Abstract

The Grand Challenge of Space Weather Prediction

Gabor Toth
University of Michigan
Engineering

Space weather is the interaction of the Sun and the Earth that can affect human life and technology. Prediction of space weather can mitigate the harmful effects of solar eruptions and magnetic storms. Physics based modeling of space weather is one of the most challenging problems for computational fluid dynamics. The complexity of the physical system, the huge computational costs, and the requirement of modeling space weather faster than real time make this problem a true grand challenge.

There are disparate spatial scales ranging from the Sun-Earth distance to 100-s of kilometers resolution required near the Earth. One of the successful approaches to this problem is the use of adaptive grids. A predictive model must run faster than real time. This can only be achieved on massively parallel computers and the code must scale well up to hundreds of processors. The fast magnetosonic speed can approach the speed of light near the magnetic poles of the Earth. The stiffness of the equations can lead to restrictively small time steps, which can be avoided by the use of local time stepping, Boris correction
and implicit time integration schemes. Huge gradients of the magnetic field near the Earth can lead to large numerical errors, which can result in negative pressure. The divergence of the numerically obtained magnetic field should be controlled.

Successful modeling of space weather cannot be achieved with only solving the ideal magnetohydrodynamic equations. We have built a framework comprising of several numerical models spanning from the surface of the Sun to the surface of the Earth. These models include effects of resistivity, heat conduction, multi-species plasma, high energy particles. The various models need to communicate with the framework and with each other, which requires efficient parallel algorithms.

I will discuss the challenges and the successful approaches we developed in the past years, which resulted in the Space Weather Modeling Framework (SWMF). Although our main goal is space weather simulation, the algorithms are general and can be used successfully in many applications.