A parallel solution-adaptive scheme for ideal magnetohydrodynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77232/1/AIAA-1999-3273-200.pd

Computational magnetohydrodynamic model of a gasdynamic mirror propulsion system

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76720/1/AIAA-1999-2702-308.pd

Geodynamo alpha-effect derived from box simulations of rotating magnetoconvection

The equations for fully compressible rotating magnetoconvection are numerically solved in a Cartesian box assuming conditions roughly suitable for the geodynamo. The mean electromotive force describing the generation of mean magnetic flux by convective turbulence in the rotating fluid is directly calculated from the simulations, and the corresponding alpha-coefficients are derived. Due to the very weak density stratification the alpha-effect changes its sign in the middle of the box. It is positive at the top and negative at the bottom of the convection zone. For strong magnetic fields we also find a clear downward advection of the mean magnetic field. Both of the simulated effects have been predicted by quasi-linear computations (Soward, 1979; Kitchatinov and Ruediger, 1992). Finally, the possible connection of the obtained profiles of the EMF with mean-field models of oscillating alpha^2-dynamos is discussed.Comment: 17 pages, 9 figures, submitted to Phys. Earth Planet. Inte

Adaptive Method of Lines for Magneto-Hydrodynamic PDE Models

An adaptive grid technique for use in the solution of multi-dimensional time-dependent PDEs is applied to several magnetohydrodynamic model problems. The technique employs the method-of-lines and can be viewed both in a continuous and semi-discrete setting. By using an equidistribution principle, it has the ability to track individual features of the physical solutions in the developing plasma ows. Moreover, it can be shown that the underlying grid varies smoothly in time and space. The results of several numerical experiments are presented which cover many aspects typifying nonlinear magneto- uid dynamics

Phurbas: An Adaptive, Lagrangian, Meshless, Magnetohydrodynamics Code. II. Implementation and Tests

We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is required to ensure the particles fill the computational volume, and gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. We have parallelized the code by adapting the framework provided by GADGET-2. A set of standard test problems, including 1e-6 amplitude linear MHD waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities is presented. Finally we demonstrate good agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry. This paper documents the Phurbas algorithm as implemented in Phurbas version 1.1.Comment: 14 pages, 14 figures, ApJS accepted, revised in accordance with changes to paper I (arXiv:1110.0835

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, II: Minimization of ∇·B Numerical Error

An adaptive numerical dissipation control in a class of high order filter methods for compressible MHD equations is systematically discussed. The filter schemes consist of a divergence-free preserving high order spatial base scheme with a filter approach which can be divergence-free preserving depending on the type of filter operator being used, the method of applying the filter step, and the type of flow problem to be considered. Some of these filter variants provide a natural and efficient way for the minimization of the divergence of the magnetic field (∇·B) numerical error in the sense that commonly used divergence cleaning is not required. Numerical experiments presented emphasize the performance of the ∇·B numerical error. Many levels of grid refinement and detailed comparison of the filter methods with several commonly used compressible MHD shock-capturing schemes will be illustrated

Solving the system of radiation magnetohydrodynamics for solar physical simulations in 3d

In this study we present a finite-volumen scheme for solving the equations of radiation magnetohydrodynamics in two and three space dimensions. Among other applications this system is used to model the plasma in the solar convection zone and in the solar photosphere. It is a non--linear system of balance laws derived from the Euler equations of gas dynamics and the Maxwell equations; the energy transport through radiation is also included in the model. The starting point of our presentation is a standard explicit first and second order finite-volume scheme on both structured and unstructured grids. We first study the convergence of a finite-volume scheme applied to a scalar model problem for the full system of radiation magnetohydrodynamics. We then present modifications of the base scheme. These make it possible to approximate the system of magnetohydrodynamics with an arbitrary equation of state; they reduce errors due to a violation of the divergence constraint on the magnetic field, and they lead to an improved accuracy in the approximation of solution near an equilibrium state. These modifications significantly increase the robustness of the scheme and are essential for an accurate simulation of processes in the solar atmosphere ...thesi

Global MHD simulations of Mercury's magnetosphere with coupled planetary interior: Induction effect of the planetary conducting core on the global interaction

Mercury's comparatively weak intrinsic magnetic field and its close proximity to the Sun lead to a magnetosphere that undergoes more direct space‐weathering interactions than other planets. A unique aspect of Mercury's interaction system arises from the large ratio of the scale of the planet to the scale of the magnetosphere and the presence of a large‐size core composed of highly conducting material. Consequently, there is strong feedback between the planetary interior and the magnetosphere, especially under conditions of strong external forcing. Understanding the coupled solar wind‐magnetosphere‐interior interaction at Mercury requires not only analysis of observations but also a modeling framework that is both comprehensive and inclusive. We have developed a new global MHD model for Mercury in which the planetary interior is modeled as layers of different electrical conductivities that electromagnetically couple to the surrounding plasma environment. This new modeling capability allows us to characterize the dynamical response of Mercury to time‐varying external conditions in a self‐consistent manner. Comparison of our model results with observations by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft shows that the model provides a reasonably good representation of the global magnetosphere. To demonstrate the capability to model induction effects, we have performed idealized simulations in which Mercury's magnetosphere is impacted by a solar wind pressure enhancement. Our results show that due to the induction effect, Mercury's core exerts strong global influences on the way Mercury responds to changes in the external environment, including modifying the global magnetospheric structure and affecting the extent to which the solar wind directly impacts the surface. The global MHD model presented here represents a crucial step toward establishing a modeling framework that enables self‐consistent characterization of Mercury's tightly coupled planetary interior‐magnetosphere system.Key PointsDeveloped global MHD model of Mercury's magnetosphere with coupled interiorThe global model is able to self‐consistently model induction effect at the coreInduction effect is shown to have significant effects on the global interactionPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/112187/1/jgra51879.pd

Wavelet transforms and their applications to MHD and plasma turbulence: a review

Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented.Comment: Journal of Plasma Physics, 201

Flare‐generated shock evolution and geomagnetic storms during the “Halloween 2003 epoch”: 29 October to 2 November

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95151/1/jgra17876.pd