A cloud resolving model with implicit time stepping: orographic flow application

1
A cloud resolving model with implicit time
stepping orographic flow application

• Oswald Knoth, Detlev Hinneburg
• Institute for Tropospheric Research, Leipzig,
  Germany

2
Model Formulation
anelastic model
Momentum equation
Potential temperature
Continuity equation
Water vapour
Cloud water
3
Source terms
4
Buoyancy
5
Condensation/Evaporation
6
Condensation/Evaporation
7
Condensation/Evaporation
8
Cut Cell Approach
Grid is described by free face area F Free cell
Volume V
9
Cut Cell Approach
10
Time integration method by a projected Rosenbrock
method
11
Including of Projection
12
Solution of the linear systems
a)Rosenbrock step CG-method (BiCGStab) with
preconditioning

• Jacobian

13
Solution of the linear systems
Preconditioner approximate matrix factorization
Reduction of matrix operations through
14
Solution of the linear systems
b) Pressure solver Nonoverlapping domain
decomposition Inner variables cell centered
pressure Interface variables pressure
gradient Global problem indefinit
preconditioned QMR Preconditioner
Neumann and Dirichlet problems on each
subdomain (Multigrid) Coarse problem
Neumann like problem with one variable
for each subdomain
15
Example Orographic Cloud
Hill is described by Witch of Agnessi mountain,
defined by
A stable atmosphere is used with 90 relative
humidity
16
Orographic Cloud
17
Orographic Cloud
18
Orographic Cloud
0 sec.
19
Orographic Cloud
0 sec.
20
Orographic Cloud
1000 sec.
21
Orographic Cloud
1500 sec.
22
Orographic Cloud
2000 sec.
23
Orographic Cloud
3000 sec.
24
Orographic Cloud
3000 sec.
25
Orographic Cloud
3000 sec.
26
Orographic Cloud
27
Moist Bubble

• Computational domain 3,6 km by 2,4 km,
• dxdz10 m

28
Moist Bubble
0 min.
29
Moist Bubble
4 min.
30
Moist Bubble
6 min.
31
Moist Bubble
8 min.
32
Moist Bubble
8 min.
33
Moist Bubble
8 min.
34
Moist Bubble