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784 ZAMM · Z. angew. Math. Mech. 80 (2000) 11-12 5 Botta, N.; Klein, R.; Almgren, A.: Dry atmosphere asymptotics. Techn. rep.,Potsdam Institute for Climate Impact Research,Potsdam,Germany,1999. 6 Casulli, V.; Greenspan, D.: Pressure method for the numerical solution or transient compressible fluid flow. Int. J. Num. Meth. Fluids, 4 (1984),1001–1012. 7 Chorin, A. J.: A numerical method for solving incompressible flow problems. J. Comput. Phys., 2 (1967),12–26. 8 Chorin, A. J.: Numerical solution of the Navier-Stokes equations. Math. Comp., 22 (1968),745–762. 9 Durran, D. R.: Improving the anelastic approximation. Journal of the Atmospheric Sciences, 46 (1989),1453–1461. 10 Durran, D. R.: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer,1999. 11 Ebin, D. G.: Motion of Slightly Compressible Fluids in a Bounded Domain. i. Comm. Pure Appl. Math., 35 (1982), 451–485. 12 Emanuel, K. A.: Atmospheric Convection. Oxford University Press,1994. 13 Embid, P.; Majda, A. J.: Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity. Communications in Partial Differential Equations, 21 (1996),619–658. 14 Embid, P.; Majda, A. J.: Averaging over fast gravity waves for geophysical flows with unbalanced initial data. Theoretical and Computational Fluid Dynamics, 11 (1998),155–169. 15 Geratz, K. J.: Erweiterung eines Godunov-Typ-Verfahrens für mehrdimensionale kompressible Strömungen auf die Fälle kleiner und verschwindender Machzahl. PhD thesis,RWTH Aachen,1998. 16 Geratz, K.; Klein, R.; Munz, C.-D.; Roller, S.: Multiple Pressure Variable (MPV) Approach for Low Mach Number Flows Based on Asymptotic Analysis. In: Hirschel, E. H. (ed.): Flow simulation with high-performance computers II. DFG priority research programme results. Notes on Numerical Fluid Mechanics,52. Vieweg Verlag,Braunschweig, 1996. 17 Gill, A. E. (ed.): Atmosphere-Ocean Dynamics. International Geophysical Series,30. Academic Press,London,1982. 18 Guillard, H.; Viozat, C.: On the behoviour of upwind schemes in the low mach number limit. Computers and Fluids, 28 (1999),63–86. 19 Harlow, F. H.; Welch, J. E.: Numerical calculation of time dependent viscous incompressible flow. Phys. Fluids, 8 (1965),2182–2189. 20 Kaper, G.; Garbey, M. (eds.): Asymptotic analysis and the numerical solution of partial differential equations. Lecture Notes in Pure and Applied Mathematics,130. Marcel Dekker,New York,1991. 21 Karki, K. C.; Patankar, S. V.: Pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations. AIAA J., 27 (1989),1167–1174. 22 Klainerman, S.; Majda, A. J.: Compressible and Incompressible fluids. Comm. Pure Appl. Math., 35 (1982),629–. 23 Klein, R.: Semi-implicit extension of a godunov-type scheme based on low mach number asymptotics i: One-dimensional flow. Journal of Computational Physics, 121 (1995),213–237. 24 Klein, R.; Botta, N.; Schneider, T.; Munz, C.; Roller, S.; Meister, A.; Hoffmann, L.; Sonar, T.: Asymptotic adaptive methods for multi-scale problems in fluid mechanics. Journal of Engineering Mathematics, – (2000),—.
Klein, R.: Atmosphere Asymptotics and Numerics – AUTHOR’S UPDATED PRINT 785 submitted. 25 Lai, M.; Bell, J. B.; Colella, P.: A projection method for combustion in the zero Mach number limit. AIAA Paper, 3369 (1993). 26 LeVeque, R. J.: A large time step generalization of Godunov’s method for systems of conservation laws. SIAM J. Num. Anal., 22 (1985),1051–1073. 27 LeVeque, R. J.: Numerical Methods for Conservation Laws. Birkhäuser Verlag,Zürich,Schweiz,1992. IBSN 0-521- 43009-7. 28 Majda, A.; Sethian, J.: The derivation and numerical solution of the equations for zero mach number combustion. Combustion Science and Technology, 42 (1985),185–205. 29 Merkle, C. L.; Choi, Y.-H.: Computation of low speed flow with heat addition. AIAA J., 25 (1987),831–838. 30 Muraki, D. J.; Snyder, C.; Rotunno, R.: The next-order corrections to quasigeostrophic theory. Journal of the Atmospheric Sciences, 56 (1998),1547–1560. 31 Ogura, Y.; Phillips, N. A.: Scale analysis of deep moist convection and some related numerical calculations. Journal of Atmosphere Science, 19 (1962),173–179. 32 Pedlosky, J. (ed.): Geophysical Fluid Dynamics. Springer,2 edition,1987. 33 Roller, S.; Munz, C.-D.; Geratz, K.; Klein, R.: The extension of incompressible flow solvers to the weakly compressible regime. Theoretical and Numerical Fluid Dynamics,(1999),submitted for publication. 34 Schlichting, H. (ed.): Boundary Layer Theory. MacGraw-Hill,1968. 35 Schneider, T.; Botta, N.; Klein, R.; Geratz, K. J.: Extension of finite volume compressible flow solvers to multi-dimensional,variable density zero mach number flows. Journal of Computational Physics,155 (1999),248–286. 36 Schneider, W. (ed.): Mathematische Methoden in der Strömungsmechanik. Vieweg,1978. 37 Schochet, S.: Fast singular limits of hyperbolic pdes. Journal of Differential Equations, 114 (1994),476–512. 38 Sesterhenn, J.; Müller, B.; Thomann, H.: Computation of compressible low mach number flow. Computational Fluid Dynamics, 2 (1992),829–833. 39 Smith, R. B.: Why can’t stably stratified air rise over high ground. In: Blumen, W. (ed.): Atmospheric processes over complex terrain. Meteorological Monographs,23,1990,pp. 105–107. 40 Turkel, E.: Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations. Journal of Computational Physics, 72 (1987),277 – 298. 41 van Dyke, M. (ed.): Perturbation Methods in Fluid Mechanics,Annotated Ed. Parabolic Press,1975. 42 Volpe, G.: On the use and accuracy of compressible flow codes at low mach numbers. AIAA Paper 91-1662,1991. 43 Worlikar, A.; Knio, O.; Klein, R.: Numerical simulation of a thermo-acoustic refrigerator: Ii stratified flow around the stack. Journal of Computational Physics, 144 (1998),299–324. 44 Zeytounian, R. K. (ed.): Meteorological Fluid Dynamics. Lecture Notes in Physics,m5. Springer,1991. Address: Prof. Rupert Klein,Potsdam Institut für Klimafolgenforschung,Telegrafenberg C4,14412 Potsdam,Germany, email: rupert.klein@pik-potsdam.de
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