1 / 20

Status report of WG2 - Numerics and Dynamics COSMO General Meeting 10-13 Sept. 2012, Lugano

Status report of WG2 - Numerics and Dynamics COSMO General Meeting 10-13 Sept. 2012, Lugano. Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany. Topics New Fast Waves Solver A new idealized test case for non-hydrostatic compressible Models

akina
Download Presentation

Status report of WG2 - Numerics and Dynamics COSMO General Meeting 10-13 Sept. 2012, Lugano

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Status report of WG2 - Numerics and Dynamics COSMO General Meeting 10-13 Sept. 2012, Lugano Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany M. Baldauf (DWD)

  2. Topics • New Fast Waves Solver • A new idealized test case for non-hydrostatic compressible Models • COSMO-DG: Discontinuous Galerkin dynamical core for COSMO • outlook • CONSOL: development of an implicit finite volume solver see CDC presentation M. Baldauf (DWD)

  3. Development of a new fast waves solver for the Runge-Kutta scheme M. Baldauf (DWD) • Main changes towards the current solver: • improvement of the vertical discretization: use of weighted averaging operators for all vertical operations • divergence in strong conservation form • optional: complete 3D (=isotropic) divergence damping • optional: Mahrer (1984) discretization of horizontal pressure gradients • additionally some 'technical' improvements; • hopefully a certain increase in code readability • overall goal: improve numerical stability of COSMO M. Baldauf (DWD)

  4. Improved stability in real case applications • COSMO-DE 28.06.2011, 6 UTC runs (shear instability case)must be cured by Smagorinsky diffusionoperational deterministic and several COSMO-DE-EPS runscrashed after ~16 h • COSMO-DE 12.07.2011, 6 UTC run (‚explosion‘ of qr in Alps)only stable with Bott2_Strang • COSMO-DE L65, 15.07.2011, 12 UTC runmodel crash after 215 timesteps (~ 1.5 h) • COSMO-2, 16.06.2011, 0 UTC run (reported by O. Fuhrer)model crash after 1190 timesteps (~6.6 h) • ‚COSMO-1, 24.08.2011‘, resolution 0.01° (~ 1.1km) 1700 * 1700 grid points (reported by A. Seifert) model crash after 10 time steps • ... • COSMO-DE L65 run stable for 2 months ('1.7.-31.8.2012') M. Baldauf (DWD) 4

  5. Discretization error in stretched grids; Divergence Divergence with weighted average of u (andv) to the half levels: s·dz dz 1/s ·dz Divergence with only arithmetic average of u (and v) to the half levels: not a consistent discretization if s1 !

  6. Discretization error in stretched grids; Buoyancy (T'/T0) buoyancy term with weighted average of T' (T0 exact): s·dz dz 1/s ·dz buoyancy term with arithmetic average of T'(T0 exact): buoyancy term with weighted average for T' and T0:

  7. Winter case experiment COSMO-DE New / Old fast waves solver M. Baldauf (FE13)

  8. Summer case experiment COSMO-DE New / Old fast waves solver M. Baldauf (FE13)

  9. M. Baldauf (FE13)

  10. upper air verification of COSMO-DE L65 with new FW solver compared with Parallel-Routine COSMO-DE L50

  11. Summary • New fast waves solver cures crashes in several realistic test cases • this is partly due to the fact that it allows steeper slopes • dynamic bottom BC probably not necessary • problems with geopotential bias are solved due to improved buoyancy formulation • efficiency: the new fast waves solver needs about 30% more computation time than the current one on the NEC-SX9  about 6% more time in total for COSMO-DE • new fast_waves_sc.f90 is now available in COSMO 4.24(if irefatm=1 is used  use int2lm 1.20 with lanalyt_calc_p0T0=.TRUE.) M. Baldauf (DWD) 06.-08. March 2012 11

  12. Outlook • Work on • lateral radiation BC • alternative upper damping layer (Klemp et al., 2008) • lw_freeslip • is finished  COSMO 5.1 • Documentation in COSMO Sci. Doc. Part I(currently new fast waves doc. only available in German) • Currently new FW runs in Parallelroutine at DWD • further investigation of the Mahrer-discretization;benefits from Zängl (2012) MWR ? • Other stuff: • Consolidation on dynamical bottom BC • Consolidation and inspection of 3D divergence damping M. Baldauf (DWD)

  13. An analytic solution for linear gravity waves in a channel as a test case for solvers of the non-hydrostatic, compressible Euler equations M. Baldauf (DWD) For development of dynamical cores (or numerical methods in general) idealized test cases are an important evaluation tool • Existing analytic solutions: • stationary flow over mountains linear: Queney (1947, ...), Smith (1979, ...), Baldauf (2008)non-linear: Long (1955) for Boussinesq-approx. atmosphere • non-stationary, linear expansion of gravity waves in a channelSkamarock, Klemp (1994) for Boussinesq-approx. atmosphere • Most of the other idealized tests only possess 'known solutions' gained • by other numerical models. There exist even less analytic solutions which use the exact equations, i.e. in a sense that a numerical model would converge to this solution. One exception is presented here: linear expansion of gravity/sound waves in a channel

  14. Small scale test with a basic flow U0=20 m/s f=0 Initialization similar to Skamarock, Klemp (1994) Black lines: analytic solution Shaded: COSMO

  15. Analytic solution of the fully compressible, non-hydrostatic Euler equations for the Fourier transformed vertical velocity w analogous expressions for ub(kx, kz, t), ... The frequencies ,  are the gravity wave and acoustic branch, respecticely, of the dispersion relation for compressible waves in a channel with height H; kz = ( / H)  m m=2    cs / g m=1 m=0  kx cs2 / g

  16. Convergence properties of COSMO

  17. A new dynamical core based on Discontinuous Galerkin methods Project ‘Adaptive numerics for multi-scale flow’, DFG priority program ‘Metström’ • cooperation between • DWD, • Univ. Freiburg, • Univ. Warwick • goals of the DWD: new dynamical core for COSMO • high order • conservation of mass, momentum and energy / potential temperature • scalability to thousands of CPUs. • ➥use of discontinuous Galerkin methods • HEVI time integration (horizontal explicit, vertical implicit) • terrain following coordinates • coupling of the physical parameterisations • reuse of the existing parameterisations D. Schuster, M. Baldauf (DWD) M. Baldauf (DWD)

  18. COSMO-RK test case linear mountain overflow COSMO-DG Test case of: Sean L. Gibbons. Impacts of sigma coordinates on the Euler and Navier-Stokes equations using continuous Galerkin methods. PhD thesis, Naval Postgradudate School, March 2009. M. Baldauf (DWD)

  19. test case density current (Straka et al., 1993) ‘ after 900 sec. COSMO-DG-simulation without diffusion M. Baldauf (DWD)

  20. Outlook, Milestones • Further consolidation of the explicit DG solver in COSMO • Use of implicit solver and HE-VI • Coupling of Turbulence scheme DFG bundle project: 'Gravity waves' together with the group of U. Achatz (Univ. Frankfurt) • Coupling of Microphysics : more realistic test simulations • Coupling to remaining physics: COSMO-DG ready for realistic simulations M. Baldauf (DWD)

More Related