Book ChapterDOI
A Finite Volume MHD Code in Spherical Coordinates for Background Solar Wind
Xueshang Feng
- pp 339-429
TLDR
In this article, a second-order Godunov-type finite volume method (FVM) to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time has been implemented into a numerical code.Abstract:
A second-order Godunov-type finite volume method (FVM) to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time has been implemented into a numerical code. This code operates on a three-dimensional (3D) spherical shell with both non-staggered and staggered grids on the overlapping grid system with hexahedral cells of quadrilateral frustum type. By merging geometrical factors in spherical coordinates into the reformulation of fluxes, flux evaluation is made easy to achieve, and thus many numerical schemes with the total variation diminishing (TVD) slope limiters and approximate Roe solvers intended for Cartesian case can follow in the present context of spherical grid described here. At the same time, alternative strategies to ensure a solenoidal magnetic field, such as projection Poisson (PP) solver, hyperbolic divergence cleaning (HDC) method derived from generalized Lagrange multiplier (GLM) formulation of MHD system and constrained transport (CT) method, are employed. In this chapter, an FVM is described exemplarily on a six-component composite grid system by using a minmod limiter for oscillation control. Additionally, an implicit dual time-stepping technique is demonstrated to model the steady state solar wind ambient. Being of second order in space and time, this model is written in FORTRAN language with Message Passing Interface (MPI) parallelization, and validated in modeling the large-scale structure of solar wind from the Sun to Earth process (hereafter called Sun-to-Earth Process MHD model, also STEP-MHD model for brief). To demonstrate the suitability of our code for the simulation of solar wind ambient from the Sun to Earth, selected results from Carrington rotations (CR) during different solar activity phases are presented to show its capability of producing structured solar wind in agreement with observations.read more
Citations
More filters
Journal Article
Magnetohydrodynamic simulation of interplanetary propagation of multiple coronalmass ejections with internalmagnetic flux rope (SUSANOO-CME)
Daikou Shiota,Ryuho Kataoka +1 more
An unsplit, cell-centered Godunov method for ideal MHD - eScholarship
TL;DR: A second-order Godunov algorithm for multidimensional, ideal MHD based on the unsplit formulation of Colella, with all of the primary dependent variables centered at the same location is presented.
The Athena Astrophysical MHD Code in Cylindrical Geometry
Aaron Skinner,Eve C. Ostriker +1 more
TL;DR: In this paper, a method for implementing cylindrical coordinates in the Athena magnetohydrodynamics (MHD) code is described, which is suitable for use in a wide variety of astrophysical applications and is freely available on the web.
Journal ArticleDOI
A Numerical Study of the Effects of Corotating Interaction Regions on Cosmic-Ray Transport
Waves and Magnetism in the Solar Atmosphere (WAMIS)
Yuan-Kuen Ko,F. Auchere,Roberto Casini,Silvano Fineschi,Sarah Gibson,M. Knoelker,Clarence M. Korendyke,J. M. Laming,Scott W. McIntosh,John D. Moses,Marco Romoli,Jan Rybak,Dennis G. Socker,Leonard Strachan,Steven Tomczyk,Angelos Vourlidas,Qian Wu +16 more
TL;DR: WAMIS as mentioned in this paper is a long-duration high-altitude balloon payload designed to obtain a breakthrough in the measurement of coronal magnetic fields and in advancing the understanding of the interaction of these fields with space plasmas.
References
More filters
Journal ArticleDOI
On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
TL;DR: This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes.
Proceedings ArticleDOI
The design and application of upwind schemes on unstructured meshes
TL;DR: Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures which differ from existing algorithms (even on structured meshes).
Proceedings ArticleDOI
Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings
Journal ArticleDOI
Regular Article: A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics
TL;DR: In this article, the authors present a computational scheme for compressible magnetohydrodynamics (MHD) based on the same elements that make up many modern compressible gas dynamics codes: high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-stepping scheme; and solution-adaptive refinement and coarsening.