Status report of WG2 - Numerics and Dynamics COSMO General Meeting 10-13 Sept. 2012, Lugano
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10-13 Sept. 2012M. Baldauf (DWD) 1
Status report of
WG2 - Numerics and Dynamics
COSMO General Meeting10-13 Sept. 2012, Lugano
Michael BaldaufDeutscher Wetterdienst, Offenbach, Germany
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10-13 Sept. 2012M. 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
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M. Baldauf (DWD) 3
Main changes towards the current solver:
1. improvement of the vertical discretization: use of weighted averaging operators for all vertical operations
2. divergence in strong conservation form
3. optional: complete 3D (=isotropic) divergence damping
4. 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
Development of a new fast waves solver for the Runge-Kutta scheme
M. Baldauf (DWD)
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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')
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Divergence with weighted average of u (and v) to the half levels:
Divergence with only arithmetic average of u (and v) to the half levels:
Discretization error in stretched grids; Divergence
not a consistent discretization if s1 !
1/s ·dz
dz
s·dz
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buoyancy term with weighted average of T'(T0 exact):
buoyancy term with arithmetic average of T'(T0 exact):
buoyancy term with weighted average for T' and T0:
Discretization error in stretched grids; Buoyancy (T'/T0)
dz
s·dz
1/s ·dz
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24.04.2012M. Baldauf (FE13) 7
Winter case experiment COSMO-DENew / Old fast waves solver
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24.04.2012M. Baldauf (FE13) 8
Summer case experiment COSMO-DENew / Old fast waves solver
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24.04.2012M. Baldauf (FE13) 9
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upper air verificationof COSMO-DE L65with new FW solvercompared with Parallel-RoutineCOSMO-DE L50
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06.-08. March 2012M. Baldauf (DWD) 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.)
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10-13 Sept. 2012M. Baldauf (DWD) 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
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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
For development of dynamical cores (or numerical methods in general)idealized test cases are an important evaluation tool
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)
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Small scale testwith a basic flow U0=20 m/sf=0
Black lines: analytic solutionShaded: COSMO
Initialization similar toSkamarock, Klemp (1994)
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Analytic solution of the fully compressible, non-hydrostatic Euler equations for the Fourier transformed vertical velocity w
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
kx cs2 / g
cs /
g
m=0
m=1
m=2
analogous expressions for ub(kx, kz, t), ...
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Convergence properties of COSMO
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10-13 Sept. 2012M. Baldauf (DWD) 17
• 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
A new dynamical core based on Discontinuous Galerkin methodsProject ‘Adaptive numerics for multi-scale flow’, DFG priority program ‘Metström’
D. Schuster, M. Baldauf (DWD)
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10-13 Sept. 2012M. Baldauf (DWD) 18
test case linear mountain overflow
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.
COSMO-RK
COSMO-DG
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10-13 Sept. 2012M. Baldauf (DWD) 19
test case density current (Straka et al., 1993)
‘ after 900 sec.COSMO-DG-simulation without diffusion
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10-13 Sept. 2012M. 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