Numerical simulations of neutron star mergers as the central engines of short-period gamma-ray bursts

We present the results of fully three dimensional, post-Newtonian hydrodynamical simulations of the dynamical evolution of mergers between compact stellar remnants (neutron stars and black holes). Although the code is essentially Newtonian, we simulate gravitational wave emission and the corresponding effect on the fluid flow via a post-Newtonian correction. Also, we use a modified Newtonian potential which reproduces certain aspects of the Schwarzschild and Kerr solutions to improve the physics in the vicinity of the black hole. Changes to the energy by neutrino/antineutrino emission are accounted for by an extensive neutrino leakage scheme. The hydrodynamical equations are integrated using the piecewise parabolic method (PPM) and the neutron star matter is described by a tabulated equation of state (EoS). Since the physics of matter at the extreme densities found in neutron stars is not yet certain, we compare results computed using two such tables to ascertain whether this uncertainty in the micro-physics extends to an uncertainty in the energy available to power a short-period gamma-ray burst. With an aim to including magnetic field physics to these simulations, we present a survey of approximate Riemann solvers which may be more easily extended to the system of equations of magnetohydrodynamics (MHD) than the exact or iterative Riemann solver used in the PPM scheme. Tests are performed using the linearised solver of Roe and the approximate Harten, Lax, van Leer and Einfeldt Riemann solvers (HLLE and HLLEM) with the PPM reconstruction scheme. Finally, we discuss the effectiveness of these approximate Riemann solvers in the simulation of mergers between compact stellar remnants

Numerical investigation of MPD thrusters using a density-based method with semi-discrete central-upwind schemes for MHD equations

The magnetohydrodynamic (MHD) equations which combines the Navier-Stokes equations with the Maxwell equations are essential for the investigations of many research areas as earth's core modelling, metal casting, fusion devices and electrical and aerospace devices. In the present work, the central-upwind schemes proposed by Kurganov, Noelle and Petrova for hydrodynamics are extended and combined with the divergence cleaning method of Dedner in order to investigate the performance of the self-field and applied magneto-plasma dynamic thrusters which still involving some outstanding problems. This new algorithm is developed for the single temperature, ideal and resistive MHD equations in a finite volume discretization framework with Gaussian integration. The electrical conductivity is predicted according to the Spitzer-Härm formulation and the real gas ratio of specific heats proposed by Sankaran is implemented for higher discharge current. To improve the quality of the solution, the limiter function of first and second order interpolation scheme is used. The accuracy and the robustness of the obtained solver are demonstrated through numerical simulations of ideal MHD benchmark problems. first, the ability of the developed code to handle shocks, rarefactions and contact discontinuities is tested with the Brio-Wu shock-tube problem. The Minmod and the Van Albada limiter functions has been found to perform better than the other limiter used and the obtained results agree well with both the analytic and the simulations results of previous work. Secondly, the complex and multiple shock interactions and the transition from smooth to turbulent flow involved in the Orszag-Tang vortex problem is well described by the present code and the comparison with the WENO-5 scheme of Shen shows good agreement. Lastly, The ability to described the interaction of an denser cloud with a MHD shock is tested by simulating the 2D cloud-shock interaction problem. The main phases of the interaction are well captured by the solver and the temporal progression of the density contour is in accordance with those obtained by Xisto. The ability of the developed resistive solver to deal with plasma flow acceleration is tested by simulating the well experimental investigated thrusters: The full scale benchmark thruster and the extended anode thruster of Princeton. The results show good agreement with the experimental and simulations results of previous work for discharge current less than the critical current just before the beginning of the onset phenomenon. Simulations are also conducted on the Villani-H thruster to determine the effect of geometric changes over the thruster performance and a first designing attempts is proposed according to the stability analysis. Confident with the results obtained with ideal and resistive MHD problems, the present code is extended to applied-field MPD thrusters. The purpose is to achieve a high thrust level required for space missions with less input power than with self-field MPD thrusters and thus avoid the onset instabilities. For the verification of the code, the NASA Lewis Research Center's (NASALeRC) MPD thruster is chosen because of its wide range of experimental data bank. The method presented reproduce the theory of thrust production and plasma acceleration. Some difficulties as the limitation of the maximum rotational speed and the depletion of the plasma density on the anode surface have been captured. Moreover, the present density-based method compares very well with experimental data of Myers and simulations of Mikellides

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

Finite volume modelling of low speed structural impact problems

Two investigations are described in this thesis on the common theme of applying finite volume methods to simulate structural impact problems. The first investigation is the application of the Eulerian Finite Volume Method (EFVM) to simulate the low-speed impact of ductile materials. Simulation results are validated against experiment showing that it is possible to accurately predict crater deformation profiles over the low speed speed impact regime for different projectile and substrate materials. We demonstrate how the rate dependent Johnson-Cook plasticity model is crucial to ensure correspondence to experiment. The second investigation is concerned with the application of EFVM to simulate impact damage to thin polymeric coatings applied to the surface of metals. The aim of this work is to demonstrate how new simulation methods can help understand coating damage due stone impact. We simulate the debonding phenomenon of single layer coatings under impact by setting boundary conditions at the plate and paint interface. We show how EFVM can capture two limits of interface behaviour, sliding and separation 'slip' at one extreme and zero sliding 'welded' at the other. Results compare well to previously published experimental and simulation work, and our own finite element simulations in Abaqus. We also demonstrate how EFVM brings greater robustness and stability compared to FEM when modelling adhesive failure and higher energy impact penetration

衝突性および無衝突性の降着円盤における角運動量輸送メカニズムに関する研究

学位の種別: 課程博士審査委員会委員 : （主査）東京大学准教授 横山 央明, 東京大学教授 今村 剛, 東京大学教授 鈴木 建, 東京大学教授 藤本 正樹, 千葉大学教授 松元 亮治University of Tokyo(東京大学