A nonhydrostatic unstructured-mesh soundproof model for simulation of internal gravity waves

• Autorzy: Smolarkiewicz P.K. , Szmelter J.
• Języki publikacji: EN

Abstrakty

EN

A semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic soundproof equations, inclusive of anelastic and pseudo-incompressible systems of partial differential equations. The model builds on nonoscillatory forward-in-time MPDATA approach using finite-volume discretization and unstructured meshes with arbitrarily shaped cells. Implicit treatment of gravity waves benefits both accuracy and stability of the model. The unstructured-mesh solutions are compared to equivalent structured-grid results for intricate, multiscale internal-wave phenomenon of a non-Boussinesq amplification and breaking of deep stratospheric gravity waves. The departures of the anelastic and pseudoincompressible results are quantified in reference to a recent asymptotic theory [Achatz et al. 2010, J. Fluid Mech., 663, 120-147)].

Słowa kluczowe

EN

unstructured mesh models; nonoscillatory forward-in-time schemes; atmospheric models; soundproof equations; mountain waves

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2011
• Tom: Vol. 59, no. 6
• Strony: 1109--1134
• Opis fizyczny: Bibliogr. 55 poz.

Twórcy

autor

Smolarkiewicz P.K.

autor

Szmelter J.

• National Center for Atmospheric Research, Boulder, CO, USA,

Bibliografia

• Achatz, U., R. Klein, and F. Senf (2010), Gravity waves, scale asymptotics and the pseudo-incompressible equations, J. Fluid Mech. 663, 120-147.
• Axelsson, O. (1994), Iterative Solution Methods, Cambridge University Press, Cambridge.
• Bacon, D.P., N.N. Ahmad, Z. Boybeyi, T.J. Dunn, M.S. Hall, P.C.S. Lee, R.A. Sarma, M.D. Turner, K.T. Waight, S.H. Young, and J.W. Zack (2000), A dynamically adapting weather and dispersion model: The operational multiscale environment model with grid adaptivity (OMEGA), Month. Weather Rev. 128, 7, 2044-2067.
• Bacon, D.P., N.N. Ahmad, T.J. Dunn, M.C. Monteith, and A. Sarma (2008), An operational multiscale system for hazards prediction, mapping, and response, Nat. Hazards 44, 3, 317-327.
• Barth, T.J. (1992), Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations. In: Special Course on Unstructured Grid Methods for Advection Dominated Flows, AGARD Reports series 787, AGARD, Neuilly sur Seine, 6.1-6.61.
• Behrens, J., S. Reich, M. Lauter, B. Wingate, and D. Williamson (2010), The 2010 Workshop on the Solution of PDEs on the Sphere, http://www.awipotsdam.de/pde2010/pdes2010\_program.pdf.
• Birkhoff, G., and R.E. Lynch (1984), Numerical Solution of Elliptic Problems, SIAM 6, Cambridge University Press, Cambridge.
• Bunge, H.-P., M.A. Richards, and J.R. Baumgardner (1997), A sensitivity study of three-dimensional spherical mantle convection at 108 Rayleigh number: Effects of depth-dependent viscosity, heating mode, and an endothermic chase change, J. Geophys. Res. 102, B6, 11,991-12,007.
• Davies, H.C. (1983), Limitations of some common lateral boundary schemes used in regional NWP models, Month. Weather Rev. 111, 5, 1002-1012.
• Davies, T., A. Staniforth, N. Wood, and J. Thuburn (2003), Validity of anelastic and other equation sets as inferred from normal-mode analysis, Quart. J. Roy. Met. Soc. 129, 2761-2775.
• Doyle, J.D., D.R. Durran, C. Chen, B.A. Colle, M. Georgelin, V. Grubisic, W.R. Hsu, C.Y. Huang, D. Landau, Y.L. Lin, G.S. Poulos, W.Y. Sun, D.B. Weber, M.G. Wurtele, and M. Xue (2000), An intercomparison of model-predicted wave breaking for the 11 January 1972 Boulder Windstorm, Month. Weather Rev. 128, 3, 901-914.
