The GeoClaw software for depth-averaged flows with adaptive refinement

Many geophysical flow or wave propagation problems can be modeled with two-dimensional depth-averaged equations, of which the shallow water equations are the simplest example. We describe the GeoClaw software that has been designed to solve problems of this nature, consisting of open source Fortran programs together with Python tools for the user interface and flow visualization. This software uses high-resolution shock-capturing finite volume methods on logically rectangular grids, including latitude--longitude grids on the sphere. Dry states are handled automatically to model inundation. The code incorporates adaptive mesh refinement to allow the efficient solution of large-scale geophysical problems. Examples are given illustrating its use for modeling tsunamis, dam break problems, and storm surge. Documentation and download information is available at www.clawpack.org/geoclawComment: 18 pages, 11 figures, Animations and source code for some examples at http://www.clawpack.org/links/awr10 Significantly modified from original posting to incorporate suggestions of referee

Critical Collapse of an Ultrarelativistic Fluid in the Γ→1\Gamma\to 1 Limit

In this paper we investigate the critical collapse of an ultrarelativistic perfect fluid with the equation of state $P=(\Gamma-1)\rho$ in the limit of $\Gamma\to 1$. We calculate the limiting continuously self similar (CSS) solution and the limiting scaling exponent by exploiting self-similarity of the solution. We also solve the complete set of equations governing the gravitational collapse numerically for $(\Gamma-1) = 10^{-2},...,10^{-6}$ and compare them with the CSS solutions. We also investigate the supercritical regime and discuss the hypothesis of naked singularity formation in a generic gravitational collapse. The numerical calculations make use of advanced methods such as high resolution shock capturing evolution scheme for the matter evolution, adaptive mesh refinement, and quadruple precision arithmetic. The treatment of vacuum is also non standard. We were able to tune the critical parameter up to 30 significant digits and to calculate the scaling exponents accurately. The numerical results agree very well with those calculated using the CSS ansatz. The analysis of the collapse in the supercritical regime supports the hypothesis of the existence of naked singularities formed during a generic gravitational collapse.Comment: 23 pages, 16 figures, revised version, added new results of investigation of a supercritical collapse and the existence of naked singularities in generic gravitational collaps

Raman signatures of classical and quantum phases in coupled dots: A theoretical prediction

We study electron molecules in realistic vertically coupled quantum dots in a strong magnetic field. Computing the energy spectrum, pair correlation functions, and dynamical form factor as a function of inter-dot coupling via diagonalization of the many-body Hamiltonian, we identify structural transitions between different phases, some of which do not have a classical counterpart. The calculated Raman cross section shows how such phases can be experimentally singled out.Comment: 9 pages, 2 postscript figures, 1 colour postscript figure, Latex 2e, Europhysics Letters style and epsfig macros. Submitted to Europhysics Letter

Accurate discretization of advection-diffusion equations

We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provides an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates

Construction and Test of a Flux Modulation Superconducting Machine for Aircraft

International audienceThe increasing of drives towards More Electric Aircraft (MEA) or the development of electric propulsion aircraft calls for MW-class electrical machines with more compact and power dense designs. One way is to explore the use of superconducting materials to create a high magnetic field in order to reduce the mass of ferromagnetic components. This paper presents the construction and the test of a brushless axial flux superconducting machine. The brushless topology satisfies the aeronautics industry requirements in terms of maintenance, while the axial configuration ensures an optimal use of the anisotropic HTS tapes. The machine is classed as partially superconducting, only the inductor is made with superconducting materials. A special design concerning the use of a stationary cryostat is presented. This improvement reduces significantly the electromagnetic air-gap length. A 50kW prototype is manufactured with a minimal mass objective. The prototype constitutes a first step to a scale-up MW-class machine design

Are gauge shocks really shocks?

The existence of gauge pathologies associated with the Bona-Masso family of generalized harmonic slicing conditions is proven for the case of simple 1+1 relativity. It is shown that these gauge pathologies are true shocks in the sense that the characteristic lines associated with the propagation of the gauge cross, which implies that the name ``gauge shock'' usually given to such pathologies is indeed correct. These gauge shocks are associated with places where the spatial hypersurfaces that determine the foliation of spacetime become non-smooth.Comment: 7 pages, 5 figures, REVTEX 4. Revised version, including corrections suggested by referee

Analytical Model for the Magnetic Field Distribution in a Flux Modulation Superconducting Machine

International audienceThis paper presents a theoretical analysis of an axial field machine using High Temperature Superconductors (HTS) wires and bulks. The air-gap magnetic field obtained with the HTS coil and modulated by the HTS bulks is predicted by two 2D axisymmetric models. Analytical models are based on the solution of Laplace's equation by the separation of variable method. The torque is obtained by a quick numerical integration of the Laplace force that acts on the armature winding. The proposed model is compared with 3D finite element simulations and good agreement is obtained. This model can be used with an optimization design procedure with a large reduction of the computational time

Comparison of Earthquake Source Models for the 2011 Tohoku Event Using Tsunami Simulations and Near‐Field Observations

Selection of the earthquake source used in tsunami models of the 2011 Tohoku event affects the simulated tsunami waveform across the near field. Different earthquake sources, based on inversions of seismic waveforms, tsunami waveforms, and Global Positioning System (GPS) data, give distinguishable patterns of simulated tsunami heights in many locations in Tohoku and at near‐field Deep‐ocean Assessment and Reporting of Tsunamis (DART) buoys. We compared 10 sources proposed by different research groups using the GeoClaw code to simulate the resulting tsunami. Several simulations accurately reproduced observations at simulation sites with high grid resolution. Many earthquake sources produced results within 20% difference from the observations between 38° and 39° N, including realistic inundation on the Sendai plain, reflecting a common reliance on large initial seafloor uplift around 38° N (±0.5°), 143.25° E (±0.75°). As might be expected, DART data was better reproduced by sources created by inversion techniques that incorporated DART data in the inversion. Most of the earthquake sources tested at sites with high grid resolution were unable to reproduce the magnitude of runup north of 39° N, indicating that an additional source of tsunamigenic energy, not present in most source models, is needed to explain these observations

Finite difference lattice Boltzmann model with flux limiters for liquid-vapor systems

In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio.Comment: 10 pages, 10 figures, to be published in Phys. Rev.

A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the thicknesses of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee [J. Comput. Phys. 86, 187] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin [J. Comput. Phys. 163, 216] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving and the statistical average of this method is shown to significantly delay the onset of pinning