wang, Cheng Communications in Mathematical Sciences, Vol. 1, Issue 1 https://doi.org/10.4310/CMS.2003.v1.n1.a11	journal	January 2003