Particle Methods for Viscous Flows: Analogies and Differences Between the SPH and DVH Methods

In this work two particle methods are studied in the context of viscous flows. The first one is a Vortex Particle Method, called Diffused Vortex Hydrodynamics (DVH), recently developed to simulate complex viscous flows at medium and high Reynolds regimes. This method presents some similarities with the SPH model and its Lagrangian meshless nature, even if it is based on a different numerical approach. Advantages and drawbacks of the two methods have been previously studied in Colagrossi et al. [1] from a theoretical point of view and in Rossi et al. [2], where these particle methods have been tested on selected benchmarks. Further investigations are presented in this article highlighting analogies and differences between the two particle models.

[1]  J. Morris,et al.  Modeling Low Reynolds Number Incompressible Flows Using SPH , 1997 .

[2]  J. Monaghan SPH without a Tensile Instability , 2000 .

[3]  D. Violeau,et al.  Dissipative forces for Lagrangian models in computational fluid dynamics and application to smoothed-particle hydrodynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  J. Monaghan Simulating Free Surface Flows with SPH , 1994 .

[5]  Andrea Colagrossi,et al.  Numerical simulation of 2D-vorticity dynamics using particle methods , 2015, Comput. Math. Appl..

[6]  Ted Belytschko,et al.  Stability Analysis of Particle Methods with Corrected Derivatives , 2002 .

[7]  Jinchao Xu,et al.  A scalable consistent second-order SPH solver for unsteady low Reynolds number flows , 2015 .

[8]  S. Attaway,et al.  Smoothed particle hydrodynamics stability analysis , 1995 .

[9]  Jean-Paul Vila,et al.  ON PARTICLE WEIGHTED METHODS AND SMOOTH PARTICLE HYDRODYNAMICS , 1999 .

[10]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[11]  Nathan J. Quinlan,et al.  Extension of the finite volume particle method to viscous flow , 2009, J. Comput. Phys..

[12]  A. Colagrossi,et al.  Nonlinear water wave interaction with floating bodies in SPH , 2013 .

[13]  Salvatore Marrone,et al.  Smoothed-particle-hydrodynamics modeling of dissipation mechanisms in gravity waves. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  P. Meakin,et al.  A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and the two-dimensional Rayleigh-Taylor instability , 2005 .

[15]  M. Lastiwka,et al.  Truncation error in mesh‐free particle methods , 2006 .

[16]  Salvatore Marrone,et al.  An accurate SPH modeling of viscous flows around bodies at low and moderate Reynolds numbers , 2013, J. Comput. Phys..

[17]  Salvatore Marrone,et al.  A measure of spatial disorder in particle methods , 2014, Comput. Phys. Commun..

[18]  J. Brackbill,et al.  Flip: A low-dissipation, particle-in-cell method for fluid flow , 1988 .

[19]  S. J. Lind,et al.  Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves , 2012, J. Comput. Phys..

[20]  David Le Touzé,et al.  Adaptive particle refinement and derefinement applied to the smoothed particle hydrodynamics method , 2014, J. Comput. Phys..

[21]  Ted Belytschko,et al.  A unified stability analysis of meshless particle methods , 2000 .

[22]  Pep Español,et al.  Smoothed dissipative particle dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  A. Colagrossi,et al.  Particles for fluids: SPH versus vortex methods , 2014 .

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

[25]  Salvatore Marrone,et al.  Simulating 2D open-channel flows through an SPH model , 2012 .

[26]  Rui Xu,et al.  Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method , 2008, J. Comput. Phys..

[27]  E. Rossi,et al.  The Diffused Vortex Hydrodynamics Method , 2015 .

[28]  P. W. Randles,et al.  Normalized SPH with stress points , 2000 .

[29]  Salvatore Marrone,et al.  Numerical diffusive terms in weakly-compressible SPH schemes , 2012, Comput. Phys. Commun..

[30]  Salvatore Marrone,et al.  Particle packing algorithm for SPH schemes , 2012, Comput. Phys. Commun..

[31]  A. Colagrossi,et al.  Energy-decomposition analysis for viscous free-surface flows. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Andrea Colagrossi,et al.  A critical investigation of smoothed particle hydrodynamics applied to problems with free‐surfaces , 2013 .

[33]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[34]  A. Colagrossi,et al.  Prediction of energy losses in water impacts using incompressible and weakly compressible models , 2015 .

[35]  J. Monaghan,et al.  Shock simulation by the particle method SPH , 1983 .

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

[37]  John S. Anagnostopoulos,et al.  An improved MUSCL treatment for the SPH‐ALE method: comparison with the standard SPH method for the jet impingement case , 2013 .

[38]  Giorgio Graziani,et al.  From a boundary integral formulation to a vortex method for viscous flows , 1995 .

[39]  A. Colagrossi,et al.  Theoretical considerations on the free-surface role in the smoothed-particle-hydrodynamics model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  I. Gladwell,et al.  A VISCOUS SPLITTING ALGORITHM APPLIED TO LOW REYNOLDS-NUMBER FLOWS ROUND A CIRCULAR CYLINDER , 1989 .

[41]  Francis Leboeuf,et al.  Free surface flows simulations in Pelton turbines using an hybrid SPH-ALE method , 2010 .

[42]  Damien Violeau,et al.  Optimal time step for incompressible SPH , 2015, J. Comput. Phys..

[43]  Sivakumar Kulasegaram,et al.  Remarks on tension instability of Eulerian and Lagrangian corrected smooth particle hydrodynamics (CSPH) methods , 2001 .

[44]  Rui Xu,et al.  Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach , 2009, J. Comput. Phys..

[45]  M. Antuono,et al.  Conservation of circulation in SPH for 2D free‐surface flows , 2013 .

[46]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[47]  R. Fatehi,et al.  Error estimation in smoothed particle hydrodynamics and a new scheme for second derivatives , 2011, Comput. Math. Appl..