Three dimensional evolution of differentially rotating magnetized neutron stars

We construct a new three-dimensional general relativistic magnetohydrodynamics code, in which a fixed mesh refinement technique is implemented. To ensure the divergence-free condition as well as the magnetic flux conservation, we employ the method by Balsara (2001). Using this new code, we evolve differentially rotating magnetized neutron stars, and find that a magnetically driven outflow is launched from the star exhibiting a kink instability. The matter ejection rate and Poynting flux are still consistent with our previous finding (Shibata et al., 2011) obtained in axisymmetric simulations.Comment: 12 pages, 14 figures, accepted by PR

A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of standard fluxes from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Comment: 30 pages, 27 figures, 3 table

Modelling urban floods using a finite element staggered scheme with an anisotropic dual porosity model

In porosity models for urban flooding, artificial porosity is used as a statistical descriptor of the urban medium. Buildings are treated as subgrid-scale features and, even with the use of relatively coarse grids, their effects on the flow are accounted for. Porosity models are attractive for large-scale applications due to limited computational demand with respect to solving the classical Shallow Water Equations on high-resolution grids. In the last decade, effective schemes have been developed that allowed accounting for a wealth of sub-grid processes; unfortunately, they are known to suffer from over-sensitivity to mesh design in the case of anisotropic porosity fields, which are typical of urban layouts. In the present study, a dual porosity approach is implemented into a two-dimensional Finite Element numerical scheme that uses a staggered unstructured mesh. The presence of buildings is modelled using an isotropic porosity in the continuity equation, to account for the reduced water storage, and a tensor formulation for conveyance porosity in the momentum equations, to account for anisotropy and effective flow velocity. The element-by-element definition of porosities, and the use of a staggered grid in which triangular cells convey fluxes and continuity is balanced at grid nodes, allow avoiding undesired mesh-dependency. Tested against refined numerical solutions and data from a laboratory experiment, the model provided satisfactory results. Model limitations are discussed in view of applications to more complex, real urban layouts

Aeronautical engineering: A continuing bibliography, supplement 122

This bibliography lists 303 reports, articles, and other documents introduced into the NASA scientific and technical information system in April 1980

Particle hydrodynamics with tessellation techniques

Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. We find that the new `Voronoi Particle Hydrodynamics' described here produces comparable results than SPH in shocks, and better ones in turbulent regimes of pure hydrodynamical simulations. We also discuss formulations of the artificial viscosity needed in this scheme and how judiciously chosen correction forces can be derived in order to maintain a high degree of particle order and hence a regular Voronoi mesh. This is especially helpful in simulating self-gravitating fluids with existing gravity solvers used for N-body simulations.Comment: 26 pages, 24 figures, currentversion is accepted by MNRA

Computation of viscoelastic shear shock waves using finite volume schemes with artificial compressibility

The formation of shear shock waves in the brain has been proposed as one of the plausible explanations for deep intracranial injuries. In fact, such singular solutions emerge naturally in soft viscoelastic tissues under dynamic loading conditions. To improve our understanding of the mechanical processes at hand, the development of dedicated computational models is needed. The present study concerns three-dimensional numerical models of incompressible viscoelastic solids whose motion is analysed by means of shock-capturing finite volume methods. More specifically, we focus on the use of the artificial compressibility method, a technique that has been frequently employed in computational fluid dynamics. The material behaviour is deduced from the Fung--Simo quasi-linear viscoelasiticity theory (QLV) where the elastic response is of Yeoh type. We analyse the accuracy of the method and demonstrate its applicability for the study of nonlinear wave propagation in soft solids. The numerical results cover accuracy tests, shock formation and wave diffraction