The 13th seminar of the Open-source Software Laboratory for Digital Modeling of Technical Systems was held 13 November 2020 in the Institute for System Programming of the RAS.
The topic of the seminar:
Two-dimensional models in magnetic hydrodynamics and dynamo theory
Mikhailov Evgeny (Moscow State University)
The study of the evolution of magnetic fields in a conducting medium is an important task for magnetic hydrodynamics. In the past, such problems were solved using simple models that allowed us to get fairly rough estimates for the results. The development of computer technologies has made it possible to solve complete three-dimensional problems using direct numerical modeling. However, in this case, the result often depends on a large number of parameters that are chosen quite randomly. In addition, it is often difficult to establish the fundamental laws that are inherent in the tasks. For this reason, two-dimensional models that use various symmetry considerations play a special role. They are, on the one hand, quite accurate, and on the other hand, they allow both numerical and asymptotic analysis.
The following models of magnetic hydrodynamics are developed and analyzed:
- planar approximation in galactic dynamo;
- the dynamo model in a torus and the associated rz-approximation for thick disks;
- two-dimensional approximations for electric vortex flows of liquid metals;
- models of magnetic field amplification by closed flows of a special type.