SPH Numerical Modeling for Ballistic-Diffusive Heat Conduction

REFERENCES

• M. I. Flik , B. I. Choi , and K. E. Goodson , Heat Transfer Regimes in Microstructures , Trans. ASME, J. Heat Transfer , vol. 114 , pp. 666 – 674 , 1992 . [CSA]
   Web of Science ®Google Scholar
• C. Cattaneo , A Form of Heat Conduction Equation Which Eliminates the Paradox of Instantaneous Propagation , Compt. Rend. , vol. 247 , pp. 431 – 433 , 1958 . [CSA]
   Google Scholar
• A. Haji-Sheikh , W. J. Minkowycz , and E. M. Sparrow , Certain Anomalies in the Analysis of Hyperbolic Heat Conduction , Trans. ASME, J. Heat Transfer , vol. 124 , pp. 307 – 319 , 2002 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• F. Jiang and A. C. M. Sousa , Analytical Solution to Hyperbolic Heat Propagation in a Hollow Sphere , J. Thermophys. Heat Transfer , vol. 19 , pp. 595 – 598 , 2005 . [CSA]
   Web of Science ®Google Scholar
• G. Chen , Ballistic-Diffusive Equations for Transient Heat Conduction from Nano to Macroscales , Trans. ASME, J. Heat Transfer , vol. 124 , pp. 320 – 328 , 2002 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• G. Chen , Ballistic-Diffusive Heat Conduction Equations , Phys. Rev. Lett. , vol. 86 , pp. 2297 – 2300 , 2001 . [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• D. B. Olfe , A Modification of the Differential Approximation for Radiative Transfer , AIAA J. , vol. 5 , pp. 638 – 643 , 1967 . [CSA]
   Google Scholar
• M. F. Modest , The Modified Differential Approximation for Radiative Transfer in General Three-Dimensional Media , J. Thermophys. Heat Transfer , vol. 3 , pp. 283 – 288 , 1989 . [CSA]
   Google Scholar
• R. Yang , G. Chen , M. Laroche , and Y. Taur , Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation , Trans. ASME, J. Heat Transfer , vol. 127 , pp. 298 – 306 , 2005 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• R. A. Gingold and J. J. Monaghan , Smoothed Particle Hydrodynamics: Theory and Application to Non-spherical Stars , Mon. Not. R. Astron. Soc. , vol. 181 , pp. 375 – 398 , 1977 . [CSA]
   Web of Science ®Google Scholar
• L. B. Lucy , A Numerical Approach to the Testing of the Fission Hypothesis , Astron. J. , vol. 82 , pp. 1013 – 1024 , 1977 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• M. Steinmetz and E. Muller , On the Capabilities and Limits of Smoothed Particle Hydrodynamics , Astron. Astrophys. , vol. 268 , pp. 391 – 410 , 1992 . [CSA]
   Web of Science ®Google Scholar
• J. J. Monaghan , Smoothed Particle Hydrodynamics , Annu. Rev. Astron. Astrophys. , vol. 30 , pp. 543 – 574 , 1992 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• R. W. Randle and L. D. Libersky , Smoothed Particle Hydrodynamics: Some Recent Improvements and Applications , Comput. Met. Appl. M. , vol. 139 , pp. 375 – 408 , 1996 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• F. Jiang , M. C. A. Oliveira , and A. C. M. Sousa , SPH Simulation of Transition to Turbulence for Planar Shear Flow Subjected to a Streamwise Magnetic Field , Available at http://www.sciencedirect.com/science/journal/00219991 . [CSA]
   Google Scholar
• P. W. Cleary , Modeling Confined Multi-material Heat and Mass Flows Using SPH , Appl. Math. Model , vol. 22 , pp. 981 – 993 , 1998 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• A. K. Chaniotis , D. Poulikakos , and P. Koumoutsakos , Remeshed Smoothed Particle Hydrodynamics for the Simulation of Viscous and Heat Conducting Flow, J. Comput. Phys. , vol. 182, pp. 67–90, 2002. [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• J. P. Morris , P. J. Fox , and Y. Zhu , Modeling Low Reynolds Number Incompressible Flows Using SPH , J. Comput. Phys. , vol. 136 , pp. 214 – 226 , 1997 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• S. Nugent and H. A. Posch , Liquid Drops and Surface Tension with Smoothed Particle Applied Mechanics , Phys. Rev. E , vol. 62 , pp. 4968 – 4975 , 2000 . [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• J. J. Monaghan and A. Kocharyan , SPH Simulation of Multi-phase Flow , Comput. Phys. Commun. , vol. 87 , pp. 225 – 235 , 1995 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• A. K. Chaniotis , C. E. Frouzakis , J. C. Lee , A. G. Tomboulides , D. Poulikakos , and K. Boulouchos , Remeshed Smoothed Particle Hydrodynamics for the Simulation of Laminar Chemically Reactive Flows , J. Comput. Phys. , vol. 191 , pp. 1 – 17 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• C. S. McCormick and T. F. Miller , Simulation of Shock-Wave Reflection in a One-Dimensional Shock-Tube Using Smoothed Particle Hydrodynamics , Numer. Heat Transfer B , vol. 26 , pp. 473 – 488 , 1994 . [CSA]
   Web of Science ®Google Scholar
• J. K. Chen , J. E. Beraun , and T. C. Camey , A Corrective Smoothed Particle Method for Boundary Value Problems in Heat Conduction , Int. J. Numer. Meth. Eng. , vol. 46 , pp. 231 – 252 , 1999 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• J. H. Jeong , M. S. Jhon , J. S. Halow , and J. van Osdol , Smoothed Particle Hydrodynamics: Applications to Heat Conduction , Comput. Phys. Commun. , vol. 153 , pp. 71 – 84 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• P. W. Cleary and J. J. Monaghan , Conduction Modelling Using Smoothed Particle Hydrodynamics , J. Comput. Phys. , vol. 148 , pp. 227 – 264 , 1999 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• J. K. Chen and J. E. Beraun , Numerical Study of Ultrashort Laser Pulse Interactions with Metal Films , Numer. Heat Transfer A , vol. 40 , pp. 1 – 20 , 2001 . [CSA]
   Web of Science ®Google Scholar
• T. Q. Qiu and C. L. Tien , Heat Transfer Mechanisms during Short-Pulse Laser Heating of Metals , Trans. ASME, J. Heat Transfer , vol. 115 , pp. 835 – 841 , 1993 . [CSA]
   Web of Science ®Google Scholar
• L. Brookshaw , A Method of Calculating Radiative Heat Diffusion in Particle Simulations , Publ. Astron. Soc. Aust. , vol. 6 , pp. 207 – 210 , 1985 . [CSA]
   Google Scholar
• H. Takeda , S. Miyama , and M. Sekiya , Numerical Simulation of Viscous Flow by Smoothed Particle Hydrodynamics , Prog. Theor. Phys. , vol. 92 , pp. 939 – 960 , 1994 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• M. B. Liu , G. R. Liu , and K. Y. Lam , Constructing Smoothing Functions in Smoothed Particle Hydrodynamics with Applications , J. Comput. Appl. Math. , vol. 155 , pp. 263 – 284 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar