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Stochastic Lagrangian Approach for Wind Farm Simulation

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Renewable Energy: Forecasting and Risk Management (FRM 2017)

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Abstract

We present a stochastic Lagrangian approach for atmospheric boundary layer simulation. Based on a turbulent-fluid-particle model, a stochastic Lagrangian particle approach could be an advantageous alternative for some applications, in particular in the context of down-scaling simulation and wind farm simulation. This paper presents two recent advances in this direction, first the analysis of an optimal rate of convergence result for the particle approximation method that grounds the space discretisation of the Lagrangian model, and second a preliminary illustration of our methodology based on the simulation of a Zephyr ENR wind farm of six turbines.

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Notes

  1. 1.

    We consider here only the case of constant mass density flow, for the sake of clarity.

References

  1. F. Bernardin, M. Bossy, C. Chauvin, P. Drobinski, A. Rousseau, T. Salameh, Stochastic downscaling methods: application to wind refinement. Stoch. Environ. Res. Risk Assess. 23(6), 851–859 (2009)

    Article  MathSciNet  Google Scholar 

  2. F. Bernardin, M. Bossy, C. Chauvin, J.-F. Jabir, A. Rousseau, Stochastic Lagrangian method for downscaling problems in computational fluid dynamics. ESAIM: M2AN 44(5), 885–920 (2010)

    Article  MathSciNet  Google Scholar 

  3. M. Bossy, Some stochastic particle methods for nonlinear parabolic PDEs, in GRIP—Research Group on Particle Interactions. ESAIM: Proceedings, vol. 15 (EDP Sciences, Les Ulis, 2005), pp. 18–57

    Article  MathSciNet  Google Scholar 

  4. M. Bossy, L. Violeau, Optimal rate of convergence of particle approximation for conditional McKean–Vlasov kinetic processes (2018)

    Google Scholar 

  5. M. Bossy, J. Espina, J. Morice, C. Paris, A. Rousseau, Modeling the wind circulation around mills with a Lagrangian stochastic approach. SMAI J. Comput. Math. 2, 177–214 (2016)

    Article  MathSciNet  Google Scholar 

  6. P.A. Durbin, A Reynolds stress model for near-wall turbulence. J. Fluid Mech. 249, 465–498 (1993)

    Article  Google Scholar 

  7. P.-A. Durbin, C.-G. Speziale, Realizability of second-moment closure via stochastic analysis. J. Fluid Mech. 280, 395–407 (1994)

    Article  Google Scholar 

  8. W. McCarty, L. Coy, R. Gelano, A. Huang, D. Merkova, E.B. Smith, M. Sienkiewicz, K. Wargan, MERRA-2 input observations: summary and assessment, in NASA Technical Report Series on Global Modeling and Data Assimilation, vol. 46 (2016)

    Google Scholar 

  9. J.-P. Minier, Statistical descriptions of polydisperse turbulent two-phase flows. Phys. Rep.665(Supplement C), 1–122 (2016)

    Article  MathSciNet  Google Scholar 

  10. J.-P. Minier, S. Chibbaro, S.B. Pope, Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows. Phys. Fluids 26(11), 113303 (2014)

    Article  Google Scholar 

  11. A. Niayifar, F. Porté-Agel, Analytical modeling of wind farms: a new approach for power prediction. Energies 9(9), 741 (2016)

    Article  Google Scholar 

  12. S.B. Pope, Lagrangian PDF methods for turbulent flows. Annu. Rev. Fluid Mech. 26, 23–63. Annual Reviews, Palo Alto, CA, 1994

    Google Scholar 

  13. S.B. Pope, Lagrangian pdf methods for turbulent flows. Annu. Rev. Fluid Mech. 26, 23–63 (1994)

    Article  MathSciNet  Google Scholar 

  14. S.B. Pope, Particle method for turbulent flows: tegration of stochastic model equations. J. Comput. Phys. 117(2), 332–349 (1995)

    Article  Google Scholar 

  15. S.B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000)

    Book  Google Scholar 

  16. P.E. Réthoré, N.N. Sørensen, A. Bechmann, F. Zahle, Study of the atmospheric wake turbulence of a CFD actuator disc model, in Proceedings of European Wind Energy Conference, Marseille, France, 16–19 March 2009

    Google Scholar 

  17. J.N. Sørensen, Aerodynamic aspects of wind energy conversion. Annu. Rev. Fluid Mech. 43(1), 427–448 (2011)

    Article  Google Scholar 

  18. A. Stohl, Computation, accuracy and applications of trajectories. A review and bibliography. Atmos. Environ. 32(6), 947–966 (1998)

    Article  Google Scholar 

  19. M. Waclawczyk, J. Pozorski, J.-P. Minier, Probability density function computation of turbulent flows with a new near-wall model. Phys. Fluids 16(5), 1410–1422 (2004)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Université Côte d’Azur, Inria, Sophia Antipolis, France

    Mireille Bossy & Laurent Violeau

  2. LMD/IPSL, École polytechnique, Université Paris Saclay, ENS, PSL Research University, Sorbonne Universités, UPMC Univ Paris 06, CNRS, Palaiseau, France

    Aurore Dupré & Philippe Drobinski

  3. Zephyr ENR, Saint-Avertin, France

    Christian Briard

Authors
  1. Mireille Bossy
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  2. Aurore Dupré
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  3. Philippe Drobinski
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  4. Laurent Violeau
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  5. Christian Briard
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Corresponding author

Correspondence to Mireille Bossy .

Editor information

Editors and Affiliations

  1. Laboratoire de Méteorologie Dynamique, CNRS, Palaiseau, France

    Philippe Drobinski

  2. UFR de Mathématiques, Université Paris Diderot, Paris, France

    Mathilde Mougeot

  3. UFR de Mathématiques, Université Paris Diderot, Paris, France

    Dominique Picard

  4. Laboratoire de Météorologie Dynamique, Ecole Polytechnique, Palaiseau, France

    Riwal Plougonven

  5. CREST—ENSAE Paris Tech, Palaiseau, France

    Peter Tankov

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Bossy, M., Dupré, A., Drobinski, P., Violeau, L., Briard, C. (2018). Stochastic Lagrangian Approach for Wind Farm Simulation. In: Drobinski, P., Mougeot, M., Picard, D., Plougonven, R., Tankov, P. (eds) Renewable Energy: Forecasting and Risk Management. FRM 2017. Springer Proceedings in Mathematics & Statistics, vol 254. Springer, Cham. https://doi.org/10.1007/978-3-319-99052-1_3

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