A consistent and fast weakly compressible smoothed particle hydrodynamics with a new wall boundary condition

International Journal for Numerical Methods in Fluids

Volumn 68, Issue 7, 2012, Pages 905-921

  Fatehi, R ^a,b   Manzari, M T ^a  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

^b PERSIAN GULF UNIVERSITY   (Iran)

Author keywords

Consistency; Navier Stokes equations; Smoothed particle hydrodynamics (SPH); Wall boundary condition; Weakly compressible

Indexed keywords

ANALYTICAL SOLUTIONS; BENCH-MARK PROBLEMS; CONSISTENCY; DISCRETIZATION SCHEME; FLOW EQUATIONS; INTERNAL FLOWS; MASS CONSERVATION EQUATIONS; NORMAL DIRECTION; NUMERICAL FILTERS; SMOOTHED PARTICLE HYDRODYNAMICS; SPATIAL DERIVATIVES; THROUGH WALLS; WALL BOUNDARY CONDITION; WEAKLY COMPRESSIBLE;

BENCHMARKING; BOUNDARY CONDITIONS; HYDRODYNAMICS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS;

INCOMPRESSIBLE FLOW;

EID: 84856405136     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2586     Document Type: Article

References (38)

1. Lucy LB. A numerical approach to the testing of fission hypothesis. Astrophysical Journal 1977; 82:1013-1020.
2. Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and application to nonspherical stars. Astrophysical Journal 1977; 181:275-389.
3. Monaghan JJ. Simulating free surface flows with SPH. Journal of Computational Physics 1994; 110:399-406.
4. Takeda H, Miyama SM, Sekiya M. Numerical simulation of viscous flow by smoothed particle hydrodynamics. Progress of Theoretical Physics 1994; 92(5):939-960.
5. Morris JP, Fox PJ, Zhu Y. Modeling low Reynolds number incompressible flows using SPH. Journal of Computational Physics 1997; 136(1):214-226.
6. Cleary PW. Modelling confined multi-material heat and mass flows using SPH. Applied Mathematical Modelling 1998; 22:981-993.
7. Gray JP, Monaghan JJ, Swift RP. SPH elastic dynamics. Computer Methods in Applied Mechanics and Engineering 2001; 190(49-50):6641-6662.
8. Monaghan JJ. Smoothed particle hydrodynamics. Reports on Progress in Physics 2005; 68:1703-1759.
9. Hu XY, Adams NA. A multi-phase SPH method for macroscopic and mesoscopic flows. Journal of Computational Physics 2006; 213(2):844-861.
10. Kajtar J, Monaghan JJ. SPH simulations of swimming linked bodies. Journal of Computational Physics 2008; 227(19):8568-8587.
11. Cummins SJ, Rudman M. An SPH projection method. Journal of Computational Physics 1999; 152(2):584-607.
12. Shao S, Lo EYM. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Advances in Water Resources 2003; 26(7):787-800.
13. Hosseini SM, Manzari MT, Hannani SK. A fully explicit three-step SPH, algorithm for simulation of non-Newtonian fluid flow. International Journal of Numerical Methods for Heat and Fluid Flow 2007; 17(7):715-735.
14. Ellero M, Serrano M, Espańol P. Incompressible smoothed particle hydrodynamics. Journal of Computational Physics 2007; 226(2):1731-1752.
15. Hu XY, Adams NA. An incompressible multi-phase SPH method. Journal of Computational Physics 2007; 227(1):264-278.
16. Lee ES, Moulinec C, Xu R, Violeau D, Laurence D, Stansby P. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. Journal of Computational Physics 2008; 227(10):8417-8436.
17. Monaghan JJ. On the problem of penetration in particle methods. Journal of Computational Physics 1989; 82(1):1-15.
18. Colagrossi A, Landrini M. Numerical simulation of interfacial flows by smoothed particle hydrodynamics. Journal of Computational Physics 2003; 191(2):448-475.
19. Antuono M, Colagrossi A, Marrone S, Molteni D. Free-surface flows solved by means of SPH schemes with numerical diffusive terms. Computer Physics Communications 2010; 181(3):532-549.
20. Ferrari A, Dumbser M, Toro EF, Armanini A. A new 3D parallel SPH scheme for free surface flows. Computers & Fluids 2009; 38(6):1203-1217.
21. Rhie CM, Chow WL. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal 1983; 21(11):1525-1532.
22. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139((1-4):3-47.
23. Batchelor GK. Introduction to Fluid Dynamics. Cambridge University Press: Cambridge, 1967.
24. Wendland H. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Advances in Computational Mathematics 1995; 4(1):389-396.
25. Di Lisio R, Grenier E, Pulvirenti M. The convergence of the SPH method. Computers and Mathematics with Applications 1998; 35(1-2):95-102.
26. Quinlan NJ, Basa M, Lastiwka M. Truncation error in mesh-free particle methods. International Journal for Numerical Methods in Engineering 2006; 66(13):2064-2085.
27. Ben Moussam B, Vila JP. Convergence of SPH method for scalar nonlinear conservation laws. SIAM Journal on Numerical Analysis 2000:863-887.
28. Ben Moussa B, Lanson N, Vila JP. Convergence of meshless methods for conservation laws applications to Euler equations. In Hyperbolic Problems: Theory, Numerics, Applications; Seventh International Conference. Birkhauser: Basel, 1999; 31.
29. Randles PW, Libersky LD. Smoothed particle hydrodynamics: some recent improvements and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139(1-4):375-408.
30. Bonet J, Lok TSL. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Computer Methods in Applied Mechanics and Engineering 1999; 180(1-2):97-115.
31. Vila JP. On particle weighted methods and smooth particle hydrodynamics. Mathematical Models and Methods in Applied Sciences 1999; 9(2):161-210.
32. Fatehi R, Manzari MT. Error estimation in smoothed particle hydrodynamics and a new scheme for second derivatives. Computers & Mathematics with Applications 2011; 61:482-498. DOI: 10.1016/j.camwa.2010.11.028.
33. Ferziger JH, Peric M. Computational Methods for Fluid Dynamics. Springer: Berlin, 2002.
34. Xu R, Stansby P, Laurence D. Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach. Journal of Computational Physics 2009; 228(18):6703-6725.
35. Hieber SE, Koumoutsakos P. An immersed boundary method for smoothed particle hydrodynamics of self-propelled swimmers. Journal of Computational Physics 2008; 227(19):8636-8654.
36. Oger G, Doring M, Alessandrini B, Ferrant P. An improved SPH method: towards higher order convergence. Journal of Computational Physics 2007; 225(2):1472-1492.
37. Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48(3):387-411.
38. Bing-Hai W, Hai-Yan L, Chao-Ying Z, Qiang W. Lattice Boltzmann simulation of fluid flows in two-dimensional channel with complex geometries. Chinese Physics B 2009; 18:4353-4359.