• Durran, D.R. (1989), Improving the anelastic approximation, J. Atmos. Sci. 46, 11, 1453-1461.
• Durran, D.R. (2008), A physically motivated approach for filtering acoustic waves from the equations governing compressible stratified flow, J. Fluid Mech. 601, 365-379.
• Eisenstat, S.C., H.C. Elman, and M.H. Schultz (1983), Variational iterative methods for nonsymmetric systems of linear equations, SIAM J. Numer. Anal. 20, 2, 345-357.
• Ghizaru, M., P. Charbonneau, and P.K. Smolarkiewicz (2010), Magnetic cycles in global large-eddy simulations of solar convection, Astrophys. J. Lett. 715, 2, L133-L137.
• Grabowski, W.W., and P.K. Smolarkiewicz (2002), A multiscale anelastic model for meteorological research, Month. Weather Rev. 130, 4, 939-956.
• Greenbaum, A. (2002), Iterative Methods for Solving Linear Systems, SIAM, Philadelphia, PA.
• Klein, R. (2011), On the regime of validity of sound-proof model equations for atmospheric flows. In: Proc. of the ECMWF Workshop on Nonhydrostatic Modelling, 8-10 November, 2010, Reading, UK, 35-53.
• Klein, R., U. Achatz, D. Bresch, O.M. Knio, and P.K. Smolarkiewicz (2010), Regime of validity of soundproof atmospheric flow models, J. Atmos. Sci. 67, 10, 3226-3237.
• Kosloff, R., and D. Kosloff (1986), Absorbing boundaries for wave propagation problems, J. Comput. Phys. 63, 2, 363-376.
• Lipps, F.B. (1990), On the anelastic approximation for deep convection, J. Atmos. Sci. 47, 14, 1794-1798.
• Lipps, F.B., and R.S. Hemler (1982), A scale analysis of deep moist convection and some related numerical calculations, J. Atmos. Sci. 39, 10, 2192-2210.
• Miller, M.J., and P.K. Smolarkiewicz (2008), Predicting weather, climate and extreme events, Preface, J. Comput. Phys. 227, 7, 3429-3430.
• Nikiforakis, N. (2009), Mesh generation and mesh adaptation for large-scale Earthsystem modelling, Introduction, Phil. Trans. R. Soc. A 367, 4473-4481.
• Piotrowski, Z.P., A.A.Wyszogrodzki, and P.K. Smolarkiewicz (2011), Towards petascale simulation of atmospheric circulations with soundproof equations, Acta Geophys. 59, 6.
• Prusa, J.M., and P.K. Smolarkiewicz (2003), An all-scale anelastic model for geophysical flows: dynamic grid deformation, J. Comput. Phys. 190, 2, 601-622.
• Prusa, J.M., P.K. Smolarkiewicz, and R.R. Garcia (1996), Propagation and breaking at high altitudes of gravity waves excited by tropospheric forcing, J. Atmos. Sci. 53, 15, 2186-2216.
• Prusa, J.M., P.K. Smolarkiewicz, and A.A.Wyszogrodzki (2001), Simulations of gravity wave induced turbulence using 512 PE Cray T3E, Int. J. Appl. Math. Comput. Sci. 11, 4, 883-897.
• Prusa, J.M., P.K. Smolarkiewicz, and A.A. Wyszogrodzki (2008), EULAG, a computational model for multiscale flows, Comput. Fluids 37, 9, 1193-1207.
• Saad, Y. (1995), Iterative Methods for Sparse Linear Systems, PWS Publishing, Boston, 447 pp.
• Smith, R.B. (1979), The influence of the mountains on the atmosphere, Adv. Geophys. 21, 87-230.
• Smolarkiewicz, P.K. (1983), A simple positive definite advection scheme with small implicit diffusion, Month.Weather Rev. 111, 3, 479-486.
• Smolarkiewicz, P.K. (1984), A fully multidimensional positive definite advection transport algorithm with small implicit diffusion, J. Comput. Phys. 54, 2, 325-362.
• Smolarkiewicz, P.K. (2006), Multidimensional positive definite advection transport algorithm: an overview, Int. J. Numer. Meth. Fluids 50, 10, 1123-1144.
