Stokes IQUV mapping of α2\alpha^2 CVn & other Ap stars using ESPaDOnS and NARVAL

New spectral line polarisation observations of 7 bright Ap stars have been obtained with the ESPaDOnS and Narval high resolution spectropolarimeters (Silvester et al. 2012). The aim of this data set is produce a series of surface magnetic field and surface chemistry maps for these Ap stars. We present new magnetic maps for the Ap star $\alpha^2$ CVn using these new data and the MDI inversion code INVERS10. $\alpha^2$ CVn is the first Ap star to be observed during two separate epochs using high resolution phase resolved spectropolarimetric $IQUV$ observations and as such allows us an insight into how stable the surface magnetic structure is over a decade timescale. We show that the new maps give a magnetic field structure consistent with the previous maps obtained by Kochukhov and Wade (2010) from lower quality MuSiCoS spectra taken a decade ago and that the field topology cannot be described by a dipolar or quadrupolar field.Comment: 6 pages, 3 figures. Proceedings of New advances in stellar physics: from microscopic to macroscopic processes (Roscoff 2013

The magnetic field topology and chemical abundance distributions of the Ap star HD 32633

Previous observations of the Ap star HD 32633 indicated that its magnetic field was unusually complex in nature and could not be characterised by a simple dipolar structure. Here we derive magnetic field maps and chemical abundance distributions for this star using full Stokes vector (Stokes $IQUV$) high-resolution observations obtained with the ESPaDOnS and Narval spectropolarimeters. Our maps, produced using the Invers10 magnetic Doppler imaging (MDI) code, show that HD 32633 has a strong magnetic field which features two large regions of opposite polarity but deviates significantly from a pure dipole field. We use a spherical harmonic expansion to characterise the magnetic field and find that the harmonic energy is predominately in the $\ell=1$ and $\ell=2$ poloidal modes with a small toroidal component. At the same time, we demonstrate that the observed Stokes parameter profiles of HD 32633 cannot be fully described by either a dipolar or dipolar plus quadrupolar field geometry. We compare the magnetic field topology of HD 32633 with other early-type stars for which MDI analyses have been performed, supporting a trend of increasing field complexity with stellar mass. We then compare the magnetic field topology of HD 32633 with derived chemical abundance maps for the elements Mg, Si, Ti, Cr, Fe, Ni and Nd. We find that the iron-peak elements show similar distributions, but we are unable to find a clear correlation between the location of local chemical enhancements or depletions and the magnetic field structure.Comment: 15 pages, 11 figures, accepted for publication in MNRA

Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations

We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics

A preconditioner for the 3D Oseen equations

We describe a preconditioner for the linearised incompressible Navier-Stokes equations (the Oseen equations) which requires as components only a preconditioner/solver for each of a discrete Laplacian and a discrete advection-diffusion operator. With this preconditioner, convergence of an iterative method such as GMRES is independent of the mesh size and depends only mildly on the viscosity parameter (the inverse Reynolds number). Thus when the component preconditioner/solvers are effective on their respective subproblems (as one expects with an appropriate multigrid cycle for instance) a fast Oseen solver results

Iterative Methods for Problems in Computational Fluid Dynamics

We discuss iterative methods for solving the algebraic systems of equations arising from linearization and discretization of primitive variable formulations of the incompressible Navier-Stokes equations. Implicit discretization in time leads to a coupled but linear system of partial differential equations at each time step, and discretization in space then produces a series of linear algebraic systems. We give an overview of commonly used time and space discretization techniques, and we discuss a variety of algorithmic strategies for solving the resulting systems of equations. The emphasis is on preconditioning techniques, which can be combined with Krylov subspace iterative methods. In many cases the solution of subsidiary problems such as the discrete convection-diffusion equation and the discrete Stokes equations plays a crucial role. We examine iterative techniques for these problems and show how they can be integrated into effective solution algorithms for the Navier-Stokes equations