Skip to main content
Log in

Comparison of dynamical cores for NWP models: comparison of COSMO and Dune

  • Original Article
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

We present a range of numerical tests comparing the dynamical cores of the operationally used numerical weather prediction (NWP) model COSMO and the university code Dune, focusing on their efficiency and accuracy for solving benchmark test cases for NWP. The dynamical core of COSMO is based on a finite difference method whereas the Dune core is based on a Discontinuous Galerkin method. Both dynamical cores are briefly introduced stating possible advantages and pitfalls of the different approaches. Their efficiency and effectiveness is investigated, based on three numerical test cases, which require solving the compressible viscous and non-viscous Euler equations. The test cases include the density current (Straka et al. in Int J Numer Methods Fluids 17:1–22, 1993), the inertia gravity (Skamarock and Klemp in Mon Weather Rev 122:2623–2630, 1994), and the linear hydrostatic mountain waves of (Bonaventura in J Comput Phys 158:186–213, 2000).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ahmad N., Lindeman J.: Euler solutions using flux-based wave decomposition. Int. J. Numer. Methods Fluids 54, 41–72 (2007)

    Article  MathSciNet  Google Scholar 

  2. Arnold D., Brezzi F., Cockburn B., Marini L.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749–1779 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baldauf M.: Stability analysis for linear discretisations of the advection equation with Runge-Kutta time integration. J. Comput. Phys. 227, 6638–6659 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baldauf, M.: A linear solution for flow over mountains and its comparison with the COSMO model. COSMO-Newsletter 9, 19–24 (2008). http://www.cosmo-model.org/content/model/documentation/newsLetters/

  5. Baldauf M.: Linear stability analysis of Runge-Kutta based partial time-splitting schemes for the Euler equations. Mon. Weather Rev. 138, 4475–4496 (2010)

    Article  Google Scholar 

  6. Baldauf M., Seifert A., Förstner J., Majewski D., Raschendorfer M., Reinhardt T.: Operational convective-scale numerical weather prediction with the COSMO model: description and sensitivities. Mon. Weather Rev. 139(12), 3887–3905 (2011)

    Article  Google Scholar 

  7. Bastian P., Blatt M., Dedner A., Engwer C., Klöfkorn R., Kornhuber R., Ohlberger M., Sander O.: A generic grid interface for parallel and adaptive scientific computing. II: implementation and tests in dune. Computing 82, 121–138 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bastian P., Blatt M., Dedner A., Engwer C., Klöfkorn R., Ohlberger M., Sander O.: A generic grid interface for parallel and adaptive scientific computing. I: abstract framework. Computing 82, 103–119 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bonaventura L.: A semi-implicit semi-Lagrangian scheme using the height coordinate for a nonhydrostatic and fully elastic model of atmospheric flows. J. Comput. Phys. 158, 186–213 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Botta N., Klein R., Langenberg S., Lützenkirchen S.: Well balanced finite volume methods for nearly hydrostatic flows. J. Comput. Phys. 196, 539–565 (2003)

    Article  Google Scholar 

  11. Brdar S., Dedner A., Klöfkorn R.: Compact and stable Discontinuous Galerkin methods for convection-diffusion problems. SIAM J. Sci. Comput. 34(1), 263–282 (2012)

    Article  MathSciNet  Google Scholar 

  12. Cockburn, B., Hou, S., Shu, C.W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case. Math. Comput. 54, 545–581 (1990)

    Google Scholar 

  13. Cockburn B., Lin S.Y., Shu C.W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems. J. Comput. Phys. 84, 90–113 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  14. Cockburn B., Shu C.W.: Runge-Kutta Discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16(3), 173–261 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Colonius T.: Modeling artificial boundary conditions for compressible flow. Ann. Rev. Fluid Mech. 36, 315–345 (2004)

    Article  MathSciNet  Google Scholar 

  16. Dedner, A.: Solving the system of Radiation Magnetohydrodynamics : for solar physical simulations in 3d. Ph.D. thesis, Universität Freiburg (2003)

  17. Dedner A., Klöfkorn R.: A generic stabilization approach for higher order Discontinuous Galerkin methods for convection dominated problems. J. Sci. Comput. 47(3), 365–388 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Dedner, A., Klöfkorn, R., Nolte, M., and Ohlberger, M.: A generic interface for parallel and adaptive scientific computing: Abstraction principles and the dune-fem module. Computing 90(3–4), 165–196 (2010)

    Google Scholar 

  19. Feistauer, M., Kučera, V.: A new technique for the numerical solution of the compressible Euler equations with arbitrary Mach numbers. In: Benzoni-Gavage, S. et al. (ed.) Hyperbolic problems. Theory, numerics and applications. Proceedings of the 11th International Conference on Hyperbolic Problems, Ecole Normale Supérieure, Lyon, France, July 17–21, 2006. Springer, Berlin, pp. 523–531 (2008)

