A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry

We develop a high-order kinetic scheme for entropy-based moment models of a one-dimensional linear kinetic equation in slab geometry. High-order spatial reconstructions are achieved using the weighted essentially non-oscillatory (WENO) method, and for time integration we use multi-step Runge-Kutta methods which are strong stability preserving and whose stages and steps can be written as convex combinations of forward Euler steps. We show that the moment vectors stay in the realizable set using these time integrators along with a maximum principle-based kinetic-level limiter, which simultaneously dampens spurious oscillations in the numerical solutions. We present numerical results both on a manufactured solution, where we perform convergence tests showing our scheme converges of the expected order up to the numerical noise from the numerical optimization, as well as on two standard benchmark problems, where we show some of the advantages of high-order solutions and the role of the key parameter in the limiter

High-Order Fully General-Relativistic Hydrodynamics: new Approaches and Tests

We present a new approach for achieving high-order convergence in fully general-relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new code that makes use of state-of-the-art numerical schemes and was key in achieving, for the first time, higher than second-order convergence in the calculation of the gravitational radiation from inspiraling binary neutron stars Radice et al. (2013). Here, we give a detailed description of the algorithms employed and present results obtained for a series of classical tests involving isolated neutron stars. In addition, using the gravitational-wave emission from the late inspiral and merger of binary neutron stars, we make a detailed comparison between the results obtained with the new code and those obtained when using standard second-order schemes commonly employed for matter simulations in numerical relativity. We find that even at moderate resolutions and for binaries with large compactness, the phase accuracy is improved by a factor 50 or more.Comment: 34 pages, 16 figures. Version accepted on CQ

Effiziente numerische Methoden zur Lösung von reaktiven Euler-Gleichungen für mehrere Spezies

This cumulative thesis is devoted to the efficient simulation of compressible chemically reactive flows with multiple species and reactions being involved. In addition, the mass-fraction based reactive Euler equations with multiple species can be used to describe two-phase flows with multiple 'components' (corresponding to 'species') in a diffuse-interface manner, with suitable equations of state or thermodynamical models being employed. Three numerical methods towards computational high-efficiency solution of the above equation system are proposed.Diese kumulative Doktorarbeit widmet sich der effizienten Simulation kompressibler chemisch reaktiver Strömungen, wo mehrere Arten und Reaktionen beteiligt sind. Darüber hinaus können die auf Massenfraktionen basierenden reaktiven Euler-Gleichungen für mehrere Spezies mit geeigneten Zustandsgleichungen oder thermodynamischen Modellen verwendet werden, um zweiphasige Strömungen mit mehreren "Komponenten" (entsprechend "Spezies") auf diffuse Weise zu beschreiben. Drei numerische Methoden zur numerischen hocheffizienten Lösung des obigen Gleichungssystems warden vorgeschlagen