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## On Discretization of Second-order Derivatives in Smoothed Particle Hydrodynamics

Citations: | 1 - 0 self |

### Citations

306 |
Smoothed particle hydrodynamics: theory and application to nonspherical stars”.
- Gingold, Monaghan
- 1977
(Show Context)
Citation Context ...hod, each computational point carries field variables (such as velocity, pressure, temperature, and etc) and moves with the fluid in time. SPH was first presented by Lucy [1] and Gingold and Monaghan =-=[2]-=- simultaneously in 1977 to simulate astrophysical problems. In 1982, Gingold and Monaghan [3] used it for non-dissipative compressible flows. In 1994 Monaghan [4] extended the SPH method to incompress... |

302 |
A numerical approach to the testing of the fission hypothesis,
- Lucy
- 1977
(Show Context)
Citation Context ...rangian approach. In this method, each computational point carries field variables (such as velocity, pressure, temperature, and etc) and moves with the fluid in time. SPH was first presented by Lucy =-=[1]-=- and Gingold and Monaghan [2] simultaneously in 1977 to simulate astrophysical problems. In 1982, Gingold and Monaghan [3] used it for non-dissipative compressible flows. In 1994 Monaghan [4] extended... |

122 |
Simulating free surface flows with SPH,"
- Monaghan
- 1994
(Show Context)
Citation Context ... by Lucy [1] and Gingold and Monaghan [2] simultaneously in 1977 to simulate astrophysical problems. In 1982, Gingold and Monaghan [3] used it for non-dissipative compressible flows. In 1994 Monaghan =-=[4]-=- extended the SPH method to incompressible free surface flows and it was successfully applied to low-Reynolds viscous flow [5], [6] and other problems in fluid dynamics, heat transfer, Authors are wit... |

75 |
Modeling low Reynolds number incompressible flows using SPH”.
- Morris, Fox, et al.
- 1997
(Show Context)
Citation Context ...[3] used it for non-dissipative compressible flows. In 1994 Monaghan [4] extended the SPH method to incompressible free surface flows and it was successfully applied to low-Reynolds viscous flow [5], =-=[6]-=- and other problems in fluid dynamics, heat transfer, Authors are with the Center of Excellence in Energy Conversion, School of Mechanical Engineering, Sharif University of Technology, Iran, emails: f... |

22 |
Smoothed Particle Hydrodynamics. Report on
- Monaghan
- 2005
(Show Context)
Citation Context ...cal Engineering, Sharif University of Technology, Iran, emails: fatehi@mech.sharif.edu , fayazbakhsh@mech.sharif.edu, mtmanzari@sharif.edu and solid mechanics. For a concise review of the method, see =-=[7]-=-. To evaluate first-order spatial derivative in SPH, a kernel interpolation is used. For second-order derivatives, three different schemes are frequently used; ”double summation scheme”, ”second-order... |

18 |
Numerical simulation of viscous flow by smoothed particle hydrodynamics,
- TAKEDA, MIYAMA, et al.
- 1994
(Show Context)
Citation Context ...ghan [3] used it for non-dissipative compressible flows. In 1994 Monaghan [4] extended the SPH method to incompressible free surface flows and it was successfully applied to low-Reynolds viscous flow =-=[5]-=-, [6] and other problems in fluid dynamics, heat transfer, Authors are with the Center of Excellence in Energy Conversion, School of Mechanical Engineering, Sharif University of Technology, Iran, emai... |

11 |
A new prescription for viscosity in Smoothed Particle Hydrodynamics”.
- Watkins, Bhattal, et al.
- 1996
(Show Context)
Citation Context ...ive (eqn. (3)) to 〈 ( ∂ K ∂u )〉 = 1 ψi N∑ j ( 〈 K ∂u ∂xp ∂xq 〉 − j ∂xp 〈 K ∂u ∂xp i 〉 ) i ∂Wij ∂xq where K is a diffusion coefficient. This formulation is used by Flebbe et al. [8] and Watkins et al. =-=[9]-=- to include physical viscosity in astrophysical problems and by Jeong et al. [10] for two-dimensional heat conduction problem. Also [11], [12], [13], [14], [15] used it to handle viscous term in low-R... |

4 |
Smoothed particle hydrodynamics: Applications to heat conduction”
- Jeong, Jhon, et al.
- 2003
(Show Context)
Citation Context ...p i 〉 ) i ∂Wij ∂xq where K is a diffusion coefficient. This formulation is used by Flebbe et al. [8] and Watkins et al. [9] to include physical viscosity in astrophysical problems and by Jeong et al. =-=[10]-=- for two-dimensional heat conduction problem. Also [11], [12], [13], [14], [15] used it to handle viscous term in low-Reynolds number incompressible flows. Since double summation scheme uses the value... |

3 |
estimates as a basis for general particle methods in hydrodynamics
- Kernel
- 1982
(Show Context)
Citation Context ...e, and etc) and moves with the fluid in time. SPH was first presented by Lucy [1] and Gingold and Monaghan [2] simultaneously in 1977 to simulate astrophysical problems. In 1982, Gingold and Monaghan =-=[3]-=- used it for non-dissipative compressible flows. In 1994 Monaghan [4] extended the SPH method to incompressible free surface flows and it was successfully applied to low-Reynolds viscous flow [5], [6]... |

3 |
Smoothed particle hydrodynamicsphysical viscosity and the simulation of accretion disks,"
- Flebbe, Münzel, et al.
- 1994
(Show Context)
Citation Context ...n for the first derivative (eqn. (3)) to 〈 ( ∂ K ∂u )〉 = 1 ψi N∑ j ( 〈 K ∂u ∂xp ∂xq 〉 − j ∂xp 〈 K ∂u ∂xp i 〉 ) i ∂Wij ∂xq where K is a diffusion coefficient. This formulation is used by Flebbe et al. =-=[8]-=- and Watkins et al. [9] to include physical viscosity in astrophysical problems and by Jeong et al. [10] for two-dimensional heat conduction problem. Also [11], [12], [13], [14], [15] used it to handl... |