A Constrained Transport Scheme for MHD on Unstructured Static and Moving Meshes

Magnetic fields play an important role in many astrophysical systems and a detailed understanding of their impact on the gas dynamics requires robust numerical simulations. Here we present a new method to evolve the ideal magnetohydrodynamic (MHD) equations on unstructured static and moving meshes that preserves the magnetic field divergence-free constraint to machine precision. The method overcomes the major problems of using a cleaning scheme on the magnetic fields instead, which is non-conservative, not fully Galilean invariant, does not eliminate divergence errors completely, and may produce incorrect jumps across shocks. Our new method is a generalization of the constrained transport (CT) algorithm used to enforce the $\nabla\cdot \mathbf{B}=0$ condition on fixed Cartesian grids. Preserving $\nabla\cdot \mathbf{B}=0$ at the discretized level is necessary to maintain the orthogonality between the Lorentz force and $\mathbf{B}$. The possibility of performing CT on a moving mesh provides several advantages over static mesh methods due to the quasi-Lagrangian nature of the former (i.e., the mesh generating points move with the flow), such as making the simulation automatically adaptive and significantly reducing advection errors. Our method preserves magnetic fields and fluid quantities in pure advection exactly.Comment: 13 pages, 9 figures, accepted to MNRAS. Animations available at http://www.cfa.harvard.edu/~pmocz/research.htm

Analysis of measurement and simulation errors in structural system identification by observability techniques

This is the peer reviewed version of the following article: [Lei, J., Lozano-Galant, J. A., Nogal, M., Xu, D., and Turmo, J. (2017) Analysis of measurement and simulation errors in structural system identification by observability techniques. Struct. Control Health Monit., 24: . doi: 10.1002/stc.1923.], which has been published in final form at http://onlinelibrary.wiley.com/wol1/doi/10.1002/stc.1923/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.During the process of structural system identification, errors are unavoidable. This paper analyzes the effects of measurement and simulation errors in structural system identification based on observability techniques. To illustrate the symbolic approach of this method a simply supported beam is analyzed step-by-step. This analysis provides, for the very first time in the literature, the parametric equations of the estimated parameters. The effects of several factors, such as errors in a particular measurement or in the whole measurement set, load location, measurement location or sign of the errors, on the accuracy of the identification results are also investigated. It is found that error in a particular measurement increases the errors of individual estimations, and this effect can be significantly mitigated by introducing random errors in the whole measurement set. The propagation of simulation errors when using observability techniques is illustrated by two structures with different measurement sets and loading cases. A fluctuation of the observed parameters around the real values is proved to be a characteristic of this method. Also, it is suggested that a sufficient combination of different load cases should be utilized to avoid the inaccurate estimation at the location of low curvature zones.Peer ReviewedPostprint (author's final draft

CAD-based approach for identification of elasto-static parameters of robotic manipulators

The paper presents an approach for the identification of elasto-static parameters of a robotic manipulator using the virtual experiments in a CAD environment. It is based on the numerical processing of the data extracted from the finite element analysis results, which are obtained for isolated manipulator links. This approach allows to obtain the desired stiffness matrices taking into account the complex shape of the links, couplings between rotational/translational deflections and particularities of the joints connecting adjacent links. These matrices are integral parts of the manipulator lumped stiffness model that are widely used in robotics due to its high computational efficiency. To improve the identification accuracy, recommendations for optimal settings of the virtual experiments are given, as well as relevant statistical processing techniques are proposed. Efficiency of the developed approach is confirmed by a simulation study that shows that the accuracy in evaluating the stiffness matrix elements is about 0.1%.Comment: arXiv admin note: substantial text overlap with arXiv:0909.146

A Two-moment Radiation Hydrodynamics Module in Athena Using a Time-explicit Godunov Method

We describe a module for the Athena code that solves the gray equations of radiation hydrodynamics (RHD), based on the first two moments of the radiative transfer equation. We use a combination of explicit Godunov methods to advance the gas and radiation variables including the non-stiff source terms, and a local implicit method to integrate the stiff source terms. We adopt the M1 closure relation and include all leading source terms. We employ the reduced speed of light approximation (RSLA) with subcycling of the radiation variables in order to reduce computational costs. Our code is dimensionally unsplit in one, two, and three space dimensions and is parallelized using MPI. The streaming and diffusion limits are well-described by the M1 closure model, and our implementation shows excellent behavior for a problem with a concentrated radiation source containing both regimes simultaneously. Our operator-split method is ideally suited for problems with a slowly varying radiation field and dynamical gas flows, in which the effect of the RSLA is minimal. We present an analysis of the dispersion relation of RHD linear waves highlighting the conditions of applicability for the RSLA. To demonstrate the accuracy of our method, we utilize a suite of radiation and RHD tests covering a broad range of regimes, including RHD waves, shocks, and equilibria, which show second-order convergence in most cases. As an application, we investigate radiation-driven ejection of a dusty, optically thick shell in the interstellar medium (ISM). Finally, we compare the timing of our method with other well-known iterative schemes for the RHD equations. Our code implementation, Hyperion, is suitable for a wide variety of astrophysical applications and will be made freely available on the Web.Comment: 30 pages, 29 figures, accepted for publication in ApJ

Structural sensitivity analysis: Methods, applications, and needs

Some innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. These techniques include a finite-difference step-size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, a simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Finally, some of the critical needs in the structural sensitivity area are indicated along with Langley plans for dealing with some of these needs

A Static Analyzer for Large Safety-Critical Software

We show that abstract interpretation-based static program analysis can be made efficient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to particular programs of the family by the end-user through parametrization. This is applied to the proof of soundness of data manipulation operations at the machine level for periodic synchronous safety critical embedded software. The main novelties are the design principle of static analyzers by refinement and adaptation through parametrization, the symbolic manipulation of expressions to improve the precision of abstract transfer functions, the octagon, ellipsoid, and decision tree abstract domains, all with sound handling of rounding errors in floating point computations, widening strategies (with thresholds, delayed) and the automatic determination of the parameters (parametrized packing)