Oswald Knoth, Detlev Hinneburg

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A cloud resolving model with implicit time stepping: orographic flow application Oswald Knoth, Detlev Hinneburg Institute for Tropospheric Research, Leipzig, Germany

Model Formulation anelastic model Momentum equation Potential temperature Continuity equation Water vapour Cloud water Bad Orb 2003

Source terms Bad Orb 2003

Buoyancy Bad Orb 2003

Condensation/Evaporation Bad Orb 2003

Condensation/Evaporation Bad Orb 2003

Condensation/Evaporation Bad Orb 2003

Cut Cell Approach Grid is described by free face area F Free cell Volume V Bad Orb 2003

Cut Cell Approach Free face aerea Free volume Bad Orb 2003

Time integration method by a projected Rosenbrock method approximation at time step size approximation of the Jacobian Bad Orb 2003

Including of Projection Bad Orb 2003

Solution of the linear systems a)Rosenbrock step CG-method (BiCGStab) with preconditioning Jacobian: Transport: Advection Diffusion Source: Bouyancy Condensation Drag Curvature effects Coriolis force Bad Orb 2003

Solution of the linear systems replaced by first order upwinding Preconditioner: approximate matrix factorization is inverted approximately by Gauss-Seidel iteration, is inverted exactly Reduction of matrix operations through Bad Orb 2003

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 Bad Orb 2003

Example: Orographic Cloud Hill is described by Witch of Agnessi mountain, defined by A stable atmosphere is used with 90% relative humidity Bad Orb 2003

Orographic Cloud Bad Orb 2003

Orographic Cloud Bad Orb 2003

Orographic Cloud 0 sec. Bad Orb 2003

Orographic Cloud 0 sec. Bad Orb 2003

Orographic Cloud 1000 sec. Bad Orb 2003

Orographic Cloud 1500 sec. Bad Orb 2003

Orographic Cloud 2000 sec. Bad Orb 2003

Orographic Cloud 3000 sec. Bad Orb 2003

Orographic Cloud 3000 sec. Bad Orb 2003

Orographic Cloud 3000 sec. Bad Orb 2003

Orographic Cloud Bad Orb 2003

Moist Bubble Computational domain 3,6 km by 2,4 km, dx=dz=10 m Bad Orb 2003

Moist Bubble 0 min. Bad Orb 2003

Moist Bubble 4 min. Bad Orb 2003

Moist Bubble 6 min. Bad Orb 2003

Moist Bubble 8 min. Bad Orb 2003

Moist Bubble 8 min. Bad Orb 2003

Moist Bubble 8 min. Bad Orb 2003

Moist Bubble Bad Orb 2003