Development of a Particle Interaction Kernel for Convection-Diffusion Scalar Transport Equation

REFERENCES

• C. W. Hirt , A. A. Amsden , and J. L. Cook , An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds , J. Comput. Phys. , vol. 14 , pp. 227 – 253 , 1974 .
   Web of Science ®Google Scholar
• F. H. Harlow and J. E. Welch , Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with a Free Surface , Phys. Fluids , vol. 8 , pp. 2182 – 2189 , 1965 .
   Web of Science ®Google Scholar
• C. W. Hirt and B. D. Nichols , Volume of Fluid (VOF) Method for Dynamics of Free Boundaries , J. Comput. Phys. , vol. 39 , pp. 201 – 221 , 1981 .
   Web of Science ®Google Scholar
• S. Osher and R. P. Fedkiw , Level Set Methods: An Overview and Some Recent Results , J. Comput. Phys. , vol. 169 , pp. 463 – 502 , 2001 .
   Web of Science ®Google Scholar
• F. H. Harlow , A Machine Calculation Method for Hydrodynamic Problems , Los Alamos Scientific Laboratory Report LAMS-1956 , 1955 .
   Google Scholar
• L. B. Lucy , A Numerical Approach to the Testing of the Fission Hypothesis , Astr. J. , vol. 82 , pp. 1013 – 1024 , 1977 .
   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. J. , vol. 181 , pp. 375 – 389 , 1977 .
   Web of Science ®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
• S. Koshizuka , H. Tamako , and Y. Oka , A Particle Method for Incompressible Viscous Flow with Fluid Fragmentation , CFD Journal , vol. 4 , pp. 29 – 46 , 1995 .
   Google Scholar
• H. Y. Yoon , S. Koshizuka , and Y. Oka , A Particle-Gridless Hybrid Method for Incompressible Flows , Int. J. Numer. Meth. Fluids , vol. 30 , pp. 407 – 424 , 1999 .
   Web of Science ®Google Scholar
• J. Liu , S. Koshizuka , and Y. Oka , A Hybrid Particle-Mesh Method for Viscous, Incompressible Multiphase Flows , J. Comput. Phys. , vol. 202 , pp. 65 – 93 , 2005 .
   Web of Science ®Google Scholar
• B. Ataie-Ashtiani and L. Farhadi , A Stable Moving-Particle Semi-implicit Method for Free Surface Flows , Fluid Dynam. Res. , vol. 38 , pp. 241 – 256 , 2006 .
   Web of Science ®Google Scholar
• S. Hibi and K. Yabushita , A Study on Reduction of Unusual Pressure Fluctuation of MPS Method , J. Kansai Soc. N. A. Japan , vol. 241 , pp. 125 – 131 , 2004 .
   Google Scholar
• M. Sueyoshi , Validation of Numerical Code by a Particle Method for Violent Free-Surface Problems , Int. J. Offshore Polar Eng. , vol. 16 , pp. 261 – 267 , 2006 .
   Web of Science ®Google Scholar
• A. Khayyer and H. Gotoh , Development of CMPS Method for Accurate Water Surface Tracking in Breaking Waves , Coast Eng. J. , vol. 50 , pp. 179 – 207 , 2008 .
   Web of Science ®Google Scholar
• A. Khayyer and H. Gotoh , Modified Moving Particle Semi-implicit Methods for the Prediction of 2D Wave Impact Pressure , Coast. Eng. , vol. 56 , pp. 419 – 440 , 2009 .
   Web of Science ®Google Scholar
• M. Kondo and S. Koshizuka , Improvement of Stability in Moving Particle Semi-implicit Method , Int. J. Numer. Meth. Fluids , vol. 65 , pp. 638 – 654 , 2011 .
   Google Scholar
• S. Zhang , K. Morita , K. Fukuda , and 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
• T. Belytschko , Y. Krongaux , D. Organ , M. Fleming , and P. Krys , Meshless Methods: An Overview and Recent Developments , Comput. Meth. Appl. Mech. Eng. , vol. 139 , pp. 3 – 47 , 1996 .
   Web of Science ®Google Scholar
• S. Koshizuka and Y. Oka , Moving-Particle Semi-implicit Method for Fragmentation of Incompressible Fluids , Nucl. Sci. Eng. , vol. 123 , pp. 421 – 434 , 1996 .
   Web of Science ®Google Scholar
• S. Koshizuka , A. Nobe , and Y. Oka , Numerical Analysis of Breaking Waves Using the Moving Particle Semi-implicit Method, Int. J. Numer. Meth. Fluids , vol. 26, pp. 751–769, 1998.
   Web of Science ®Google Scholar
• A. Shakibaeinia and Y. C. Jin , A Weakly Compressible MPS Method for Modeling of Open-Boundary Free-Surface Flow , Int. J. Numer. Meth. Fluids , vol. 63 , pp. 1208 – 1232 , 2010 .
   Web of Science ®Google Scholar
• R. M. Smith and A. G. Hutton , The Numerical Treatment of Convection—A Performance Comparison of Current Methods , Int. J. Numer. Meth. Heat Transfer , vol. 5 , pp. 439 – 461 , 1982 .
   Google Scholar
• J. Zhang and J. J. Zhao , Truncation Error and Oscillation Property of the Combined Compact Difference Scheme , Appl. Math. Comput. , vol. 161 , pp. 241 – 251 , 2005 .
   Web of Science ®Google Scholar
• E. C. Gartland , Discrete Weighted Mean Approximation of a Model Convection-Diffusion Equation , SIAM J. Sci. Stat. Comput. , vol. 3 , pp. 460 – 472 , 1982 .
   Google Scholar
• M. M. Gupta , R. P. Manohar , and J. W. Stephenson , High-Order Difference Schemes For Two-Dimensional Elliptic Equations , Numer. Meth. Partial Differ. Eqs. , vol. 1 , pp. 71 – 80 , 1985 .
   Google Scholar