An efficient shock capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.

Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Assessing the accuracy of CME speed and trajectory estimates from STEREO observations through a comparison of independent methods

We have estimated the speed and direction of propagation of a number of Coronal Mass Ejections (CMEs) using single-spacecraft data from the STEREO Heliospheric Imager (HI) wide-field cameras. In general, these values are in good agreement with those predicted by Thernisien, Vourlidas, and Howard in Solar Phys. 256, 111 -aEuro parts per thousand 130 (2009) using a forward modelling method to fit CMEs imaged by the STEREO COR2 coronagraphs. The directions of the CMEs predicted by both techniques are in good agreement despite the fact that many of the CMEs under study travel in directions that cause them to fade rapidly in the HI images. The velocities estimated from both techniques are in general agreement although there are some interesting differences that may provide evidence for the influence of the ambient solar wind on the speed of CMEs. The majority of CMEs with a velocity estimated to be below 400 km s(-1) in the COR2 field of view have higher estimated velocities in the HI field of view, while, conversely, those with COR2 velocities estimated to be above 400 km s(-1) have lower estimated HI velocities. We interpret this as evidence for the deceleration of fast CMEs and the acceleration of slower CMEs by interaction with the ambient solar wind beyond the COR2 field of view. We also show that the uncertainties in our derived parameters are influenced by the range of elongations over which each CME can be tracked. In order to reduce the uncertainty in the predicted arrival time of a CME at 1 Astronomical Unit (AU) to within six hours, the CME needs to be tracked out to at least 30 degrees elongation. This is in good agreement with predictions of the accuracy of our technique based on Monte Carlo simulations.