Numerical methods applied to space magnetohydrodynamics for high performance computing - Müller Moreira Souza Lopes (2019)
The study of physical systems related to the space sciences presents several challenges regarding the great variety of phenomena and scales. In particular, magnetohydrodynamic models are applied in space weather to study phenomena that reach the Earths atmosphere, affecting infrastructure services provided to society. In this context, many fields of study complement each other to obtain a better understanding of these systems. Among these approaches are the numerical simulations, which provide an approximated prediction of the system behaviour from a predefined setup. However, in order for this simulations to be viable, they must be performed in a realistic time, which is a challenge for complex models such as the magnetohydrodynamic equations. Thus, the use of adaptive computational meshs that present higher refinements in regions of interest is an effective strategy to reduce the computational time required for simulations. In particular, the simulations of the magnetohydrodynamic equations present a fundamental challenge that is the emergence of a non-realistic divergence over the magnetic field caused by numerical errors, which requires special techniques to be treated in order to maintain the correctness and the numerical stability. This work presents a code for solving magnetohydrodynamic equations using a high-performance environment that allows the use of adaptive meshs and parallel algorithms. Also, a new technique is proposed to overcome the divergence problem. The code is applied in several test problems in order to verify its performance. Then it is applied to a Earth magnetosphere model. As a product of this thesis, an innovative, high-performance tool for the future space weather research conducted at INPE.