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

The numerical simulation of flows with interfaces and free-surface flows is a vast topic, with applications to domains as varied as environment, geophysics, engineering, and fundamental physics. In engineering, as well as in other disciplines, the study of liquid-gas interfaces is important in combustion problems with liquid and gas reagents. The formation of droplet clouds or sprays that subsequently burn in combustion chambers originates in interfacial instabilities, such as the Kelvin-Helmholtz instability. What can numerical simulations do to improve our understanding of these phenomena? The limitations of numerical techniques make it impossible to consider more than a few droplets or bubbles. They also force us to stay at low Reynolds or Weber numbers, which prevent us from finding a direct solution to the breakup problem. However, these methods are potentially important. First, the continuous improvement of computational power (or, what amounts to the same, the drop in megaflop price) continuously extends the range of affordable problems. Second, and more importantly, the phenomena we consider often happen on scales of space and time where experimental visualization is difficult or impossible. In such cases, numerical simulation may be a useful prod to the intuition of the physicist, the engineer, or the mathematician. A typical example of interfacial flow is the collision between two liquid droplets. Finding the flow involves the study not only of hydrodynamic fields in the air and water phases but also of the air-water interface. This latter part

Direct numerical simulation of free-surface and interfacial flow

Electromagnetic forming—A review

https://escholarship.org/content/qt4nc7s7bp/qt4nc7s7bp.pdf?t=p21n9r

Second-order accurate volume-of-fluid algorithms for tracking material interfaces

https://www.math.u-bordeaux.fr/~rabgrall/mes_papiers/JCP_169_2_2001.pdf

Computations of compressible multifluids

A High-Order Godunov Method for Multiple Condensed Phases

Green−Kubo relations for the mutual diffusion coefficients of an n-component system are derived from hydrodynamic equations, linear response theory, and the statistical theory of fluctuations. The mutual diffusion coefficients, which form an (n − 1)-dimensional matrix, are formulated as a product of a kinetic matrix and a thermodynamic matrix. The kinetic matrix consists of time integrals of diffusion flux correlation functions, i.e., the Onsager phenomenological coefficients. The thermodynamic matrix is determined by spatial integrals of radial distribution functions. The formulas are derived initially in the barycentric reference frame and then transformed to the volume-fixed reference frame, which is more appropriate to laboratory studies. Explicit expressions for binary and ternary mixtures are presented, from which various empirical relations between the mutual diffusion coefficients and self-diffusion coefficients are obtained using particular assumptions regarding the velocity cross-correlation fun...

Green−Kubo Formulas for Mutual Diffusion Coefficients in Multicomponent Systems

Molecular dynamics simulations of four binary Ar-Kr mixtures are used to compute self- and mutual-diffusion coefficients. Results using mean squared displacements and using velocity correlation functions are presented. The diffusivity coefficients are also presented in the time and frequency domains where a comparatively low frequency structure is evident in some simulations. The computed diffusivities are dependent on the maximum time over which the velocity correlation functions are integrated and the time at which the Einstein relationships are evaluated. This dependence explains in part the small systematic differences between our results (20--80 ps) and earlier molecular dynamics results (4 ps) in the system Ar-Kr. We compare the computed mutual diffusion coefficients to two empirical models, Darken's model and the common force model. Darken's model is consistent with our results over the entire frequency range we resolve. At frequencies lower than about 5 ${\mathrm{ps}}^{\mathrm{\ensuremath{-}}1}$ Darken's model and the common force model converge and we cannot discriminate between them. At higher frequencies the common force model prediction is significantly different from the computed mutual diffusion coefficient. Assumptions regarding the contribution of cross correlations that are implicit in the empirical models are discussed and tested against our simulation results. The net contribution of velocity cross correlations is found to be negligible, as is often assumed in deriving Darken's model, but the individual cross-correlation terms are substantial and negative---a finding contrary to common assumptions. \textcopyright{} 1996 The American Physical Society.

Mutual diffusion in binary Ar-Kr mixtures and empirical diffusion models

Jetting in Oblique, Asymmetric Impacts

Electrical arcs commonly occur in electrical injury incidents. Historically, safe work distances from an energized surface along with personal barrier protection have been employee safety strategies used to minimize electrical arc hazard exposures. Here, the two-dimensional computational simulation of an electrical arc explosion is reported using color graphics to depict the temperature and acoustic force propagation across the geometry of a hypothetical workroom during a time from 0 to 50 ms after the arc initiation. The theoretical results are compared to the experimental findings of staged tests involving a mannequin worker monitored for electrical current flow, temperature, and pressure, and reported data regarding neurologic injury thresholds. This report demonstrates a credible link between electrical explosions and the risk for pressure (acoustic) wave trauma. Our ultimate goal is to protect workers through the design and implementation of preventive strategies that properly account for all electrical arc-induced hazards, including electrical, thermal, and acoustic effects. Language: en

Gregory H. Miller

Papers

A High-Order Godunov Method for Multiple Condensed Phases

Green−Kubo Formulas for Mutual Diffusion Coefficients in Multicomponent Systems

Mutual diffusion in binary Ar-Kr mixtures and empirical diffusion models

Jetting in Oblique, Asymmetric Impacts

Thermoacoustic Energy Effects in Electrical Arcs