Smoothed Particle Hydrodynamics method

Particle methods that require a predefinition of particles for their computations. Such methods require some kind of mesh to predefine the particles. Smoothed particle hydrodynamics method belongs to this category. 

In 1977, Lucy [1] and Gingold and Monaghan [2] independently introduced the so-called smoothed particle hydrodynamics method which is one of the oldest meshless methods. The method was originally developed for astrophysi-cal studies such as formation of asteroids and the evolution of galaxies and has now become a standard tool in this field. In recent years, SPH has been extensively used for various fluid flow problems including both compressible and incompressible flow regimes. The method has been recently used for simulation of the generalized non-Newtonian and viscoelastic fluid flow problems. The SPH method has been also... 

Mesh-free methods are used as an alternative to the mesh methods. One of them is the mesh-free Lagrangian smoothed-particle hydrodynamics method... 

J. S. Cintra and C. L. Tucker, Orthotropic closuere approximations for flow-induced fiber orientation, J. Rheol. 39, 1095-1122 (1995) C. V. Chaubal, A. Srinivasan, O. Egecioglu, and L. G. Leal, Smoothed particle hydrodynamics technique for the solution of kinetic theory problems. Part 1. Method, J. Non-Newtonian Fluid Mech. 70, 125-54 (1997). 

The smoothed-particle hydrodynamics (SPH) method is an empirical alternative to the two above discussed methods, since it is grid-free and the results are, therefore, independent of a prescribed coordinate system and numerical grid resolution. It is... 

Other methods include particle-based methods and also techniques that do not rely on the Navier-Stokes equation for flow solution. Particle-based methods are roughly divided into two main categories those that use particles in conjunction with a grid, namely, particle-in-cell (PIC) methods, and those that are massless, such as the smoothed particle hydrodynamics (SPH). The most striking feature of particle-based methods is their ease of implementation. They are essentially as easy to implement on 3D unstmcmred meshes as on 2D strucmred meshes. However, they are very demanding in terms of memory and processing power, which has caused their limited use in interfacial flows so far. 

The molecular dynamics, Monte Carlo methods, the Lagrangian probability density function (PDF) methods, and the Lattice Boltzmann (LBM) method are among these methods. Methods such as the smoothed particle hydrodynamics (SPH) and the vortex method initially developed as probabiUstic methods, but nowadays they are most frequently used as deterministic. 

The computational problems involving multi-million particle ensembles, found in modeling mesoscopic phenomena, were considered only recently as the typical problems. Rapid increase of computational power of modem processors and growing popularity of coarse-grained discrete particle methods, such as dissipative particle dynamics, fluid particle model, smoothed particle hydrodynamics and LEG, allow for the modehng of complex problems by using smaller shared-memory systems [101]. 

Among several numerical methods, the finite element method (FEM) is a robust and thoroughly developed method. However, the accuracy and efficiency of the method rely on the quality of meshes or elements. Usually the FEM user has to spend considerable time in mesh creation or in fixing mesh problems. Therefore, some efforts have also been made to explore the applicability of meshless methods, such as the Smoothed Particle Hydrodynamics (SPH) method. 

Lin B, Jin X, Zheng R, Costa FS, Fan Z (2004) 3D fiber orientation simulation for plastic injection molding. NUMIFORM 2004. AIP Conference Proceedings,vol 712, pp 282-287 Lipscomb DD II, Denn MM, Hur DU, Boger DV (1988) The flow of fiber suspension in complex geometry. J Non-Newtonian Fluid Mech 26 297-325 Liu GR, Liu MB (2003) Smoothed particle hydrodynamics, a meshfree particle method. World Scientific, Singapore... 

Particle-based simulation techniques include atomistic MD and coarse-grained molecular dynamics (CG-MD). Accelerated dynamics methods, such as hyperdynamics and replica exchange molecular dynamics (REMD), are very promising for circumventing the timescale problem characteristic of atomistic simulations. Structure and dynamics at the mesoscale level can be described within the framework of coarse-grained particle-based models using such methods as stochastic dynamics (SD), dissipative particle dynamics (DPD), smoothed-particle hydrodynamics (SPH), lattice molecular dynamics (LMD), lattice Boltzmann method (IBM), multiparticle collision dynamics (MPCD), and event-driven molecular dynamics (EDMD), also referred to as collision-driven molecular dynamics or discrete molecular dynamics (DMD). 

Cloutman, L.D. An evaluation of smoothed particle hydrodynamics. In Advances in the Free-Lagrange Method Trease, H.E., Fritts, M.J., Crowley, W.P., Eds. Springer Berlin, 1991. 

Vila, J.P. On Particle Weighted Methods and Smooth Particle Hydrodynamics. Mathematical Models and Methods in Applied Sciences 9(2), 161-209 (1999)... 

Abstract A numerical model is constructed for the viscoelastic phase separation in polymer solutions based upon the two-fluid model using the method of the smoothed-particle hydrodynamics. Computer simulations are carried out with this model in two dimensions and efiects of the stress relaxation time on morphology of domains are examined. It is observed that the more... 

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