Influence of Smoothing Length and Virtual Particles on SPH Accuracy

 Abstract—Using a well known 2-D transient heat conduction benchmark, a parametric study is conducted to identify the best values for the smoothing length (h) as function of particles spacing in order to minimize the error in the temperature distribution particularly at the center of the domain when applying the Smooth Particle Hydrodynamics (SPH) algorithm. Also the effect of the virtual particles on the numerical solution has been investigated. The results showed that the predefined smoothing length can have significant influence on the accuracy of the prediction and using the optimum value leads to minimum error in temperature prediction values. The results obtained with and without virtual particles has been presented and compared with the analytical solution.

[1]  Kim F. Ferris,et al.  Lagrangian particle model for multiphase flows , 2009, Comput. Phys. Commun..

[2]  L. Libersky,et al.  High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response , 1993 .

[3]  A. Steinfeld,et al.  A diffusion-based approximate model for radiation heat transfer in a solar thermochemical reactor , 2007 .

[4]  Jianyu Tan,et al.  Least-Squares Collocation Meshless Approach for Coupled Radiative and Conductive Heat Transfer , 2006 .

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

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

[7]  I. V. Singh,et al.  A Meshfree Solution of Tow-Dimensional Potential Flow Problems , 2009 .

[8]  P. Cleary,et al.  Conduction Modelling Using Smoothed Particle Hydrodynamics , 1999 .

[9]  J. Monaghan,et al.  A refined particle method for astrophysical problems , 1985 .

[10]  W. Tao,et al.  Weighted Least-Squares Collocation Method ( WLSCM ) for 2-D and 3-D Heat Conduction Problems in Irregular Domains , 2011 .

[11]  Sadik Dost,et al.  Modeling Transient Heat Transfer Using SPH and Implicit Time Integration , 2007 .

[12]  Paul W. Cleary,et al.  Flow modelling in casting processes , 2002 .

[13]  J. Monaghan,et al.  Solidification using smoothed particle hydrodynamics , 2005 .

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

[15]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics: A Meshfree Particle Method , 2003 .

[16]  I. Singh,et al.  HEAT TRANSFER ANALYSIS OF TWO-DIMENSIONAL FINS USING MESHLESS ELEMENT FREE GALERKIN METHOD , 2003 .