• Smolarkiewicz, P.K. (2011), Modeling atmospheric circulations with soundproof equations. In: Proc. of the ECMWF Workshop on Nonhydrostatic Modelling, 8-10 November, 2010, Reading, UK, 1-15.
• Smolarkiewicz, P.K., and A. Dörnbrack (2008), Conservative integrals of adiabatic Durran’s equations, Int. J. Numer. Meth. Fluids 56, 8, 1513-1519.
• Smolarkiewicz, P.K., and L.G. Margolin (1993), On forward-in-time differencing for fluids: Extension to a curvilinear framework, Month. Weather Rev. 121, 6, 1847-1859.
• Smolarkiewicz, P.K., and L.G. Margolin (1994), Variational solver for elliptic problems in atmospheric flows, Appl. Math. Comp. Sci. 4, 527-551.
• Smolarkiewicz, P.K., and L.G. Margolin (1997), On forward-in-time differencing for fluids: an Eulerian/semi-Lagrangian non-hydrostatic model for stratified flows, Atmos. Ocean Sp. 35, 1, 127-152.
• Smolarkiewicz, P.K., and L.G. Margolin (2000), Variational methods for elliptic problems in fluid models. In: Proc. Workshop on Developments in Numerical Methods for Very High Resolution Global Models’, 5-7 June 2000, ECMWF, Reading, UK, 137-159.
• Smolarkiewicz, P.K., and J. Szmelter (2005a), Multidimensional positive definite advection transport algorithm (MPDATA): an edge-based unstructured-data formulation, Int. J. Numer. Meth. Fluids 47, 10-11, 1293-1299.
• Smolarkiewicz, P.K., and J. Szmelter (2005b), MPDATA: An edge-based unstructured-grid formulation, J. Comput. Phys. 206, 2, 624-649.
• Smolarkiewicz, P.K., and J. Szmelter (2009), Iterated upwind schemes for gas dynamics, J. Comput. Phys. 228, 33-54.
• Smolarkiewicz, P.K., and C.L. Winter (2010), Pores resolving simulation of Darcy flows, J. Comput. Phys. 229, 9, 3121-3133.
• Smolarkiewicz, P.K., V. Grubisic, and L.G. Margolin (1997), On forward-in-time differencing for fluids: Stopping criteria for iterative solutions of anelastic pressure equations, Month. Weather Rev. 125, 4, 647-654.
• Smolarkiewicz, P.K., L.G. Margolin, and A.A. Wyszogrodzki (2001), A class of nonhydrostatic global models, J. Atmos. Sci. 58, 4, 349-364.
• Smolarkiewicz, P.K., C. Temperton, S.J. Thomas, and A.A. Wyszogrodzki (2004), Spectral preconditioners for nonhydrostatic atmospheric models: extreme applications. In: Proc. ECMWF Seminar Series on Recent Developments in Numerical Methods for Atmospheric and Ocean Modelling, 6-10 September, 2004, Reading, UK, 203-220.
• Smolarkiewicz, P.K., R. Sharman, J. Weil, S.G. Perry, D. Heist, and G. Bowker (2007), Building resolving large-eddy simulations and comparison with wind tunnel experiments, J. Comput. Phys. 227, 633-653.
• Szmelter, J., and P.K. Smolarkiewicz (2006), MPDATA error estimator for mesh adaptivity, Int. J. Numer. Meth. Fluids 50, 10, 1269-1293.
• Szmelter, J., and P.K. Smolarkiewicz (2010), An edge-based unstructured mesh discretisation in geospherical framework, J. Comput. Phys. 229, 13, 4980-4995.
• Szmelter, J., and P.K. Smolarkiewicz (2011), An edge-based unstructured mesh framework for atmospheric flows, Comput. Fluids 46, 455-460.
• Warn-Varnas, A., J. Hawkins, P.K. Smolarkiewicz, S.A. Chin-Bing, D. King, and Z. Hallock (2007), Solitary wave effects north of Strait of Messina, Ocean Model. 18, 2, 97-121.
• Wedi, N.P., and P.K. Smolarkiewicz (2004), Extending Gal-Chen and Somerville terrain-following coordinate transformation on time-dependent curvilinear boundaries, J. Comput. Phys. 193, 1-20.
• Williamson, D.L. (2008), The evolution of dynamical cores for global atmospheric models, J. Meteorol. Soc. Jpn. 85B, 241-268.
• Wurtele, M.G., R.D. Sharman, and A. Datta (1996), Atmospheric lee waves, Ann. Rev. Fluid. Mech. 28, 429-476.