Combined Explicit-Implicit Techniques for Faster than Real-Time Space Weather Simulations

Details Combined Explicit-Implicit Techniques for Faster than Real-Time Space Weather Simulations Combined Explicit-Implicit Techniques for Faster than Real-Time Space Weather Simulations

May 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agusm..sm52a03t&link_type=abstract

American Geophysical Union, Spring Meeting 2001, abstract #SM52A-03

Physics

2700 Magnetospheric Physics, 2753 Numerical Modeling, 2784 Solar Wind/Magnetosphere Interactions

Scientific paper

The Alfvén speed can approach the speed of light near the Earth. This poses a severe problem for numerical modeling of the magnetosphere, since the time steps of an explicit time integration scheme are limited by the CFL numerical stability condition: the waves must not propagate more than one cell size in one time step. In a well resolved simulation, the cell size may be as small as several 100 km-s, which limits the time step to be less than 0.01 or even 0.001 seconds. On the other hand, typical time scales of the magnetosphere are on the order of minutes. This discrepancy calls for the use of implicit time stepping techniques, which are not limited by the CFL stability condition. We are reporting our preliminary results with a newly implemented Newton-Krylov-Schwarz type implicit time stepping scheme in our block-adaptive parallel 3D MHD code. The linear problems arising from the Newton scheme are solved with a parallel Krylov subspace type iterative scheme using a Schwarz type preconditioner. We also explore the possibility of combining the implicit and explicit time stepping schemes: the expensive but stable implicit scheme is used near the Earth where the wave speeds are high, while the inexpensive explicit scheme is employed where the stability condition on the time step is not restrictive.

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