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Adaptive particle method based on moments for simulating the mass transport in natural flows

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Abstract

In this work, two modifications of an adaptive particle method based on the moments of the internal concentration of numerical particles are presented to introduce the effect of local shears on the mass transport in natural flows. This moment method uses a Taylor expansion of the flow velocity field to derive the transport equation of moments. The first modification is based on the introduction of a method of the local frame transport in order to perform an extension of the Taylor expansion of the flow velocity to a higher order. The second modification consists in applying a splitting or a merging to non-spherical numerical particles. When a non-spherical numerical particle becomes large compared to the scale of spatial variations of the velocity gradient, it is divided into two non-spherical numerical particles. On the contrary, when particles reach some other parts of the flow where they become small compared to spatial variations of the velocity gradient, then these particles should merge. The accuracy of both modifications is evaluated by simulating the mass transport in natural flows.

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References

  1. Abgrall R, Beaugendre H, Dobrzynski C (2014) An immersed boundary method using unstructured anisotropic mesh adaptation combined with level-sets and penalization techniques. J Comput Phys 257:83–101

    Article  MathSciNet  MATH  Google Scholar 

  2. Barba LA, Rossi LF (2010) Global field interpolation for particle methods. J Comput Phys 229:1292–1310

    Article  MathSciNet  MATH  Google Scholar 

  3. Berchet A, Beaudoin A, Huberson S (2016) Divergence-free condition in transport simulation. CR Mec 344:642–648

    Article  Google Scholar 

  4. Beaudoin A, Huberson S, Rivoalen E (2013) Simulation of anisotropic diffusion by means of a diffusion velocity. J Comput Phys 186:122–135

    Article  MATH  Google Scholar 

  5. Beaudoin A, Huberson S, Rivoalen E (2001) Méthode particulaire anisotrope. CR Mec 330:51–56

    Article  MATH  Google Scholar 

  6. Beaudoin A, Huberson S, Rivoalen E (2004) Méthode particulaire anisotrope pour des écoulements de fluides visqueux. CR Mec 332:499–504

    Article  MATH  Google Scholar 

  7. Chaniotis AK, Poulikakos D, Koumoutsakos P (2002) Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows. J Comput Phys 182:67–90

    Article  MATH  Google Scholar 

  8. Chen Z, Zong Z, Liu MB, Zou L, Li HT, Shu C (2015) An SPH model for multiphase flows with complex interfaces and large density differences. J Comput Phys 283:169–188

    Article  MathSciNet  MATH  Google Scholar 

  9. Chorin A.J.: A vortex method for the study of rapid flow. In: Proceedings of the third international conference on numerical methods in fluid mechanics, Springer, Berlin, Heidelberg, pp 100–104 (1973)

  10. Chorin AJ, Bernard PS (1973) Discretization of a vortex sheet, with an example of roll-up. J Comput Phys 13:423–429

    Article  MATH  Google Scholar 

  11. Chorin AJ (1978) Vortex sheet approximation of boundary layers. J Comput Phys 27:428–442

    Article  MATH  Google Scholar 

  12. Cleary PW, Monaghan JJ (1999) Conduction modelling using smoothed particle hydrodynamics. J Comput Phys 148:227–264

    Article  MathSciNet  MATH  Google Scholar 

  13. Cottet GH, Koumoutsakos PD (2000) Vortex methods: theory and practice. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  14. Cottet GH, Poncet P (2003) Advances in direct numerical simulations of 3D wall-bounded flows by vortex-in-cell methods. J Comput Phys 193:136–158

    Article  MathSciNet  MATH  Google Scholar 

  15. Dehnen W, Aly H (2012) Improving convergence in smoothed particle hydrodynamics simulations without pairing instability. Mon Not R Astron Soc 452:1068–1082

    Article  Google Scholar 

  16. Fernandez-Garcia D, Sanchez-Vila X (2011) Optimal reconstruction of concentrations, gradients and reaction rates from particle distributions. J Comput Phys 120:99–114

    Google Scholar 

  17. Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181:375–389

    Article  MATH  Google Scholar 

  18. Huberson S, Jollès A, Shen W (1992) Numercial simulation of incompressible viscous flows by means of particle methods in vortex dynamics and vortex methods. AMS Lect Appl Math 28:369–384

