An improved particle smoothing procedure for Laplacian operator in a randomly scattered cloud

References

• L. B. Lucy, Numerical Approach to the Testing of the Fission Hypothesis, Astronomical J., vol. 82, pp. 1013–1024, 1977.
   Web of Science ®Google Scholar
• R. A. Gingold, J. J. Monaghan, Smoothed Particle Hydrodynamics—Theory and Application to Non-spherical Stars, Mon. Not. R. Astron. Soc., vol. 118, pp. 357–89, 1977.
   Google Scholar
• J. J. Monaghan, Simulating Free Surface Flows with SPH, J. Comput. Phys., vol. 110, pp. 399–406, 1994.
   Web of Science ®Google Scholar
• H. Gotoh, T. Sakai, Lagrangian Simulation of Breaking Waves using Particle Method, Coastal Eng. J., vol. 41, pp. 303–326, 1999.
   Google Scholar
• S. Li, W. K. Liu, Meshfree and Particle Methods and their Applications, ASME J. Appl. Mech. Rev., vol. 55, pp. 1–34, 2002.
   Google Scholar
• C. S. Chew, K. S. Yeo, C. Shu, A Generalized Finite-difference (GFD) ALE Scheme for Incompressible Flows Around Moving Solid Bodies on Hybrid Meshfree-Cartesian Grids, J. Comput. Phys., vol. 218, pp. 510–548, 2006.
   Web of Science ®Google Scholar
• A. J. Chorin, Numerical Study of Slightly Viscous Flow, J. Fluid Mech., vol. 57, pp. 785–796, 1973.
   Web of Science ®Google Scholar
• J. J. Monaghan, Particle Methods for Hydrodynamics, Comp. Phys. Rep. vol. 3, pp. 71–124, 1985.
   Web of Science ®Google Scholar
• J. U. Brackbill, Particle Methods, Int. J. Numer. Meth. Fluids, vol. 47, pp. 693–705, 2005.
   Web of Science ®Google Scholar
• G. R. Liu, M. B. Liu, Smoothed Particle Hydrodynamics, World Scientific Publishing Co., Singapore, 2003.
   Google Scholar
• S. Koshizuka, Y. Oka, Moving-particle Semi-implicit Method for Fragmentation of Incompressible Fluid, Nucl. Sci. Eng., vol. 123, pp. 421–434, 1996.
   Web of Science ®Google Scholar
• C. L. Huang, T. W. H. Sheu, T. Ishikawa, T. Yamaguchi, Development of a Particle Interaction Kernel for Convection–Diffusion Scalar Transport Equation, Numer. Heat Transfer B, vol. 60, pp. 96–115, 2011.
   Web of Science ®Google Scholar
• S. J. Cumming, M. Rudman, An SPH Projection Method, J. Comput. Phys. vol. 152, pp. 584–607, 1999.
   Web of Science ®Google Scholar
• E.-S. Lee, C. Mouline, R. Xu, D. Violeau, D. Laurence, P. Stanley, Comparisons of Weakly Compressible and Truly Incompressible Algorithm for the SPH Mesh Free Particle Method, J. Comput. Phys., vol. 227, pp. 8417–8436, 2008.
   Web of Science ®Google Scholar
• Y.-H. Hwang, A Moving Particle Method with Embedded Pressure Mesh (MPPM) for Incompressible Flow Calculations, Numer. Heat Transfer B, vol. 60, pp. 370–398, 2011.
   Web of Science ®Google Scholar
• R. Kech, D. Hietel, A Projection Technique for Incompressible Flow in the Meshless Finite Volume Particle Method, Adv. Comput. Math., vol. 23, pp. 143–169, 2005.
   Web of Science ®Google Scholar
• A. K. Chaniotis, D. Poulikakos, P. Koumoutsakos, Re-meshed Smoothed Particle Hydrodynamics for the Simulation of Viscous and Heat Conducting Flows, J. Comput. Phys., vol. 182, pp. 67–90, 2002.
   Web of Science ®Google Scholar
• B. Naryoles, G. Touzot, P. Villon, Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elements, Comput. Mech., vol. 10, pp. 307–318, 1992.
   Google Scholar
• Y. -H. Hwang, Assessment of Diffusion Operators in a Novel Moving Particle Method, Numer. Heat Transfer B, vol. 61, pp. 329–368, 2012.
   Web of Science ®Google Scholar
• S. Zhang, K. Morita, K. Fukuda, N. Shirakawa, An Improved MPS Method for Numerical Simulations of Convective Heat Transfer Problems, Int. J. Numer. Meth. Fluids, vol. 51, pp. 31–47, 2006.
   Web of Science ®Google Scholar
• Y. -H. Hwang, Smoothing Difference Scheme in a Moving Particle Method, Numer. Heat Transfer B, vol. 60, pp. 203–234, 2011.
   Web of Science ®Google Scholar
• Y. -H. Hwang, Implementation of Point-implicit Diffusion Operator in a Moving Particle Method (MPPM), Numer. Heat Transfer B Fund., vol. 62, pp. 315–340, 2012.
   Web of Science ®Google Scholar
• Y. -H. Hwang, H. -S. Huang, Simulations of the Incompressible Axisymmetric Flow with a Moving Particle Method (MPPM), Numer. Heat Transfer B Fund., vol. 63, pp. 139–166, 2013.
   Web of Science ®Google Scholar
• E. Erturk, B. Dursum, Numerical Solutions of 2-D Steady Incompressible in a Driven Skewed Cavity, ZAMM-J. Appl. Math. Mech., vol. 87, pp. 377–392, 2007.
   Web of Science ®Google Scholar
• U. Ghia, K. N. Ghia, C. T. Shin, High-resolutions for Incompressible Flow using the Navier-Stokes Equations and a Multigrid Method, J. Comput. Phys., vol. 48, pp. 387–411, 1982.
   Web of Science ®Google Scholar
• B. F. Armaly, F. Durst, J. C. F. Pereira, B. Schoung, Experimental and Theoretical Investigation of Backward-facing Step Flow. J. Fluid Mech., vol. 127, pp. 473–496, 1983.
   Web of Science ®Google Scholar
• Y. -H. Hwang, Development of a Compact and Accurate Discretization for Incompressible Navier-Stokes Equations Based on an Equation-solving Solution Gradient, Part III: Fluid Flow Simulations on Staggered Polygonal Grids, Numer. Heat Transfer B, vol. 58, pp. 193–215, 2010.
   Web of Science ®Google Scholar