A scale-selective multilevel method for long-wave linear acoustics

• Autorzy: Vater S. , Klein R. , Knio O.M.
• Języki publikacji: EN

Abstrakty

EN

A new method for the numerical integration of the equations for onedimensional linear acoustics with large time steps is presented. While it is capable of computing the "slaved" dynamics of short-wave solution components induced by slow forcing, it eliminates freely propagating compressible short-wave modes, which are under-resolved in time. Scalewise decomposition of the data based on geometric multigrid ideas enables a scale-dependent blending of time integrators with different principal features. To guide the selection of these integrators, the discrete-dispersion relations of some standard second-order schemes are analyzed, and their response to high wave number low frequency source terms are discussed. The performance of the new method is illustrated on a test case with "multiscale" initial data and a problem with a slowly varying high wave number source term.

Słowa kluczowe

EN

linear acoustics; implicit time discretization; large time steps; balanced modes; multiscale time integration

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2011
• Tom: Vol. 59, no. 6
• Strony: 1076--1108
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Vater S.

autor

Klein R.

autor

Knio O.M.

• Institute of Mathematics, Freie Universit&aumlt Berlin, Berlin, Germany,

Bibliografia

• Courant, R., K.O. Friedrichs, and H. Lewy (1928), Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. 100, 32-74 (in German).
• 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, DOI: 10.1256/qj.02.195.
• Deuflhard, P., and F. Bornemann (2002), Scientific Computing with Ordinary Differential Equations, Texts in Applied Mathematics Series, vol. 42, Springer, New York.
• Dubois, T., F. Jauberteau, and R.M. Temam (2004), Dynamic multilevel methods and turbulence. In: E. Stein, R. de Borst, and T.J.R. Hughes (eds.), Encyclopedia of Computational Mechanics, John Wiley & Sons, New York.
• Dubois, T., F. Jauberteau, R. Temam, and J. Tribbia (2005), Multilevel schemes for the shallow water equations, J. Comput. Phys. 207, 660-694.
• Durran, D.R. (1989), Improving the anelastic approximation, J. Atmos. Sci. 46, 1453-1461.
• Durran, D.R. (2010), Numerical Methods for Fluid Dynamics: With Applications to Geophysics, 2nd ed. Texts in Applied Mathematics, vol. 32, Springer, Heidelberg.
• Fukushima, T. (1999), Super implicit multistep methods. In: H. Umehara (ed.), Proc. 31st Symposium on Celestial Mechanics, 3-5 March 1999, Kashima Space Research Center, Ibaraki, Japan, 343-366.
• Grabowski, W.W. (1998), Toward cloud resolving modeling of large-scale tropical circulations: A simple cloud microphysics parameterization, J. Atmos. Sci. 55, 3283-3298.
• Grinstein, F.F., L.G. Margolin, and W.J. Rider (2007), Implicit Large Eddy Simulation, Cambridge University Press, Cambridge.
• Hairer, E., C. Lubich, and G. Wanner (2006), Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ed. Springer Series in Computational Mathematics, vol. 31, Springer, Heidelberg.
• Klein, R. (2009), Asymptotics, structure, and integration of sound-proof atmospheric flow equations, Theor. Comput. Fluid Dyn. 23, 3, 161-195.
• 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, 3226-3237.
• Lipps, F.B., and R.S. Hemler (1982), A scale analysis of deep moist convection and some related numerical calculations, J. Atmos. Sci. 39, 2192-2210.
• Ohfuchi,W., H. Nakamura, M. Yoshioka, T. Enomoto, K. Takaya, X. Peng, S. Yamane, T. Nishimura, Y. Kurihara, and K. Ninomiya (2004), 10-km mesh meso-scale resolving simulations of the global atmosphere on the Earth Simulator: Preliminary outcomes of AFES (AGCM for the Earth Simulator), J. Earth Sim. 1, 8-34.
• Schneider, T., N. Botta, K.J. Geratz, and R. Klein (1999), Extension of finite volume compressible flow solvers to multi-dimensional, variable density zero Mach number flows, J. Comput. Phys. 155, 2, 248-286.
• Skamarock, W.C., and J.B. Klemp (1992), The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations, Monthly Weath. Rev. 120, 2109-2127.
• Smolarkiewicz, P.K., and A. Dörnbrack (2008), Conservative integrals of adiabatic Durran’s equations, Int. J. Num. Meth. Fluids 56, 1513-1519.
• Trottenberg, U., C. Oosterlee, and A. Schüller (2001), Multigrid, Academic Press, London.
• Vater, S., and R. Klein (2009), Stability of a Cartesian grid projection method for zero Froude number shallow water flows, Numer. Math. 113, 123-161.