  20. Giraldo F.X., Restelli M.: A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: equations sets and test cases. J. Comput. Phys. 227, 3849–3877 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Giraldo F., Restelli M., Läuter M.: Semi-implicit formulations of the Euler equations: Application to nonhydrostatic atmospheric modeling. SIAM J. Sci. Comput. 32, 3394–3425 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Gross E.S., Bonaventura L., Rosatti G.: Consistency with continuity in conservative advection schemes for free-surface models. Int. J. Numer. Methods Fluids 38, 307–327 (2002)

    Article  MATH  Google Scholar 

  23. Gottlieb S., Shu C.-W., Tadmor E.: Strong stability-preserving high-order time discretization methods. SIAM Rev. 43(1), 89–112 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  24. Guermond, J.L., Pasquetti, R., Popov, B.: Entropy viscosity method for nonlinear conservation laws. J. Comput. Phys. 230(11), 4248–4267 (2011) (Special issue high order methods for CFD problems)

    Google Scholar 

  25. Hu F.Q.: Absorbing boundary conditions (a review). J. Comput. Fluid Dyn. 18(6), 513–522 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  26. Klein R.: Asymptotics, structure, and integration of sound-proof atmospheric flow equations. Theor. Comput. Fluid Dyn. 23, 161–195 (2009)

    Article  MATH  Google Scholar 

  27. Klemp J.B., Lilly D.K.: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci. 35, 78–107 (1978)

    Article  Google Scholar 

  28. Krivodonova L., Berger M.: High-order accurate implementation of solid wall boundary conditions in curved geometries. J. Comput. Phys. 211(2), 492–512 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  29. Kröner D.: Numerical Schemes for Conservation Laws. Wiley & Teubner, Stuttgart (1997)

    MATH  Google Scholar 

  30. Leonard B.P., Lock A.P., MacVean M.K.: Conservative explicit unrestricted-time step multidimensional constancy-preserving advection schemes. Mon. Weather Rev. 124, 2588–2606 (1996)

    Article  Google Scholar 

  31. Lin S., Rood R.B.: Multidimensional flux-form semi-Langrangian transport schemes. Mon. Weather Rev. 125, 32–46 (1996)

    Google Scholar 

  32. Nance L.B., Durran D.R.: A comparison of the accuracy of three anelastic systems and the pseudo-incompressible system. J. Atmos. Sci. 52(24), 3549–3565 (1994)

    Article  Google Scholar 

  33. Restelli M., Giraldo F.X.: A conservative discontinuous Galerkin semi-implicit formulation for the Navier-Stokes equations in nonhydrostatic mesoscale modeling. SIAM J. Sci. Comput. 31(3), 2231–2257 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  34. Skamarock W.C., Klemp J.B.: Efficiency and accuracy of the Klemp-Wilhelmson time-splitting technique. Mon. Weather Rev. 122, 2623–2630 (1994)

    Article  Google Scholar 

  35. Skamarock, W.C., Klemp, J.B., Dudhia, J., Gill, D.O., Baker, D.M., Wang, W., Powers, J.G.: A Description of the Advances Research WRF Version 2. NCAR Technical Note NCART/TN-468+STR (2007)

  36. Skamarock W.C., Weisman M.L.: The impact of positive-definite moisture transport on NWP precipitation forecasts. Mon. Weather Rev. 137, 488–494 (2009)

    Article  Google Scholar 

  37. Steppeler J., Doms G., Schättler U., Bitzer H.W., Gassmann A., Damrath U., Gregoric G.: Meso-gamma scale forecasts using the nonhydrostatic model LM. Meteorol. Atmos. Phys. 82, 75–96 (2003)

    Article  Google Scholar 

  38. Straka J.M., Wilhelmson R.B., Wicker L.J., Anderson J.R., Droegemeier K.K.: Numerical solutions of a non-linear density current: a benchmark solution and comparison. Int. J. Numer. Methods Fluids 17, 1–22 (1993)

    Article  MathSciNet  Google Scholar 

  39. Toro E.F.: Riemann solvers and numerical methods for fluid dynamics. A practical introduction. 2nd edn. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  40. Wicker L.J., Skamarock W.C.: Time splitting methods for elastic models using forward time schemes. Mon. Weather Rev. 130, 2088–2097 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Slavko Brdar.

Additional information

Communicated by R. Klein.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brdar, S., Baldauf, M., Dedner, A. et al. Comparison of dynamical cores for NWP models: comparison of COSMO and Dune. Theor. Comput. Fluid Dyn. 27, 453–472 (2013). https://doi.org/10.1007/s00162-012-0264-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-012-0264-z

Keywords

Navigation