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# [PEM17-04] Simulation methods and visualization tools for MHD simulations in a sphere

Keywords:magnetohydrodynamics, sphere, MHD simulation, visualization

The codes are written in Fortran 2003 or in eFortran [2], which is a dialect of Fortran 2008 language. The features of eFortran include; the period “.” as the member access operator; block comments, addition/subtraction/multiplication assignment, pre-defined and user-defined aliases, automatic check of “implicit none” call, “just once” block, and “skip” block. We have developed a preprocessor to convert the dialect into the legitimate Fortran. It is a simple text converter in Python that keeps the line numbers of the input dialect and the output standard codes.

We have performed MHD simulations of relaxation process in a sphere [5]. Since the spherical geometry is free from the lateral dynamic pressure on the spherical boundary, we can observe MHD relaxation process in which flow and the magnetic field coexist. Intriguing structures of magnetic/flow fields are observed after relaxations.

One of interesting applications of the spherical MHD solver is the spherical shell convection with resistive inner core. Magnetic field generated by dynamo process in the convective spherical layer can diffuse into the inner solid core. We have solved slowly rotating spherical thin shell convection system and confirmed that the resistive inner core plays important roles to keep the dynamo operating in convection rolls in the ring- or spiral-shape.

We have also applied the Yin-Yang-Zhong simulation code to simulate MHD flows in a precessing sphere. We have confirmed that magnetic field is generated in spherical precession flows in some parameter regimes that are reported in previous studies. The structure and the generation mechanism of the magnetic field is analyzed in detail.

For the visualization purposes, we have developed two kinds of visualization tools for simulation data produced on the Yin-Yang or Yin-Yang-Zhong grid : (a) Two dimensional (cross sectional) in-situ visualization library with vector graphics format (EPS) [3], and (b) three dimensional visualization methods based on an advanced visualization framework KVS (Kyoto Visualization System) [4].

References

[1] Hiroshi Hayashi and Akira Kageyama. Yin-Yang-Zhong grid: An overset grid system for a sphere. Journal of Computational Physics, 305:895– 905, 2016.

[2] Shin’Ya Hosoyamada and Akira Kageyama. A Dialect of Modern Fortran for Computer Simulations. Proceedings of AsiaSim 2018, CCIS 946, 90:439–448, 2018.

[3] Akira Kageyama. Magnetohydrodynamics Simulation in a Sphere by Yin-Yang-Zhong Grid. Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, (Simultech):239–243, 2016.

[4] Naohisa Sakamoto and Koji Koyamada. KVS: A simple and effective framework for scientific visualization. J. Adv. Simulation. Sci. Eng., 2(1):76–95, 2015.

[5] Kohei Yamamoto and Akira Kageyama. MHD relaxation with flow in a sphere. Procedia Computer Science, 80(2):1374–1381, 2016.