An Implicit Solver for Simulating Inductive-Dynamic Magnetosphere-Ionosphere/Thermosphere Coupling

Physics

Scientific paper

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[2427] Ionosphere / Ionosphere/Atmosphere Interactions, [2431] Ionosphere / Ionosphere/Magnetosphere Interactions, [2753] Magnetospheric Physics / Numerical Modeling

Scientific paper

We present a model based on three-fluid (electrons, ions, and neutrals) and time-dependent electromagnetic field theory to describe the solar wind-magnetosphere-ionosphere/thermosphere coupling, from the ionosphere-thermosphere perspective. The present model self-consistently solves time-dependent continuity, momentum, and energy equations for the electrons, ions and neutrals, as well as Maxwell equations (Ampere's and Faraday's laws). The coupled nonlinear partial differential equation system involves various time scales with the collision time scale being as short as ~10-6 s at 80 km altitude. The very short collision time scale makes the equation system strongly stiff. It is challenging to solve such stiff equations explicitly because a very small time step is required to obtain stable numerical solutions. In this study we develop an implicit algorithm, which avoids the stringent requirement on the time step by the explicit algorithms and thus greatly reduces the CPU time consumption, to solve the equation system. The difference equations derived from the implicit scheme are mathematically more complicated, consisting of a set of nonlinear algebraic equations with unknowns on the spatial grids that are globally coupled. We apply an iterative and Jacobian-free Newton-Krylov method to efficiently obtain numerical solutions for the nonlinear algebraic equations. The comparison of the implicit algorithm with explicit methods under simple situations has shown differences less than 0.01% and improvement of 105 times in time stepping. Simulation results for the 1-D ionosphere/thermosphere response to an imposed convection velocity at the top boundary are presented to show the performance of the numerical scheme and illustrate the physics of the inductive-dynamic magnetosphere-ionosphere/thermosphere coupling.

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