On the plane wave Riemann Problem in Fluid Dynamics

The paper contains a stability analysis of the plane-wave Riemann problem for the two-dimensional hyperbolic conservation laws for an ideal compressible gas. It is proved that the contact discontinuity in the plane-wave Riemann problem is unstable under perturbations. The implications for Godunovs method are discussed and it is shown that numerical post shock noise can set of a contact instability. A relation to carbuncle instabilities is established.Comment: 27 pages, 1 figur

Hydrodynamical Simulations of Recollimation Shocks within Relativistic Astrophysical Jets

Abstract: Astrophysical jets launched from active galactic nuclei can remain tightly collimated over large distances due, in part, to recollimation shocks. Formed within the jets due to their supersonic nature, recollimation shocks are predicted to leave signatures in the observed radio emission due to magnetic flux freezing and the geometric relationship between magnetic fields and the polarization of synchrotron radiation. In the course of this work, we will compare how predictions of emission from recollimation shocks change when the flow is modelled using a hydrodynamical code, as opposed to semi-dynamical and magnetohydrodynamical codes. Jets generally exhibit low levels of polarization, which implies a substantially disordered magnetic field. It is difficult to model such fields using magnetohydrodynamics, hence this work uses hydrodynamical code and a statistical treatment of the magnetic field (c.f. Scheuer and Matthews, 1990). It should then be possible to assess whether certain radio jet phenomena, such as knots and radio-cores, may be modelled as singular or multiple recollimation shocks. To date, the hydrodynamical code has been successfully built and executed on UCLan’s supercomputer cluster, and parallelepiped vector triads have been included to monitor the fluid deformation within the simulation, so that the emergent flux and polarization may be calculated. The parallelepiped advection is currently being verified and some results are discussed. Code for radiative transfer throughout the jet is also being implemented, in order to simulate images for comparison with previous works and observations

Treenerite koolitamine ja arendamine Pärnu JK Poseidon näitel

http://www.ester.ee/record=b4696384*es

A Simple and Accurate Riemann Solver for Isothermal MHD

A new approximate Riemann solver for the equations of magnetohydrodynamics (MHD) with an isothermal equation of state is presented. The proposed method of solution draws on the recent work of Miyoshi and Kusano, in the context of adiabatic MHD, where an approximate solution to the Riemann problem is sought in terms of an average constant velocity and total pressure across the Riemann fan. This allows the formation of four intermediate states enclosed by two outermost fast discontinuities and separated by two rotational waves and an entropy mode. In the present work, a corresponding derivation for the isothermal MHD equations is presented. It is found that the absence of the entropy mode leads to a different formulation which is based on a three-state representation rather than four. Numerical tests in one and two dimensions demonstrates that the new solver is robust and comparable in accuracy to the more expensive linearized solver of Roe, although considerably faster.Comment: 19 pages, 9 figure

Optimization of the Epitaxial Growth of Undoped GaN Waveguides in GaN-Based Laser Diodes Evaluated by Photoluminescence

Non-intentionally doped c-plane GaN layers are generally employed as p-side waveguide layers in violet/blue-emitting laser diodes. The recombination and diffusion of charge carriers in the p-side GaN waveguide influence the injection efficiency of holes into the InGaN quantum wells of these devices. In this study, the non-radiative recombination and the diffusivity in the [000-1] direction for charge carriers in such GaN layers are investigated by the photoluminescence of buried InGaN quantum wells, in addition to the GaN photoluminescence. The vertical charge carrier diffusion length and the diffusion constant in GaN were determined by evaluating the intensity from InGaN quantum wells in different depths below a top GaN layer. Additionally, the intensity from the buried InGaN quantum wells was found to be more sensitive to variations in the non-radiative recombination rate in the GaN layer than the intensity from the GaN itself. The study enables conclusions to be drawn on how the growth of a p-side GaN waveguide layer has to be optimized: (1) The charge carrier diffusivity in the [000-1] direction at device operation temperature is limited by phonon scattering and can be only slightly improved by material quality. (2) The use of TMGa (trimethylgallium) instead of TEGa (triethylgallium) as a precursor for the growth of GaN lowers the background silicon doping level and is advantageous for a large hole diffusion length. (3) Small growth rates below 0.5 μm/h when using TMGa or below 0.12 μm/h when using TEGa enhance non-radiative recombination. (4) A V/III gas ratio of 2200 or more is needed for low non-radiative recombination rates in GaN

