Testing the Magnetohydrodynamic Analysis Software with Natural Convection and Geodynamo Problems

В рамках метода контрольного объема разработан программный код для численного решения задач неидеальной магнитной гидродинамики вязкой несжимаемой жидкости на структурированных разнесенных сетках в сферических координатах. При дискретизации уравнения индукции магнитного поля использован алгоритм ограниченного переноса (Сonstrained Transport Algorithm) и схема QUICK с методом отложенной коррекции для аппроксимации конвективных членов. Для решения уравнений гидродинамики использован алгоритм SIMPLER. Программный код разработан для моделирования естественной конвекции и гидромагнитного динамо во вращающемся шаре или сферическом слое. Представлены результаты решения тестовых задач естественной конвекции и геодинамо с вакуумными граничными условиями, демонстрирующие достаточно точное соответствие результатам эталонных расчетов. Программное обеспечение разработано для ускорителей вычислений, поддерживающих технологию CUDA, с использованием набора расширений к языку программирования Фортран.   Using the control volume method we developed the software for the numerical solution of viscous incompressible fluid resistive magnetohydrodynamics problems on structured staggered meshes in spherical coordinates. The constrained transport algorithm and the QUICK method with delayed correction for the approximation of the convective terms were used for the discretization of the magnetic field induction equation. The SIMPLER algorithm was applied to solving the hydrodynamic equations. We developed software for modeling natural convection and the hydromagnetic dynamo in a rotating sphere or spherical shell. We proposed an algorithm for the numerical solution of the geodynamo problem with vacuum boundary conditions. The results of solving natural convection and geodynamo benchmark problems with vacuum boundary conditions are presented; they demonstrate a fairly accurate agreement with the reference calculations. The software supports CUDA-enabled accelerators and uses a set of extensions to the Fortran programming language.

Dynamo models of the solar cycle

This paper reviews recent advances and current debates in modeling the solar cycle as a hydromagnetic dynamo process. Emphasis is placed on (relatively) simple dynamo models that are nonetheless detailed enough to be comparable to solar cycle observations. After a brief overview of the dynamo problem and of key observational constraints, I begin by reviewing the various magnetic field regeneration mechanisms that have been proposed in the solar context. I move on to a presentation and critical discussion of extant solar cycle models based on these mechanisms, followed by a discussion of recent magnetohydrodynamical simulations of solar convection generating solar-like large-scale magnetic cycles. I then turn to the origin and consequences of fluctuations in these models and simulations, including amplitude and parity modulation, chaotic behavior, and intermittency. The paper concludes with a discussion of our current state of ignorance regarding various key questions relating to the explanatory framework offered by dynamo models of the solar cycle.

Stellar magnetic cycles

The solar activity cycle is a manifestation of the hydromagnetic dynamo working inside our star. The detection of activity cycles in solar-like stars and the study of their properties allow us to put the solar dynamo in perspective, investigating how dynamo action depends on stellar parameters and stellar structure. Nevertheless, the lack of spatial resolution and the limited time extension of stellar data pose limitations to our understanding of stellar cycles and the possibility to constrain dynamo models. I briefly review some results obtained from disc-integrated proxies of stellar magnetic fields and discuss the new opportunities opened by space-borne photometry made available by MOST, CoRoT, Kepler, and GAIA, and by new ground-based spectroscopic or spectropolarimetric observations. Stellar cycles have a significant impact on the energetic output and circumstellar magnetic fields of late-type active stars which affects the interaction between stars and their planets. On the other hand, a close-in massive planet could affect the activity of its host star. Recent observations provide circumstantial evidence of such an interaction with possible consequences for stellar activity cycles.