Geodynamo simulations software package suite based on spectral hereditary models

G. M. Vodinchar ; E. A. Kazakov ; L. K. Feshenko

Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 49 (2024) no. 4, pp. 65-84

Résumé

The study of the geodynamics problem is often carried out on the basis of spectral models, when the fields are fully or partially expanded in eigenfields (eigenmodes) of suitable spectral problems. The most meaningful from the physical point of view are spectral problems of free oscillations or free decay of fields. The compilation of spectral models first of all requires calculating the parameters of the basic modes, and then the model coefficients. Most often, these are the Galerkin coefficients. Then the problem of actually solving the model equations numerically arises. The paper describes a software package developed by the authors that allows solving such problems. It includes modules for calculating the mode parameters, a module for calculating the Galerkin coefficients, two modules for numerically solving the system, and a noise generation module. The package allows calculating the model with hereditary quenching of the $\alpha$-effect by the field energy. Two types of the quenching functional kernel are provided, requiring different difference schemes. These schemes are implemented in two numerical solution modules. Random noise simulates the effect of spontaneous synchronization of small-scale field components, which is absent on average. The calculation of the parameters of the basic modes and Galerkin coefficients is performed using combined symbolic-numerical computations, so the corresponding modules are implemented in the Maple package. The need for symbolic computations is associated with the great complexity of the expressions of the modes themselves and the integrands when calculating the Galerkin coefficients. Therefore, the task arises first of all to form the necessary expressions. This is done using symbolic calculations. The remaining modules are implemented in C++. The developed package can be useful for specialists studying the geodynamo problem based on spectral models and memory effects in this problem.

Détail

Keywords: geodynamo, spectral models, memory models, simulation software packages, symbolicnumerical computations.