Initial Analysis of the Large-Scale Stein-Nordlund
Simulations Dali Georgobiani
Formerly at:
Center for Turbulence Research Stanford University/ NASA
Presenting the results of
Bob Stein (MSU) & Åke Nordlund (Denmark)with
David Benson (MSU)Stanford, August 19, 2005
The Old CodeStein – Nordlund RHD 3D simulations• Compressible (M)HD equations• LTE non-gray radiation transfer• Realistic EOS and opacities
No free parameters (except for diffusion model). Wave excitation and damping occur naturally. There is an excellent correspondence between the code results and observations.
The New CodeStein – Nordlund RHD 3D simulations• Conservative Compressible (M)HD equations• LTE non-gray radiation transfer• Realistic EOS and opacities
No free parameters (except for diffusion model). Wave excitation and damping occur naturally. There is an excellent correspondence between the code results and observations.
€
∂ρ∂t
= −∇ • ρu
€
∂ρui∂t
= −∂
∂x jρuiu j + Pδij + ρυ
∂ui∂x j
+∂u j∂x i
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥+ ρgi + J × B( )i
€
∂ρe∂t
= −∇ • ρeu− P∇ • u+ ρν∂ui∂x j
+∂u j∂x i
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
+ηJ 2 +Qrad
€
∂B∂t
= −∇ × E, E = −u× B +ηJ, J = ∇ × B /μ0
48 Mm
48
Mm
20
Mm
Numerical Convection
Oscillations are naturally driven by numerical turbulent convection
Convection
Oscillations
The New Code
• Supergranulation scale simulations• Currently 48 Mm x 48 Mm x 20 Mm• Resolution 100 km horizontally, 12 – 75 km
vertically
• Numerical Method: Staggered variables Spatial differencing: 6th order centered finite
difference Time advancement: 3rd order Runge-Kutta
Radiation Treatment
• LTR
• Non-grey, 4 bin multigroup
Equation of State• Tabular EOS
Includes ionization, excitation
H, He, H2, other abundant elements
Boundary Conditions• Density: top hydrostatic, bottom logarithmic
• Velocity: symmetric (normal derivative = 0)
• Energy (per unit mass): top – slowly evolving average, bottom – fixed energy in inflows
Initialization• Start from existing 12x12x9 Mm simulation
• Extend adiabatically to 20 Mm and relax for a solar day to develop structures
• Double horizontally + small fraction of stretched fluctuations to remove symmetry
• Relax to develop large-scale structures
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