Linear stability analysis of Runge-Kutta-based partial time-splitting schemes for the Euler equations

Monthly Weather Review

Volumn 138, Issue 12, 2010, Pages 4475-4496

  Baldauf, Michael ^a  

^a DEUTSCHER WETTERDIENST   (Germany)

Author keywords

Model evaluation performance; Model initialization; Numerical analysis modeling; Parameterization; Stability

Indexed keywords

ATMOSPHERIC SIMULATIONS; CLOUD-RESOLVING; EULER SYSTEM; FAST PROCESS; IMPLICIT SCHEMES; INTEGRATION TECHNIQUES; MODEL INITIALIZATION; NUMERICAL ANALYSIS/MODELING; NUMERICAL PARAMETERS; NUMERICAL STABILITY ANALYSIS; OPERATIONAL MODEL; OPTIMAL VALUES; RUNGE-KUTTA; SECOND ORDERS; STABILITY PROPERTIES; TIME SPLITTING; TRUNCATION ERRORS;

COMPUTER SIMULATION; LINEAR STABILITY ANALYSIS; MATHEMATICAL MODELS; RUNGE KUTTA METHODS; STABILIZATION; TURBULENT FLOW;

EULER EQUATIONS;

ADVECTION; ATMOSPHERIC MODELING; EULERIAN ANALYSIS; FORECASTING METHOD; MODEL VALIDATION; NUMERICAL METHOD; NUMERICAL MODEL; PARAMETERIZATION; WEATHER FORECASTING;

EID: 78651093205     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/2010MWR3355.1     Document Type: Article

References (22)

1. Anderson, E., and Coauthors, 1999: LAPACK users' guide. 3rd ed. Society for Industrial and Applied Mathematics, Philadelphia, PA, 407 pp.
2. Baldauf, M., 2002: Integrationby time-splitting in mesoscale models. COSMO Newsl., 2, 101-104.
3. Baldauf, M., 2008: Stability analysis for linear discretisations of the advection equation with Runge-Kutta time integration. J. Comput. Phys., 227, 6638-6659.
4. Bretherton, F. P., 1966: The propagation of group of internal gravity waves in a shear flow. Quart. J. Roy. Meteor. Soc., 92, 466-480.
5. Doms, G., and U. Schättler, 2002: A description of the nonhydrostatic regional model LM. Part I: Dynamics and numerics. LM_F90 2.18, Deutscher Wetterdienst, Offenbach, Germany, 140 pp.
6. Durran, D. R., 1998: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer, 482 pp.
7. Förstner, J., and G. Doms, 2004: Runge-Kutta time integration and high-order spatial discretization of advection-A new dynamical core for the LMK. COSMO Newsl., 4, 168-176.
8. Gassmann, A., and H.-J. Herzog, 2007: A consistent time-split numerical scheme applied to the nonhydrostatic compressible equations. Mon. Wea. Rev., 135, 20-36.
9. Jebens, S., O. Knoth, and R. Weiner, 2009: Explicit two-step peer methods for the compressible Euler equations. Mon. Wea. Rev., 137, 2380-2392.
10. Klemp, J. B., and R. B. Wilhelmson, 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 1070-1096.
11. Klemp, J. B., W. C. Skamarock, and J. Dhudia, 2007: Conservative split-explicit time integration methods for the compressible non-hydrostatic equations. Mon. Wea. Rev., 135, 2897-2913.
12. LeVeque, R. J., and J. Oliger, 1983: Numerical methods based on additive splittings for hyperbolic partial differential equations. Math. Comput., 40, 469-497.
13. Mesinger, F., 1977: Forward-backward scheme, and its use in a limited area model. Beitr. Phys. Atmos., 50, 200-210.
14. Purser, R. J., and L. M. Leslie, 1991: Reducing the error in a time-split finite difference scheme using an incremental technique. Mon. Wea. Rev., 119, 578-585.
15. Ruuth, S. J., and R. J. Spiteri, 2004: High-order strong-stability-preserving Runge-Kutta methods with downwind-biased spatial discretizations. SIAM J. Numer. Anal., 42, 974-996.
16. Shu, C.-W., 1988: Total-variation diminishing time discretizations. SIAM J. Sci. Stat. Comput., 9, 1073-1084.
17. Skamarock, W. C., and J. B. Klemp, 1992: The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations. Mon. Wea. Rev., 120, 2109-2127.
18. Skamarock, W. C., and J. B. Klemp, 2008: Atime-split nonhydrostatic atmospheric model for weather research and forecasting applications. J. Comput. Phys., 227, 3465-3485.
19. Steppeler, J., G. Doms, U. Schättler, H. W. Bitzer, A. Gassmann, U. Damrath, and G. Gregoric, 2003: Mesogamma scale forecasts using the nonhydrostatic model LM. Meteor. Atmos. Phys., 82, 75-96.
20. Viner, K. C., and C. C. Epifanio, 2008: An analysis of Klemp-Wilhelmson schemes as applied to large-scale wave modes. Mon. Wea. Rev., 136, 4730-4745
21. Wicker, L. J., and W. C. Skamarock, 1998: A time-splitting scheme for the elastic equations incorporating second-order Runge-Kutta time differencing. Mon. Wea. Rev., 126, 1992-1999.
22. Wicker, L. J., and W. C. Skamarock, 2002: Time splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130, 2088-2097.