A positioning algorithm for SPH ghost particles in smoothly curved geometries

Abstract An algorithm to place ghost particles across the domain boundary in the context of Smoothed Particle Hydrodynamics (SPH) is derived from basic principles, and constructed for several simple, three-dimensional, geometries. The performance of the algorithm is compared against the more commonly used “mirrored with respect to the local tangent plane” approach and shown to converge to it whenever the distance of the particles to the reflecting boundary is much smaller than a local measure of the surface’s curvature. The algorithm is demonstrated, tested and compared against the usual approach via simulations of a compressible flow around a cylinder, and the numerical cost of implementing it is addressed. We conclude that use of ghost particles to enforce boundary conditions is not only viable in the presence of smoothly curved boundaries, but more robust than the usual method for low-resolution scenarios.

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

[2]  Daniel J. Price.  Smoothed particle hydrodynamics and magnetohydrodynamics , 2010, J. Comput. Phys..

[3]  Stephan Rosswog,et al.  Astrophysical smooth particle hydrodynamics , 2009, 0903.5075.

[4]  Raúl Sánchez,et al.  ALARIC: An algorithm for constructing arbitrarily complex initial density distributions with low particle noise for SPH/SPMHD applications , 2017, Comput. Phys. Commun..

[5]  Federico A. Stasyszyn,et al.  A vector potential implementation for smoothed particle magnetohydrodynamics , 2014, J. Comput. Phys..

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

[7]  W. Dehnen,et al.  Improving convergence in smoothed particle hydrodynamics simulations without pairing instability , 2012, 1204.2471.

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

[9]  Wing Kam Liu,et al.  Meshfree and particle methods and their applications , 2002 .

[10]  Daniel J. Price,et al.  Phantom: A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics , 2017, Publications of the Astronomical Society of Australia.

[11]  Zhen Chen,et al.  An SPH model for multiphase flows with complex interfaces and large density differences , 2015, J. Comput. Phys..

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

[13]  Afzal Suleman,et al.  SPH with the multiple boundary tangent method , 2009 .

[14]  Joe J. Monaghan,et al.  SPH particle boundary forces for arbitrary boundaries , 2009, Comput. Phys. Commun..

[15]  Rony Keppens,et al.  GRADSPH: A parallel smoothed particle hydrodynamics code for self-gravitating astrophysical fluid dynamics , 2009, Comput. Phys. Commun..

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