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Solar Wind Propagation Model

mSWiM is a 1.5-D ideal MHD model implemented with the Versatile Advection Code (VAC), a general software package designed to solve a conservative system of hyperbolic partial differential equations with additional non-hyperbolic source terms [Tóth, 1996]. The model propagates the solar wind plasma radially outward from the Earth´s orbit at a selected helioecliptic longitude in the inertial frame of reference assuming spherical symmetry.

For a detailed description of the MHD equations and the numerical scheme used in mSWiM, please refer to the paper by Zieger and Hansen [2008].

The simulation uses solar wind conditions measured at Earth as the inner boundary. For the solar wind predictions listed in this web page, we used hourly solar wind plasma and interplanetary magnetic field (IMF) data in the RTN coordinate system from the OMNIWeb database ( as input.

inertial Since the simulation is performed in the inertial frame, the boundary conditions at 1 AU have to be rotated with the Sun, or mapped forward or backward in time, from the Earth to the simulation longitude (see Fig. 1). This kind of mapping of the boundary conditions includes the assumption that the solar corona is in steady state or changing slowly on the time scale of half a solar rotation.

Fig. 1

The primary output of the simulation is the 1.5-D MHD solution (n, v, T, B) in RTN coordinate system as a function of heliocentric distance and time at the selected helioecliptic longitude.

This solution is then mapped to the body of interest (e.g. Jupiter, Saturn, or a spacecraft) to provide the predicted solar wind conditions listed in this web page.

motion In case of fast-moving bodies like spacecraft or comets, the location of the body can change significantly during the time the solution rotates with the Sun from the simulation longitude to the body. Such a displacement of the body is taken into account in mSWiM with an appropriate iterative mapping procedure (see the mapping scheme in Fig 2).

Fig. 2

In numerical MHD, the ∇·B = 0 constraint must be enforced. In 1-D, the fact that there are no gradients in the perpendicular direction leads to the result that the BR component must be constant in time. We do include the radial component of IMF (BR) in the output files however, because BR can change due to movement of the target body in heliocentric distance. In all simulations listed in this web page, BR was set to 5 nT at Earth and the theoretically expected radial dependence of R-2 was applied.

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