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).
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References
Ahmad N., Lindeman J.: Euler solutions using flux-based wave decomposition. Int. J. Numer. Methods Fluids 54, 41–72 (2007)
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)
Baldauf M.: Stability analysis for linear discretisations of the advection equation with Runge-Kutta time integration. J. Comput. Phys. 227, 6638–6659 (2008)
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/
Baldauf M.: Linear stability analysis of Runge-Kutta based partial time-splitting schemes for the Euler equations. Mon. Weather Rev. 138, 4475–4496 (2010)
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)
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)
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)
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)
Botta N., Klein R., Langenberg S., Lützenkirchen S.: Well balanced finite volume methods for nearly hydrostatic flows. J. Comput. Phys. 196, 539–565 (2003)
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)
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)
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)
Cockburn B., Shu C.W.: Runge-Kutta Discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16(3), 173–261 (2001)
Colonius T.: Modeling artificial boundary conditions for compressible flow. Ann. Rev. Fluid Mech. 36, 315–345 (2004)
Dedner, A.: Solving the system of Radiation Magnetohydrodynamics : for solar physical simulations in 3d. Ph.D. thesis, Universität Freiburg (2003)
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)
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)
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)
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)
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)
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)
Gottlieb S., Shu C.-W., Tadmor E.: Strong stability-preserving high-order time discretization methods. SIAM Rev. 43(1), 89–112 (2001)
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)
Hu F.Q.: Absorbing boundary conditions (a review). J. Comput. Fluid Dyn. 18(6), 513–522 (2004)
Klein R.: Asymptotics, structure, and integration of sound-proof atmospheric flow equations. Theor. Comput. Fluid Dyn. 23, 161–195 (2009)
Klemp J.B., Lilly D.K.: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci. 35, 78–107 (1978)
Krivodonova L., Berger M.: High-order accurate implementation of solid wall boundary conditions in curved geometries. J. Comput. Phys. 211(2), 492–512 (2006)
Kröner D.: Numerical Schemes for Conservation Laws. Wiley & Teubner, Stuttgart (1997)
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)
Lin S., Rood R.B.: Multidimensional flux-form semi-Langrangian transport schemes. Mon. Weather Rev. 125, 32–46 (1996)
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)
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)
Skamarock W.C., Klemp J.B.: Efficiency and accuracy of the Klemp-Wilhelmson time-splitting technique. Mon. Weather Rev. 122, 2623–2630 (1994)
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)
Skamarock W.C., Weisman M.L.: The impact of positive-definite moisture transport on NWP precipitation forecasts. Mon. Weather Rev. 137, 488–494 (2009)
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)
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)
Toro E.F.: Riemann solvers and numerical methods for fluid dynamics. A practical introduction. 2nd edn. Springer, Berlin (1999)
Wicker L.J., Skamarock W.C.: Time splitting methods for elastic models using forward time schemes. Mon. Weather Rev. 130, 2088–2097 (2002)
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Communicated by R. Klein.
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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
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DOI: https://doi.org/10.1007/s00162-012-0264-z