Ajakirja The Cheers arendusprojekt

The Cheers is an online magazine launched Feb 17, 2005. It is a publication put together without any monetary resources and thus with no risk of failure due to money problems. It’s a magazine with focus on entertainment and stories by writers from around the globe. This thesis talks about the development of this online venture. How it was put together, how it was started, how it was made to actually work. This online venture has survived a good 14 months. Good because 2/3 of new internet ventures die within the first few months. The Cheers has published articled by more than 140 different writers from more than 20 countries. Even though when it started it only had around 100 daily readers and no bright outlook for making any profit with it, things have come long way since then. Although The Cheers can still be considered development-in-process and it has many issues that need solving, it has now between 1000 and 3500 daily readers and has started to show potential for actual profit. This thesis discusses the magazine from all possible sides. I explane how the magazine was created and how can such magazine be developed at all. What The Cheers is all about and where is it heading? I discuss a number of problems that have come up during the life of this magazine and I also bring out issues that are still influencing The Cheers in a non-desirable way. Problems including complications with staff, problems with advertising, with organization structure, website layout, issue planning. In case of all these problems I try to explane it and then analyze what was done to solve the problem or what could be done to solve the problem now. There is also a short overview of the content of The Cheers covering 3 different magazine issues. Among other things, the sections, number of articles and their length has been brought out. I also conducted a quantitative study among the readers of the magazine as well as a qualitative study among the staff of The Cheers. The study of the readers brings out the age and demographics of our reader. The study carried out within the magazine staff deals with what people involved with it think about the magazine. What are the good sides, what are the problems. To make it more interesting, I have also written about the financial side of the publication. How the internet profit-making works and how The Cheers can earn profit for its owner and people involved. The discussion about what could be done, how should The Cheers be further developed, is brought out near the finish line of this thesis. There are many things that should be improved, changed or added to the magazine. I also explane what this magazine has given me, what kind of experience, what kind of knowledge that could be used in the future.http://tartu.ester.ee/record=b1740375~S1*es

An Efficient Implementation of Flux Formulae in Multidimensional Relativistic Hydrodynamical Codes

We derive and analyze a simplified formulation of the numerical viscosity terms appearing in the expression of the numerical fluxes associated to several High-Resolution Shock-Capturing schemes. After some algebraic pre-processing, we give explicit expressions for the numerical viscosity terms of two of the most widely used flux formulae, which implementation saves computational time in multidimensional simulations of relativistic flows. Additionally, such treatment explicitely cancells and factorizes a number of terms helping to amortiguate the growing of round-off errors. We have checked the performance of our formulation running a 3D relativistic hydrodynamical code to solve a standard test-bed problem and found that the improvement in efficiency is of high practical interest in numerical simulations of relativistic flows in Astrophysics.Comment: 10 pages, accepted for publication in Computer Physics Communication

A Two-dimensional HLLC Riemann Solver for Conservation Laws : Application to Euler and MHD Flows

In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions. This work builds on, and improves, our prior work on two-dimensional HLL Riemann solvers. The HLL Riemann solver presented here achieves its stabilization by introducing a constant state in the region of strong interaction, where four one-dimensional Riemann problems interact vigorously with one another. A robust version of the HLL Riemann solver is presented here along with a strategy for introducing sub-structure in the strongly-interacting state. Introducing sub-structure turns the two-dimensional HLL Riemann solver into a two-dimensional HLLC Riemann solver. The sub-structure that we introduce represents a contact discontinuity which can be oriented in any direction relative to the mesh. The Riemann solver presented here is general and can work with any system of conservation laws. We also present a second order accurate Godunov scheme that works in three dimensions and is entirely based on the present multidimensional HLLC Riemann solver technology. The methods presented are cost-competitive with traditional higher order Godunov schemes

Multidimensional HLLE Riemann solver; Application to Euler and Magnetohydrodynamic Flows

In this work we present a general strategy for constructing multidimensional Riemann solvers with a single intermediate state, with particular attention paid to detailing the two-dimensional Riemann solver. This is accomplished by introducing a constant resolved state between the states being considered, which introduces sufficient dissipation for systems of conservation laws. Closed form expressions for the resolved fluxes are also provided to facilitate numerical implementation. The Riemann solver is proved to be positively conservative for the density variable; the positivity of the pressure variable has been demonstrated for Euler flows when the divergence in the fluid velocities is suitably restricted so as to prevent the formation of cavitation in the flow. We also focus on the construction of multidimensionally upwinded electric fields for divergence-free magnetohydrodynamical flows. A robust and efficient second order accurate numerical scheme for two and three dimensional Euler and magnetohydrodynamic flows is presented. The scheme is built on the current multidimensional Riemann solver. The number of zones updated per second by this scheme on a modern processor is shown to be cost competitive with schemes that are based on a one-dimensional Riemann solver. However, the present scheme permits larger timesteps