SPH Numerical Modeling for Ballistic-Diffusive Heat Conduction

The classic Fourier heat diffusion theory, in general, does not apply to micro/nanoscale or ultrafast thermal processes, where the mean free path of the heat carriers is comparable to the system size and/or typical times are comparable to the carrier relaxation time. For these processes, the ballistic-diffusive equation is a good alternative. In this context, the smoothed particle hydrodynamics (SPH) method is further developed to solve the one-dimensional ballistic-diffusive equation, by using a boundary treatment technique based on the normalization property of the SPH smoothing kernel. The results indicate that the SPH is a reliable and accurate method capable of yielding correct temperature and heat flux representations in the ballistic-diffusive heat conduction regime.

[1]  G Chen,et al.  Ballistic-diffusive heat-conduction equations. , 2001, Physical review letters.

[2]  T. F. Miller,et al.  SIMULATION OF SHOCK-WAVE REFLECTION IN A ONE-DIMENSIONAL SHOCK TUBE USING SMOOTHED PARTICLE HYDRODYNAMICS , 1994 .

[3]  Kenneth E. Goodson,et al.  Heat Transfer Regimes in Microstructures , 1992 .

[4]  Gang Chen,et al.  Ballistic-Diffusive Equations for Transient Heat Conduction From Nano to Macroscales , 2002 .

[5]  S. Miyama,et al.  Numerical Simulation of Viscous Flow by Smoothed Particle Hydrodynamics , 1994 .

[6]  E. Müller,et al.  On the capabilities and limits of smoothed particle hydrodynamics , 1993 .

[7]  Petros Koumoutsakos,et al.  Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows , 2002 .

[8]  J. K. Chen, J. E. Beraun.  NUMERICAL STUDY OF ULTRASHORT LASER PULSE INTERACTIONS WITH METAL FILMS , 2001 .

[9]  Antonio C. M. Sousa,et al.  SPH simulation of transition to turbulence for planar shear flow subjected to a streamwise magnetic field , 2006, J. Comput. Phys..

[10]  D. B. Olfe,et al.  A modification of the differential approximation for radiative transfer. , 1967 .

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

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

[13]  K. Y. Lam,et al.  Constructing smoothing functions in smoothed particle hydrodynamics with applications , 2003 .

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

[15]  Certain anomalies in the analysis of hyperbolic heat conduction , 2002 .

[16]  Yuan Taur,et al.  Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation , 2005 .

[17]  H. Posch,et al.  Liquid drops and surface tension with smoothed particle applied mechanics , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  J. Monaghan,et al.  SPH simulation of multi-phase flow , 1995 .

[19]  J. K. Chen,et al.  NUMERICAL STUDY OF ULTRASHORT LASER PULSE INTERACTIONS WITH METAL FILMS , 2001 .

[20]  J. S. Halow,et al.  Smoothed particle hydrodynamics: Applications to heat conduction , 2003 .

[21]  Konstantinos Boulouchos,et al.  Remeshed smoothed particle hydrodynamics for the simulation of laminar chemically reactive flows , 2003 .

[22]  C. L. Tien,et al.  Heat transfer mechanisms during short-pulse laser heating of metals , 1993 .

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

[24]  L. Brookshaw,et al.  A Method of Calculating Radiative Heat Diffusion in Particle Simulations , 1985, Publications of the Astronomical Society of Australia.

[25]  Michael F. Modest,et al.  The modified differential approximation for radiative transfer in general three-dimensional media , 1989 .

[26]  M. Modest.  Modified differential approximation for radiative transfer in general three-dimensional media , 1989 .

[27]  Fangming Jiang,et al.  Analytical Solution for Hyperbolic Heat Conduction in a Hollow Sphere , 2005 .

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

[29]  Paul W. Cleary,et al.  Modelling confined multi-material heat and mass flows using SPH , 1998 .

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

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