Methods for controlling the local spatial and temporal resolution of vortex particle simulations of bluff body aerodynamics problems

Abstract This paper presents a novel adaptive solution strategy for vortex particle methods that allows the efficient resolution of multiple scales that are characteristic of flows around bluff bodies with small structural details. The efficiency of the method arises from maintaining a sufficiently high spatial numerical discretisation near the fluid-solid interface and a progressive coarsening away from the bodies and their structural details. The control of the particle map is achieved through remeshing based on high-order interpolation kernels and ensures an accurate representation of the flow features of different scales whose resolution is critical to an accurate computation of the pressures on the immersed structure subjected to separated flows. As the required time step of the time integration is directly related to the spatial resolution, the adaptivity is further enhanced by a temporal adaptivity realized through a sub-stepping technique for controlling the frequency at which the particle convection and diffusion steps are performed. The validation of the proposed technique is performed by simulations of the impulsively started flow past a circular cylinder at Reynolds number 3000, where both the spatial and the temporal strategies are at first independently studied and then combined to full adaptivity. A substantially higher computational efficiency compared to equally accurate non-adaptive simulations is reported. Further studies of accuracy and efficiency are performed by simulating the flow past the cross section of a bridge arch geometry featuring small structural details. Solution properties studied include the resolution of local velocity profiles and global aerodynamic coefficients. These reveal how the application of the full adaptive strategy enables for the accurate and efficient prediction of the flow features. The results indicate speed-ups of up to factor 4 to 5 when comparing the new approach to the classical Vortex Particle Method.

[1]  Georges-Henri Cottet,et al.  Blending Finite-Difference and Vortex Methods for Incompressible Flow Computations , 2000, SIAM J. Sci. Comput..

[2]  Guido Morgenthal,et al.  An immersed interface method for the vortex-in-cell algorithm , 2007 .

[3]  A. Chorin.  Numerical study of slightly viscous flow , 1973, Journal of Fluid Mechanics.

[4]  A. Larsen,et al.  Two dimensional discrete vortex method for application to bluff body aerodynamics , 1997 .

[5]  P. Koumoutsakos.  MULTISCALE FLOW SIMULATIONS USING PARTICLES , 2005 .

[6]  Guido Morgenthal,et al.  An immersed interface method for the Vortex-In-Cell algorithm , 2007 .

[7]  Luca Bruno,et al.  Importance of Deck Details in Bridge Aerodynamics , 2002 .

[8]  Heinz-Otto Kreiss,et al.  On the smallest scale for the incompressible Navier-Stokes equations , 1989, Theoretical and Computational Fluid Dynamics.

[9]  Petros Koumoutsakos,et al.  Inviscid Axisymmetrization of an Elliptical Vortex , 1997 .

[10]  G. Pedrizzetti,et al.  Vortex Dynamics , 2011 .

[11]  Guido Morgenthal,et al.  Aerodynamic Behaviour of Very Long Cable-Stayed Bridges during Construction , 2010 .

[12]  E. Süli,et al.  An introduction to numerical analysis , 2003 .

[13]  Weimin Han,et al.  Numerical Solution of Ordinary Differential Equations: Atkinson/Numerical , 2009 .

[14]  R. Krasny.  A study of singularity formation in a vortex sheet by the point-vortex approximation , 1986, Journal of Fluid Mechanics.

[15]  Thomas Y. Hou,et al.  Convergence of a variable blob vortex method for the Euler and Navier-Stokes equations , 1990 .

[16]  Palle Thoft-Christensen,et al.  Active flap control of long suspension bridges , 2001 .

[17]  Iraj Mortazavi,et al.  Numerical convergence of the random vortex method for complex flows , 1996 .

[18]  Guido Morgenthal,et al.  Flow reproduction using Vortex Particle Methods for simulating wake buffeting response of bluff structures , 2016 .

[19]  P. Raviart.  An analysis of particle methods , 1985 .

[20]  J. Monaghan,et al.  Extrapolating B splines for interpolation , 1985 .

[21]  Guido Morgenthal,et al.  Advances in Numerical Bridge Aerodynamics and Recent Applications , 2005 .

[22]  Guido Morgenthal,et al.  A GPU-accelerated pseudo-3D vortex method for aerodynamic analysis , 2014 .

[23]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments , 2010 .

[24]  J. Sethian,et al.  Validation study of vortex methods , 1988 .

[25]  J. Wu.  Theory for Aerodynamic Force and Moment in Viscous Flows , 1981 .

[26]  G. Morgenthal,et al.  Vortex-Induced Vibrations on Cross Sections in Tandem Arrangement , 2014 .

[27]  G. Winckelmans,et al.  Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry , 2000 .

[28]  Petros Koumoutsakos,et al.  Vortex Methods: Theory and Practice , 2000 .

[29]  Ian Taylor,et al.  Numerical investigation of the effects of pedestrian barriers on aeroelastic stability of a proposed footbridge , 2004 .

[30]  P. G. Saffman,et al.  The calculation of large reynolds number two-dimensional flow using discrete vortices with random walk , 1977 .

[31]  Eric Darve,et al.  The Fast Multipole Method , 2000 .

[32]  P. Koumoutsakos,et al.  High-resolution simulations of the flow around an impulsively started cylinder using vortex methods , 1995, Journal of Fluid Mechanics.

[33]  Ole H. Hald,et al.  Convergence of Vortex methods for Euler's equations, III , 1987 .

[34]  M. J. Ryall,et al.  MANUAL OF BRIDGE ENGINEERING , 2000 .

[35]  G. Schewe.  On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers , 1983, Journal of Fluid Mechanics.

[36]  Y. Brenier.  A particle method for nonlinear reaction diffusion equations in first dimension , 1990 .

[37]  A GRID-FREE REDISTRIBUTION MODEL FOR A VORTEX METHOD AND TURBULENT FLOW ANALYSIS , 2006 .

[38]  Miguel A. Astiz,et al.  Wind-Induced Vibrations of the Alconétar Bridge, Spain , 2010 .

[39]  Georges-Henri Cottet,et al.  Multi-purpose regridding in vortex methods , 1999 .

[40]  Anil Date,et al.  Introduction to Computational Fluid Dynamics , 2023, essentials.

[41]  Chien-Cheng Chang,et al.  A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method , 1991, Journal of Fluid Mechanics.

[42]  Georges-Henri Cottet,et al.  Particle Methods for the One-Dimensional Vlasov–Poisson Equations , 1984 .

[43]  Takanori Ikeda,et al.  Prediction of aerodynamic characteristics of a box girder bridge section using the LES turbulence model , 2008 .