    MATH  Google Scholar 

  19. Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, Singapore

    Book  MATH  Google Scholar 

  20. Merriman B (1991) Particle approximation. Lect Appl Math 28:418–545

    MathSciNet  MATH  Google Scholar 

  21. Oh J, Tsai CW (2010) A stochastic jump diffusion particle tracking model (SJD-PTM) for sediment transport in open channel flows. Water Resour Res

  22. Prager W (1928) Die druckverteilung an korpen in ebener potentialstroming. Physikalische Zeitschrift 29:865–869

    MATH  Google Scholar 

  23. Rahbaralam M, Fernandez-Garcia D, Sanchez-Vila X (2015) Do we really need a large number of particles to simulate bimolecular reactive transport with random walk methods ? A kernel density estimation approach. J Comput Phys 303:95–104

    Article  MathSciNet  MATH  Google Scholar 

  24. Rosenhead L (1930) The Spread of vorticity in the wake behind a cylinder. Proc R Soc Lond A 127:590–612

    Article  MATH  Google Scholar 

  25. Rosenhead L (1931) The formation of vortices from a surface of discontinuity. Proc R Soc Lond A 134:170–192

    Article  MATH  Google Scholar 

  26. Rossi LF (1996) Resurrecting core spreading vortex methods : a new scheme that is both deterministic and convergent. SIAM J Sci Comput 17:370–397

    Article  MathSciNet  MATH  Google Scholar 

  27. Rossi LF (1997) Merging computational elements in vortex simulations. SIAM J Sci Comput 18:1014–1027

    Article  MathSciNet  MATH  Google Scholar 

  28. Rossi LF (2005) Achieving high-order convergence rates with deforming basis functions. SIAM J Sci Comput 26:885–906

    Article  MathSciNet  MATH  Google Scholar 

  29. Rossi LF (2006) A comparative study of Lagrangian methods using axisymmetric and deforming blobs. SIAM J Sci Comput 27:1168–1180

    Article  MathSciNet  MATH  Google Scholar 

  30. Smolarkiewicz PK (1982) The multi-dimensional crowley advection scheme. Mon Weather Rev 10:1968–1983

    Article  Google Scholar 

  31. Staniforth A, Côté J, Pudykiewicz J (1986) Comments on Smolarkiewicz’s deformational flow. Mon Weather Rev 115:894–900

    Article  Google Scholar 

  32. Teng ZH (1982) Elliptic-vortex method for incompressible flow at high Reynolds number. J Comput Phys 46:54–68

    Article  MathSciNet  MATH  Google Scholar 

  33. Teng ZH (1986) Variable-elliptic-vortex method for incompressible flow simulation. J Comput Math 4:255–262

    MathSciNet  MATH  Google Scholar 

  34. Wendland H (1995) Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. ADV Comput Math 4:389–396

    Article  MathSciNet  MATH  Google Scholar 

  35. Xie Z, Pavlidis D, Percival JR, Gomes JMA, Pain CC, Matar OK (2014) Adaptive unstructured mesh modelling of multiphase flow. Int J Multiph Flow 67:104–110

    Article  Google Scholar 

  36. Zimmermann S, Koumoutsakos P, Kinzelbach W (2001) Simulation of pollutant transport using a particle method. J Comput Phys 173:322–347

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut Pprime (UPR 3346, CNRS-Université de Poitiers-ENSMA), Bat H2, 11 Boulevard Marie et Pierre Curie, TSA 51124, 86073, Poitiers Cedex 9, France

    Adrien Berchet Berchet, Anthony Beaudoin & Serge Huberson Huberson

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  1. Adrien Berchet Berchet
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  2. Anthony Beaudoin
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  3. Serge Huberson Huberson
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Correspondence to Anthony Beaudoin.

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Berchet, A.B., Beaudoin, A. & Huberson, S.H. Adaptive particle method based on moments for simulating the mass transport in natural flows. Comp. Part. Mech. 8, 525–534 (2021). https://doi.org/10.1007/s40571-020-00350-5

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