Topic
Shock (mechanics)
About: Shock (mechanics) is a research topic. Over the lifetime, 30099 publications have been published within this topic receiving 360212 citations. The topic is also known as: shock.
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TL;DR: In this paper, an approach which closely maintains the non-dissipative nature of classical fourth or higher-order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient, and fine scale turbulent structures in a stable and efficient manner is described.
626 citations
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09 Jan 2006TL;DR: A shock capturing strategy for higher order Discontinuous Galerkin approximations of scalar conservation laws is presented and it is shown that the proposed approach is capable of capturing the shock as a sharp, but smooth profile, which is typically contained within one element.
Abstract: A shock capturing strategy for higher order Discontinuous Galerkin approximations of scalar conservation laws is presented. We show how the original explicit artificial viscosity methods proposed over fifty years ago for finite volume methods, can be used very eectively in the context of high order approximations. Rather than relying on the dissipation inherent in Discontinuous Galerkin approximations, we add an artificial viscosity term which is aimed at eliminating the high frequencies in the solution, thus eliminating Gibbs-type oscillations. We note that the amount of viscosity required for stability is determined by the resolution of the approximating space and therefore decreases with the order of the approximating polynomial. Unlike classical finite volume artificial viscosity methods, where the shock is spread over several computational cells, we show that the proposed approach is capable of capturing the shock as a sharp, but smooth profile, which is typically contained within one element. The method is complemented with a shock detection algorithm which is based on the rate of decay of the expansion coecients of the solution when this is expressed in a hierarchical orthonormal basis. For the Euler equations, we consider and discuss the performance of several forms of the artificial viscosity term.
613 citations
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TL;DR: In this article, the acceleration of charged particles near ultra-relativistic shocks is considered and the acceleration spectrum is shown to be a power law, with a nearly universal value s \approx 2.2 - 2.3 for the slope of this power law.
Abstract: We consider the acceleration of charged particles near ultra-relativistic shocks, with Lorentz factor Gamma_s >> 1. We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultra-relativistic shocks is a power law, N(E) \propto E^{-s}, with a nearly universal value s \approx 2.2 - 2.3 for the slope of this power law. We confirm that the ultra-relativistic equivalent of Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle theta_c \approx 1/Gamma_s around the shock normal. We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount: Delta theta ~ 1/Gamma_s. This limits the energy change per shock crossing cycle to Delta E ~ E, except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor ~ Gamma_s^2 for those particles that are scattered back across the shock into the upstream region.
605 citations
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TL;DR: In this article, the authors derive a shock capturing tool able to treat turbulence with minimum dissipation out of the shock for a large-eddy simulation (LES) of the interaction.
605 citations
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TL;DR: In this paper, the current status of knowledge about the nature, origin, and experimental pressure-temperature calibration of shock-induced deformations and phase transformations is reviewed for natural and experimental shock conditions.
Abstract: — Quartz, as a ubiquitous mineral constituent of the Earth's crust, displays the greatest variety of well-defined residual shock effects among all rock-forming minerals. It represents an important and most reliable shock barometer and thermometer for terrestrial impact formations. In this paper, the current status of knowledge about the nature, origin, and experimental pressure-temperature calibration of shock-induced deformations and phase transformations is reviewed for natural and experimental shock conditions.
594 citations