Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

https://depts.washington.edu/clawpack/book2/sample.pdf

Finite Volume Methods for Hyperbolic Problems

Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2-phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In Scale-Space'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141–151) and T. Chan and L. Vese (2001. IEEE-IP, 10(2):266–277). The multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies, including triple junctionss in the piecewise smooth case, only two level set functions formally suffice to represent any partition, based on The Four-Color Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and Sethian level set method.

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A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model

Level set methods: an overview and some recent results

Recent results utilizing proton radiography (P‐Rad) during the detonation of the high explosive PBX 9502 are presented. Specifically, the effects of confinement of the detonation are examined in the LANL detonation confinement sandwich geometry. The resulting detonation velocity and detonation shock shape are measured. In addition, proton radiography allows one to image the reflected shocks through the detonation products. Comparisons are made with detonation shock dynamics (DSD) and the reactive flow model Ignition and Growth ( I&G) for the lead detonation shock and detonation velocity. In addition, predictions of reflected shocks are made with the reactive flow model.

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Proton radiography of pbx 9502 detonation shock dynamics confinement sandwich test

A series of two-stage gus-gun driven plate impact experiments on PBX 9502 (95 wt.% tri-amino-trinitro-benzene, 5 wt.% Kel-F800 plastic binder) was completed in the 28-34 GPa pressure range. This is just above the Chapman-Jouguet state of ≈ 28 GPa. The experiments consisted of a thick oxygen free high conductivity copper (OFHC Cu) flyer plate impacting a PBX 9502 sample backed by a Lithium Fluoride (LiF) window. Photonic Doppler Velocimetry (PDV) was used to measure velocity histories (wave profiles) at the PBX 9502/LiF interface. Shock transit times and sample thicknesses were converted to shock velocities, Us. Particle velocities, up, were calculated by way of impedance matching. Lastly, the measured wave profiles were compared with numerical simulations of the experiments using the Wescott-Stewart-Davis reactive-burn model.

http://iopscience.iop.org/article/10.1088/1742-6596/500/5/052015/pdf

Plate impact experiments on the TATB based explosive PBX 9502 at pressures near the Chapman-Jouguet state

Here we consider an unsteady detonation with diffusion included. This introduces an interaction between the reaction length scales and diffusion length scales. Detailed kinetics introduce multiple length scales as shown though the spatial eigenvalue analysis of hydrogen-oxygen system; the smallest length scale is {approx} 10{sup 7} m and the largest {approx} 10{sup -2} m; away from equilibrium, the breadth can be larger. In this paper, we consider a simpler set of model equations, similar to the inviscid reactive compressible fluid equations, but include diffusion (in the form of thermal/energy, momentum, and mass diffusion). We will seek to reveal how the complex dynamics already discovered in one-step systems in the inviscid limit changes with the addition of diffusion.

/pdf/the-dynamics-of-unsteady-detonation-with-diffusion-t8n5wzrwrq.pdf

The dynamics of unsteady detonation with diffusion

The equation of state (EOS) of polymethylpentene (TPX) is examined through both single shock Hugoniot data as well as more recent multi-shock compression and release experiments Results from the recent multi-shock experiments on LANL's two-stage gas gun will be presented A simple conservative Lagrangian numerical scheme utilizing total variation diminishing interpolation and an approximate Riemann solver will be presented as well as the methodology of calibration It is shown that a simple Mie-Gruneisen EOS based on a Keane fitting form for the isentrope can replicate both the single shock and multi-shock experiments

/pdf/an-equation-of-state-for-polymethylpentene-tpx-including-2g9denvt17.pdf

An equation of state for polymethylpentene (TPX) including multi-shock response

A novel, highly accurate numerical scheme based on shock-fitting coupled with high order spatial and temporal discretization is applied to a classical unsteady detonation problem to generate solutions with unprecedented accuracy. The one-dimensional reactive Euler equations for a calorically perfect mixture of ideal gases whose reaction is described by single-step irreversible Arrhenius kinetics are solved in a series of calculations in which the activation energy is varied. In contrast with nearly all known simulations of this problem, which converge at a rate no greater than first order as the spatial and temporal grid is refined, the present method is shown to converge at a rate consistent with the fifth order accuracy of the spatial discretization scheme. This high accuracy enables more precise verification of known results and prediction of heretofore unknown phenomena. To five significant figures, the scheme faithfully recovers the stability boundary, growth rates, and wave-numbers predicted by an independent linear stability theory in the stable and weakly unstable regime. As the activation energy is increased, a series of period-doubling events are predicted, and the system undergoes a transition to chaos. Consistent with general theories of non-linear dynamics, the bifurcation points are seen to converge at a rate for which the Feigenbaum constant is 4.66 ± 0.09, in close agreement with the true value of 4.669201 . . .. As activation energy is increased further, domains are identified in which the system undergoes a transition from a chaotic state back to one whose limit cycles are characterized by a small number of non-linear oscillatory modes. This result is consistent with behavior of other non-linear dynamical systems, but not typically considered in detonation dynamics.

/pdf/highly-accurate-numerical-simulations-of-pulsating-one-55bq59ywfc.pdf

Tariq D. Aslam

Papers

Proton radiography of pbx 9502 detonation shock dynamics confinement sandwich test

Plate impact experiments on the TATB based explosive PBX 9502 at pressures near the Chapman-Jouguet state

The dynamics of unsteady detonation with diffusion

An equation of state for polymethylpentene (TPX) including multi-shock response

Highly Accurate Numerical Simulations of Pulsating One-Dimensional Detonations