Adaptive Finite Volume numerical method

• Published in: Journal of physics. Conference series Vol. 591; no. 1; pp. 12037 - 12043
• Main Author: Bilbao, L
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 24.03.2015
• Subjects: Algorithms; Apexes; Finite element method; Fluid mechanics; Hydrodynamics; Kelvin-Helmholtz instability; Mach number; Magnetopause; Numerical methods; Perturbation; Physics; Plasmas (physics); Robustness (mathematics); Spatial resolution
• ISSN: 1742-6588; 1742-6596; 1742-6596
• DOI: 10.1088/1742-6596/591/1/012037

This work describes a Finite Volume computational method for the parametric study of phenomena in plasmas, i.e. in situations where numerous runs of three-dimensional simulations are required (in many cases, thousands or tens of thousands). Such problems require simple codes, robust, modular (to add or remove physical processes) and do not require high precision. The code is based on a complex multi-component species program with transport and radiation terms. The integration domain is represented with a structured irregular mesh, with fixed connectivity. A new algorithm for the hydrodynamics was implemented in order to improve the computational efficiency plus the improved capability of adapting the mesh to the solution. The improved hydrodynamics method worked well in an ample range of Mach number from subsonic (10−3) to supersonic. After each calculation cycle, mesh vertices are moved arbitrary over the fluid. This is done in order to dynamically adapt the mesh to the solution. The adaptive method consists of shifting mesh vertices over the fluid in order to keep a reasonable mesh structure and increase the spatial resolution where the physical solution demands. As an example, we show the results of the development of the Kelvin-Helmholtz instability in local plane slab models of the magnetopause, showing the development and saturation of the instability in an initially unperturbed structure, i.e., the temporal response approach; and the response of a background equilibrium to the excitation by finite amplitude perturbations generated upstream, i.e., the spatial response of the system.