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CFD for Wind and Tidal Offshore Turbines pp 27–36Cite as

A Moving Least Squares-Based High-Order-Preserving Sliding Mesh Technique with No Intersections

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Part of the Springer Tracts in Mechanical Engineering book series (STME)

Abstract

The sliding mesh approach is widely used in numerical simulation of turbomachinery flows to take in to account the rotor/stator or rotor/rotor interaction. This technique allows relative sliding of one grid adjacent to another grid (static or in motion). However, when a high-order method is used, the interpolation used in the sliding mesh model needs to be of, at least, the same order than the numerical scheme, in order to prevent loss of accuracy. In this work we present a sliding mesh model based on the use of Moving Least Squares (MLS) approximations. It is used with a high-order ( > 2) finite volume method that computes the derivatives of the Taylor reconstruction inside each control volume using MLS approximants. Thus, this new sliding mesh model fits naturally in a high-order MLS-based finite volume framework (Cueto-Felgueroso et al., Comput Methods Appl Mech Eng 196:4712–4736, 2007; Khelladi et al., Comput Methods Appl Mech Eng 200:2348–2362, 2011) for the computation of acoustic wave propagation into turbomachinery.

Keywords

  • Riemann Problem
  • Discontinuous Galerkin Method
  • Move Little Square
  • Viscous Flux
  • Move Little Square Approximation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-319-16202-7_3
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References

  1. Chassaing JC, Khelladi S, Nogueira X (2013) Accuracy assessment of a high-order moving least squares finite volume method for compressible flows. Comput Fluids 71:41–53

    MathSciNet  CrossRef  Google Scholar 

  2. Chiocchia G (1985) Exact solutions to transonic and supersonic flows. Technical Report AR-211, AGARD

    Google Scholar 

  3. Cueto-Felgueroso L, Colominas I, Nogueira X, Navarrina F, Casteleiro M (2007) Finite-volume solvers and moving least squares approximations for the compressible Navier–Stokes equations on unstructured grids. Comput Methods Appl Mech Eng 196:4712–4736

    MATH  MathSciNet  CrossRef  Google Scholar 

  4. Ferrer E (2012) A high order discontinuous Galerkin–Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes for simulating cross-flow turbines. Ph.D., University of Oxford

    Google Scholar 

  5. Ferrer E, Willden RHJ (2012) A high order discontinuous Galerkin–Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes. J Comput Phys 231:7037–7056

    MATH  MathSciNet  CrossRef  Google Scholar 

  6. Khelladi S, Nogueira X, Bakir F, Colominas I (2011) Toward a higher order unsteady finite volume solver based on reproducing kernel methods. Comput Methods Appl Mech Eng 200:2348–2362

    MATH  MathSciNet  CrossRef  Google Scholar 

  7. Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math Comput 87:141–158

    MathSciNet  CrossRef  Google Scholar 

  8. Liu GR, Liu MB (2003) Smoothed particle hydrodynamics. A meshfree particle method. World Scientific Publishing, Singapore

    MATH  CrossRef  Google Scholar 

  9. Liu WK, Hao W, Chen Y, Jun S, Gosz J (1997) Multiresolution reproducing kernel particle methods. Comput Mech 20:295–309

    MATH  MathSciNet  CrossRef  Google Scholar 

  10. Luo JY, Gosman AD, Issa RI, Middleton JC, Fitzgerald MK (1993) Full flow field computation of mixing in baffled stirred vessels. Chem Eng Res Design A 71(3):342–344

    Google Scholar 

  11. Nogueira X, Cueto-Felgueroso L, Colominas I, Khelladi S, Navarrina F, Casteleiro M (2010) Resolution of computational aeroacoustics problems on unstructured grids with a higher-order finite volume scheme. J Comput Appl Math 234(7):2089–2097

    MATH  MathSciNet  CrossRef  Google Scholar 

  12. Nogueira X, Cueto-Felgueroso L, Colominas I, Gomez H, Navarrina F, Casteleiro M (2009) On the accuracy of finite volume and discontinuous galerkin discretizations for compressible flow on unstructured grids. Int J Numer Methods Eng 78:1553–1584

    MATH  MathSciNet  CrossRef  Google Scholar 

  13. Nogueira X, Colominas I, Cueto-Felgueroso L, Khelladi S (2010) On the simulation of wave propagation with a higher-order finite volume scheme based on reproducing kernel methods. Comput Methods Appl Mech Eng 199:1471–1490

    MATH  MathSciNet  CrossRef  Google Scholar 

  14. Rai M (1986) A conservative treatment of zonal boundaries for Euler equation calculations. J Comput Phys 62:472–503

    MATH  MathSciNet  CrossRef  Google Scholar 

  15. Rai M (1986) A relaxation approach to patched-grid calculations with the Euler equations. J Comput Phys 66:99–131

    MATH  MathSciNet  CrossRef  Google Scholar 

  16. Rai M (1987) Navier–Stokes simulations of rotor-stator interaction using patched and overlaid grids. J Comput Phys 3:387

    Google Scholar 

  17. Ramirez L, Nogueira X, Khelladi S, Chassaing JC, Colominas I (2014) A new higher-order finite volume method based on moving least squares for the resolution of the incompressible Navier–Stokes equations on unstructured grids. Comput Methods Appl Mech Eng 278: 883–901

    MathSciNet  CrossRef  Google Scholar 

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Acknowledgements

This work has been partially supported by the Ministerio de Ciencia e Innovación (#DPI2010-16496), the Ministerio de Economía y Competitividad (#DPI2012-33622) of the Spanish Government, the Consellería de Cultura, Educación e Ordenación Universitaria of the Xunta de Galicia (grant # GRC2014/039 ) cofinanced with FEDER funds, the Universidade da Coruña and the grant UDC-INDITEX.

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Authors and Affiliations

  1. Group of Numerical Methods in Engineering, Universidade da Coruña, Campus de Elviña, 15071, A Coruña, Spain

    Luis Ramírez, Xesús Nogueira & Ignasi Colominas

  2. Arts et Métiers Paris Tech, DynFluid Lab, 151 Boulevard de l’Hôpital, 75013, Paris, France

    Charles Foulquié & Sofiane Khelladi

  3. UPMC Univ. Paris 06, CNRS, UMR7190, D’Alembert Institute, Sorbonne Universités, 75005, Paris, France

    Jean-Camille Chassaing

Authors
  1. Luis Ramírez
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  2. Xesús Nogueira
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  3. Charles Foulquié
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  4. Sofiane Khelladi
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  5. Jean-Camille Chassaing
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  6. Ignasi Colominas
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Corresponding author

Correspondence to Xesús Nogueira .

Editor information

Editors and Affiliations

  1. School of Aeronautics, Universidad Politecnica de Madrid (ETSIA-UPM), Madrid, Spain

    Esteban Ferrer

  2. Universitat Politecnica de Catalunya, Escola d'Enginyeria de Telecomunicacio i Aeronautica, Catelldefels, Spain

    Adeline Montlaur

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Ramírez, L., Nogueira, X., Foulquié, C., Khelladi, S., Chassaing, JC., Colominas, I. (2015). A Moving Least Squares-Based High-Order-Preserving Sliding Mesh Technique with No Intersections. In: Ferrer, E., Montlaur, A. (eds) CFD for Wind and Tidal Offshore Turbines. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-16202-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-16202-7_3

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