A weakly compressible SPH method with WENO reconstruction

Abstract In this work, we improve a weakly-compressible SPH method which is based on our previous work [Zhang et al. J. Comput. Phys. (2017)] by employing a weighted essentially non-oscillatory (WENO) reconstruction. The key idea is to construct along each interacting particle pair a 4-point stencil and to apply a WENO reconstruction for determining the particle interaction with a low-dissipation Riemann solver. Several numerical examples on Taylor-Green vortex flow, dam break and non-linear liquid sloshing demonstrate that the method preserves the capability of producing smooth and accurate pressure fields of the original method and now achieves also very small numerical dissipation.

[1]  Andrea Colagrossi,et al.  A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH , 2009, Comput. Phys. Commun..

[2]  Ted Belytschko,et al.  Overview and applications of the reproducing Kernel Particle methods , 1996 .

[3]  Stephen Roberts,et al.  Explicit schemes for dam-break simulations , 2003 .

[4]  Bing Wang,et al.  An incremental-stencil WENO reconstruction for simulation of compressible two-phase flows , 2017, International Journal of Multiphase Flow.

[5]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[6]  Peter Stansby,et al.  The initial stages of dam-break flow , 1998, Journal of Fluid Mechanics.

[7]  Antonio Souto-Iglesias,et al.  Experimental investigation of dynamic pressure loads during dam break , 2013, 1308.0115.

[8]  Krish Thiagarajan,et al.  Study of liquid sloshing: numerical and experimental approach , 2011 .

[9]  J. Monaghan,et al.  SPH elastic dynamics , 2001 .

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

[11]  Nikolaus A. Adams,et al.  An incompressible multi-phase SPH method , 2007, J. Comput. Phys..

[12]  Michael Dumbser,et al.  A new 3D parallel SPH scheme for free surface flows , 2009 .

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

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

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

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

[17]  A. Colagrossi,et al.  Numerical simulation of interfacial flows by smoothed particle hydrodynamics , 2003 .

[18]  Stéphane Clain,et al.  High-accurate SPH method with Multidimensional Optimal Order Detection limiting , 2016 .

[19]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

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

[21]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[22]  Joseph John Monaghan,et al.  SPH and Riemann Solvers , 1997 .

[23]  Nikolaus A. Adams,et al.  A weakly compressible SPH method based on a low-dissipation Riemann solver , 2017, J. Comput. Phys..

[24]  Xiaoyang Xu.  An improved SPH approach for simulating 3D dam-break flows with breaking waves , 2016 .

[25]  Moubin Liu,et al.  A decoupled finite particle method for modeling incompressible flows with free surfaces , 2018, Applied Mathematical Modelling.

[26]  Nikolaus A. Adams,et al.  A multi-phase SPH method for macroscopic and mesoscopic flows , 2006, J. Comput. Phys..

[27]  Kazunari Iwasaki,et al.  Smoothed particle magnetohydrodynamics with a Riemann solver and the method of characteristics , 2011, 1106.3389.

[28]  P. Teuben,et al.  Athena: A New Code for Astrophysical MHD , 2008, 0804.0402.

[29]  Hakan Akyildiz,et al.  Experimental investigation of pressure distribution on a rectangular tank due to the liquid sloshing , 2005 .

[30]  Rene Kahawita,et al.  The SPH technique applied to free surface flows , 2006 .

[31]  Sergio Pirozzoli,et al.  Numerical Methods for High-Speed Flows , 2011 .

[32]  Nikolaus A. Adams,et al.  A generalized wall boundary condition for smoothed particle hydrodynamics , 2012, J. Comput. Phys..

[33]  Jean-Paul Vila,et al.  Renormalized Meshfree Schemes I: Consistency, Stability, and Hybrid Methods for Conservation Laws , 2008, SIAM J. Numer. Anal..

[34]  Jean-Paul Vila,et al.  Renormalized Meshfree Schemes II: Convergence for Scalar Conservation Laws , 2008, SIAM J. Numer. Anal..

[35]  C. Antoci,et al.  Numerical simulation of fluid-structure interaction by SPH , 2007 .

[36]  S. A. Medin,et al.  Smoothed Particle Hydrodynamics Using Interparticle Contact Algorithms , 2002 .

[37]  J. Monaghan.  Smoothed Particle Hydrodynamics and Its Diverse Applications , 2012 .

[38]  Nikolaus A. Adams,et al.  A family of high-order targeted ENO schemes for compressible-fluid simulations , 2016, J. Comput. Phys..

[39]  Riccardo Brunino,et al.  Hydrodynamic simulations with the Godunov smoothed particle hydrodynamics , 2011 .

[40]  L. Libersky,et al.  Smoothed Particle Hydrodynamics: Some recent improvements and applications , 1996 .

[41]  Michael Dumbser,et al.  A new class of Moving-Least-Squares WENO-SPH schemes , 2014, J. Comput. Phys..

[42]  J. K. Chen,et al.  A corrective smoothed particle method for boundary value problems in heat conduction , 1999 .

[43]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[44]  A. Colagrossi,et al.  δ-SPH model for simulating violent impact flows , 2011 .

[45]  Sergei Nayakshin,et al.  Kelvin-Helmholtz instabilities with Godunov smoothed particle hydrodynamics , 2010 .

[46]  V. Springel.  E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh , 2009, 0901.4107.

[47]  Wen Chen,et al.  A Contact SPH Method with High-Order Limiters for Simulation of Inviscid Compressible Flows , 2013 .

[48]  Jean-Paul Vila,et al.  SPH Renormalized Hybrid Methods for Conservation Laws: Applications to Free Surface Flows , 2005 .

[49]  Salvatore Marrone,et al.  Free-surface flows solved by means of SPH schemes with numerical diffusive terms , 2010, Comput. Phys. Commun..

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

[51]  Ivo F. Sbalzarini,et al.  PPM - A highly efficient parallel particle-mesh library for the simulation of continuum systems , 2006, J. Comput. Phys..

[52]  Murray Rudman,et al.  Comparative study on the accuracy and stability of SPH schemes in simulating energetic free-surface flows , 2012 .

[53]  Nikolaus A. Adams,et al.  A transport-velocity formulation for smoothed particle hydrodynamics , 2013, J. Comput. Phys..

[54]  Shu-ichiro Inutsuka.  Reformulation of Smoothed Particle Hydrodynamics with Riemann Solver , 2002 .

[55]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[56]  W. Benz.  Smooth Particle Hydrodynamics: A Review , 1990 .

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

[58]  Nikolaus A. Adams,et al.  Towards consistence and convergence of conservative SPH approximations , 2015, J. Comput. Phys..