Modeling 3-D Solar Wind Structure.pdf
Modeling 3-D Solar Wind Structure.pdf
Modeling 3-D Solar Wind Structure.pdf
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Formulation of ENLIL: MHD Equations<br />
∂<br />
∂t<br />
∂<br />
∂t<br />
+ ∇ ⋅<br />
( ρV) = 0<br />
⎛ BB ⎞<br />
⎜ μ ⎟<br />
⎝ o ⎠<br />
GM<br />
r<br />
( ρ V) + ∇ ⋅ ( ρVV<br />
) = −∇ ⋅⎜<br />
⎟ + ρ<br />
2<br />
∂<br />
∂t<br />
( E ) + ∇ ⋅ ( EV<br />
) = − p∇<br />
⋅ ( V )<br />
∂<br />
( B ) = ∇ × ( V × B)<br />
∂t<br />
• Ρ is the mass density, V is the mean flow velocity, B is<br />
the magnetic field, P is the pressure (thermal, p, and<br />
magnetic B 2 / 2μ o ), μ o is the permeability, G is gravity, M S<br />
is the solar mass, and E is the thermal energy density<br />
(p/(γ-1) with γ the ratio of specific heats.<br />
• A thermal energy equation is used because it gives<br />
smooth profiles of thermal pressure and temperature but<br />
may interfere with shock capture.<br />
s
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