An analytic solution for linear gravity waves in a channel as a test for numerical models using the non-hydrostatic, compressible Euler equations

Quarterly Journal of the Royal Meteorological Society

Volumn 139, Issue 677, 2013, Pages 1977-1989

  Baldauf, Michael ^a   Brdar, Slavko ^b  

^a DEUTSCHER WETTERDIENST   (Germany)

^b UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Dynamical core; Idealized test; Limited area numerical simulations

Indexed keywords

ANALYTIC SOLUTION; ATMOSPHERIC MODEL; COMPRESSIBLE EULER EQUATIONS; DYNAMICAL CORE; EXACT ANALYTIC SOLUTIONS; FLAT CHANNELS; LINEAR GRAVITY WAVE; NON-HYDROSTATIC;

COMPUTER SIMULATION; EULER EQUATIONS; GRAVITY WAVES; HYDRAULICS; NUMERICAL MODELS;

COMPUTATIONAL FLUID DYNAMICS;

ANALYTICAL METHOD; ATMOSPHERIC MODELING; COMPUTER SIMULATION; EULERIAN ANALYSIS; GRAVITY WAVE; NUMERICAL MODEL;

EID: 84890240233     PISSN: 00359009     EISSN: 1477870X     Source Type: Journal    
DOI: 10.1002/qj.2105     Document Type: Article

References (24)

1. Baldauf M. 2008. A linear solution for flow over mountains and its comparison with the COSMO model. COSMO Newsletter No. 9: 19-24. http://www.cosmo-model.org/content/model/documentation/newsLetters/.
2. Baldauf M. 2010. Linear stability analysis of Runge-Kutta based partial time-splitting schemes for the Euler equations. Mon. Weather Rev. 138: 4475-4496.
3. Baldauf M, Seifert A, Förstner J, Majewski D, Raschendorfer M, Reinhardt T. 2011. Operational convective-scale numerical weather prediction with the COSMO model: description and sensitivities. Mon. Weather Rev. 139: 3887-3905.
4. Bonaventura L. 2000. 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.
5. Brdar S, Baldauf M, Dedner A, Klöfkorn R. 2012. Comparison of dynamical cores for NWP models. Theor. Comput. Fluid Dynam. DOI: 10.1007/s00162-012-0264-z.
6. Bretherton FP. 1966. The propagation of groups of internal gravity waves in a shear flow. Q. J. R. Meteorol. Soc. 92: 466-480.
7. Bronstein IN, Semendjajew KA. 1984. Taschenbuch der Mathematik (25th edn). Harri Deutsch: Frankfurt am Main.
8. Bryan G, Fritsch JM. 2002. A benchmark simulation for moist nonhydrostatic numerical models. Mon. Weather Rev. 130: 2917-2928.
9. Cockburn B, Shu CW. 1998. The Runge-Kutta discontinuous Galerkin method for conservation laws V. J. Comput. Phys. 141: 199-224.
10. Courant R, Hilbert D. 1968. Mathematische Methoden der Physik I (3rd edn). Springer: Berlin.
11. Davies T, Staniforth A, Wood N, Thuburn J. 2003. Validity of anelastic and other equation sets as inferred from normal-mode analysis. Q. J. R. Meteorol. Soc. 129: 2761-2775.
12. Dedner A, Klöfkorn R, Nolte M, Ohlberger M. 2011. A generic interface for parallel and adaptive scientific computing: abstraction principles and the DUNE-FEM module. Computing 90: 165-196.
13. Dudhia J. 1993. A nonhydrostatic version of the Penn State-NCAR mesoscale model: validation test and simulation of an Atlantic cyclone and cold front. Mon. Weather Rev. 121: 1493-1513.
14. Gottlieb S, Shu CW. 1998. Total variation diminishing Runge-Kutta schemes. Math. Comput. 67: 73-85.
15. Long RR. 1955. Some aspects of the flow of stratified fluids. Part 3. Continuous density gradients. Tellus 7: 341-357.
16. Schär C, Leuenberger D, Fuhrer O, Lüthi D, Girard C. 2002. A new terrain-following vertical coordinate formulation for atmospheric prediction models. Mon. Weather Rev. 130: 2459-2480.
17. Skamarock WC, Klemp JB. 1992. The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations. Mon. Weather Rev. 120: 2109-2127.
18. Skamarock WC, Klemp JB. 1994. Efficiency and accuracy of the Klemp-Wilhelmson time-splitting scheme. Mon. Weather Rev. 122: 2623-2630.
19. Smith RB. 1979. The influence of mountains on the Atmosphere. Adv. Geophys. 21: 87-220.
20. Steppeler J, Doms G, Schättler U, Bitzer HW, Gassmann A, Damrath U, Gregoric G. 2003. Meso-gamma scale forecasts using the nonhydrostatic model LM. Meteorol. Atmos. Phys. 82: 75-96.
21. Straka JM, Wilhelmson RB, Wicker LJ, Anderson JR, Droegemeier KK. 1993. Numerical solutions of a non-linear density current: a benchmark solution and comparisons. Int. J. Num. Meth. Fluids 17: 1-22.
22. Takacs LL. 1985. A two-step scheme for the advection equation with minimized dissipation and dispersion errors. Mon. Weather Rev. 113: 1050-1065.
23. Weisman ML, Klemp JB. 1982. The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon. Weather Rev. 110: 504-520.
24. Wicker LJ, Skamarock WC. 2002. Time splitting method for elastic models using forward time schemes. Mon. Weather Rev. 130: 2088-2097.