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A Unifying Discontinuous CPR Formulation for the Navier–Stokes Equations on Mixed Grids

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Computational Fluid Dynamics 2010

Abstract

A unifying discontinuous formulation named the correction procedure via reconstruction (CPR) for conservation laws is extended to solve the Navier–Stokes equations for mixed grids. The CPR framework can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a differential formulation without explicit volume or surface integrations. Several test cases are computed to demonstrate its performance.

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References

  1. Bassi, F., Rebay, S.: A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131(1), 267–279 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cockburn, B., Shu, C.-W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework. Math. Comput. 52, 411–435 (1989)

    MathSciNet  MATH  Google Scholar 

  3. Cockburn, B., Shu, C.-W.: The local discontinuous Galerkin methods for time-dependent convection diffusion systems. SIAM J. Numer. Anal. 35, 2440–2463 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Huynh, H.T.: A Flux Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin Methods. AIAA paper 2007–4079

    Google Scholar 

  5. Kopriva, D.A., Kolias, J.H.: A conservative staggered-grid Chebyshev multidomain method for compressible flows. J. Comput. Phys. 125, 244 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu, Y., Vinokur, M., Wang, Z.J.: Discontinuous spectral difference method for conservation laws on unstructured grids. J. Comput. Phys. 216, 780–801 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Reed, W.H., Hill, T.R.: Triangular Mesh Methods for the Neutron Transport Equation. Los Alamos Scientific Laboratory Report, LA-UR-73-479 (1973)

    Google Scholar 

  8. Roe, P.L.: Approximate Riemann solvers, parameter vectors, and difference schems. J. Comput. Phys. 43, 357–372 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang, Z.J.: Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation. J. Comput. Phys. 178, 210–251 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang, Z.J.: High-order methods for the Euler and Navier-Stokes equations on unstructured grids. J. Prog. Aerosp. Sci. 43, 1–47 (2007)

    Article  Google Scholar 

  11. Wang, Z.J., Gao, H.: A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids. J. Comput. Phys. 228, 8161–8186 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This study has been supported by the Air Force Office of Scientific Research (AFOSR) under grant FA9550-09-1-0128.

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Authors and Affiliations

  1. Department of Aerospace Engineering, CFD Center, Iowa State University, Ames, IA, 50011, USA

    Z.J. Wang, Haiyang Gao & Takanori Haga

Authors
  1. Z.J. Wang
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  2. Haiyang Gao
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  3. Takanori Haga
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Corresponding author

Correspondence to Z.J. Wang .

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Editors and Affiliations

  1. , Department of Maths & Mechanics, St Petersburg State University, St Petersburg, Russian Federation

    Alexander Kuzmin

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Wang, Z., Gao, H., Haga, T. (2011). A Unifying Discontinuous CPR Formulation for the Navier–Stokes Equations on Mixed Grids. In: Kuzmin, A. (eds) Computational Fluid Dynamics 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17884-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-17884-9_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17883-2

  • Online ISBN: 978-3-642-17884-9

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