Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere by Xueshang Feng

Author:Xueshang Feng
Language: eng
Format: epub, pdf
ISBN: 9789811390814
Publisher: Springer Singapore

(3.22)

(3.23)

In a cell with geometrical center (i, j, k), denotes volume average for conservative variables , and denotes area average for magnetic field with in face given by Eq. (3.7). The spatial reconstruction for the magnetic field is based on the staggered magnetic field components instead of cell-centered magnetic field. Thus, magnetic field is only updated at the face center. The face-valued magnetic fields stored on the faces are only averaged to the zone center value when required. In this formulation, will be the physical time step with an integer times that of explicit time step constrained by the usual CFL stability criterion.

To solve the equations accurately in time, a dual-time algorithm [15, 210] can be used to modify the implicit form Eqs. (3.22)–(3.23) by introducing a pseudo-time derivative . We adopt a first-order backward finite difference scheme for the pseudo-time derivative, take Eqs. (3.22) for example, then the new discretized equations become

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