An accurate SPH Volume Adaptive Scheme for modeling strongly-compressible multiphase flows. Part 2: Extension of the scheme to cylindrical coordinates and simulations of 3D axisymmetric problems with experimental validations

Abstract The present work is dedicated to extending the strongly-compressible multiphase SPH Volume Adaptive Scheme (see [22] ) from Cartesian to cylindrical polar coordinates for addressing axisymmetric problems. By omitting the gradient in the circumferential direction, an Axisymmetric-SPH model is developed. Three-dimensional axisymmetric problems including rising bubbles, expanding or collapsing bubbles are conveniently and efficiently simulated using the proposed Axisymmetric-SPH model. Contrary to the purely three-dimensional SPH model established in Cartesian coordinates, with the axisymmetric model, sufficient particle resolutions can be easily adopted to reach converged simulations of complex problems. Axisymmetric-SPH results are validated either using experimental data or other numerical results. In the Axisymmetric-SPH model, a convenient and effective way of avoiding singularity at the axis is presented. In addition, the Volume Adaptive Scheme (VAS), originally developed for compressible flow simulations with large volume variations in Cartesian coordinates, is shown to be a crucial tool to adjust particle volumes in the Axisymmetric-SPH model for all flow cases, including both weakly-compressible and strongly-compressible flows.

[1]  D. García-Senz,et al.  Axisymmetric smoothed particle hydrodynamics with self-gravity , 2008, 0810.1918.

[2]  Furen Ming,et al.  Numerical simulation of interactions between free surface and rigid body using a robust SPH method , 2015 .

[3]  M. Fivel,et al.  SPH modelling of a cavitation bubble collapse near an elasto-visco-plastic material , 2019, Journal of the Mechanics and Physics of Solids.

[4]  Larry D. Libersky,et al.  Cylindrical smoothed particle hydrodynamics , 1993 .

[5]  David Le Touzé,et al.  An accurate SPH Volume Adaptive Scheme for modeling strongly-compressible multiphase flows. Part 1: Numerical scheme and validations with basic 1D and 2D benchmarks , 2020, Journal of Computational Physics.

[6]  Yuning Zhang,et al.  Numerical study of a laser generated cavitation bubble based on FVM and CLSVOF method , 2019, IOP Conference Series: Earth and Environmental Science.

[7]  A. Zhang,et al.  Jet development and impact load of underwater explosion bubble on solid wall , 2020, Applied Ocean Research.

[8]  D. Lohse,et al.  Modelling large scale airgun-bubble dynamics with highly non-spherical features , 2020, International Journal of Multiphase Flow.

[9]  Shuaijun Li,et al.  Bubble interactions and bursting behaviors near a free surface , 2019, Physics of Fluids.

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

[11]  Leigh Brookshaw.  Smooth particle hydrodynamics in cylindrical coordinates , 2003 .

[12]  Jian Wang,et al.  Stable axisymmetric SPH formulation with no axis singularity , 2016 .

[13]  Salvatore Marrone,et al.  The δplus-SPH model: Simple procedures for a further improvement of the SPH scheme , 2017 .

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

[15]  P. Helluy,et al.  Comparison and validation of compressible flow simulations of laser-induced cavitation bubbles , 2009 .

[16]  Rushdie Ibne Islam,et al.  Extending Incompressible SPH framework for simulation of axisymmetric free-surface flows , 2017 .

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

[18]  A. M. Zhang,et al.  Improved three-dimensional bubble dynamics model based on boundary element method , 2015, J. Comput. Phys..

[19]  Marianne Gjestvold Omang,et al.  SPH in spherical and cylindrical coordinates , 2006, J. Comput. Phys..

[20]  Furen Ming,et al.  An SPH modeling of bubble rising and coalescing in three dimensions , 2015 .

[21]  L. Chiron,et al.  Analysis and improvements of Adaptive Particle Refinement (APR) through CPU time, accuracy and robustness considerations , 2018, J. Comput. Phys..

[22]  M. Fivel,et al.  Bubble collapse induced cavitation erosion: Plastic strain and energy dissipation investigations , 2020, Journal of the Mechanics and Physics of Solids.

[23]  M. Fivel,et al.  An axisymmetric solid SPH solver with consistent treatment of particles close to the symmetry axis , 2020, Computational Particle Mechanics.

[24]  M. Sussman.  A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles , 2003 .

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

[26]  Furen Ming,et al.  Numerical simulation of column charge underwater explosion based on SPH and BEM combination , 2013 .

[27]  Hua Liu,et al.  Cylindrical Smoothed Particle Hydrodynamics Simulations of Water Entry , 2019, Journal of Fluids Engineering.

[28]  A. Zhang,et al.  Interaction of clustered air gun bubbles in marine prospecting , 2019, Ocean Engineering.

[29]  Nikolaus A. Adams,et al.  Numerical modelling and investigation of symmetric and asymmetric cavitation bubble dynamics , 2012 .