Numerical computation of viscous profiles for hyperbolic conservation laws

Viscous profiles of shock waves in systems of conservation laws can be viewed as heteroclinic orbits in associated systems of ordinary differential equations (ODE). In the case of overcompressive shock waves, these orbits occur in multi-parameter families. We propose a numerical method to compute families of heteroclinic orbits in general systems of ODE. The key point is a special parameterization of the heteroclinic manifold which can be understood as a generalized phase condition; in the case of shock profiles, this phase condition has a natural interpretation regarding their stability. We prove that our method converges and present numerical results for several systems of conservation laws. These examples include traveling waves for the Navier-Stokes equations for compressible viscous, heat-conductive fluids and for the magnetohydrodynamics equations for viscous, heat-conductive, electrically resistive fluids that correspond to shock wave solutions of the associated ideal models, i.e., the Euler, resp. Lundquist, equations.

     

一类非线性方程的激波解

该文是利用匹配条件讨论一类非线性方程激波解。得出了对应的激波解与边界条件的关系。     

Numerical simulation of silencers

The problem of attenuating the noise from weapons firing is studied experimentally and numerically. As a possible method of attenuating the noise significantly, a silencer with no internal baffles is attached to the M242 cannon. The internal pressures inside the muffler are measured. The near-field overpressures outside the muffler at various polar angles are also measured. A numerical simulation of the flow through the muffler is performed, using Harten's shock-capturing method to solve the Euler equations of ideal compressible flow. The numerical simulation yields a detailed picture of the flow field as displayed by the pressure and Mach contours. Pressure–time curves at selected locations are obtained and compared with experimental data. There is good agreement, except that the numerical simulation generates more vigorous oscillations.     

包装设计中最佳状态参数计算

本文提出了商品在某一高度自由落下时,商品最小冲击加速度的计算方法,并得出在最佳状态下(即商品所受冲击加速度 G 值最小时)缓冲系统应具有的初始弹性系数 k。和最大位移 Xm,从而为缓冲系统设计提供必要数据。     

A point implicit unstructured grid solver for the euler and Navier–Stokes equations

An upwind finite element technique that uses cell-centred quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive triangular grids. The approach is an extension to unstructured grids of the LAURA algorithm due to Gnoffo. A structured grid of quadrilaterals is laid out near a solid surface. For inviscid flows the method is stable at Courant numbers of over 100000. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view to simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are distinctly captured with a sequence of adaptively generated grids.     

Application of background oriented schlieren for quantitative measurements of shock waves from explosions

This paper describes application of a background oriented schlieren technique in order to obtain quantitative measurements of shock waves from explosions by processing high speed digital video recordings. The technique is illustrated by an analysis of two explosions, a high explosive test and a hydrogen gas explosion test. The visualization of the shock front is utilized to calculate the shock Mach number, leading to a predicted shock front pressure. For high explosives the method agreed quite well with a standard curve for side-on shock pressures. In the case of the gas explosion test we can also show that the shock front is non-spherical. It should be possible to develop this technique to investigate external blast waves and external explosions from vented gas explosions in more details. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Shock waves in an elliptical cavity with varying height

Transient shock waves in a confined elliptical chamber are experimentally investigated. Quantitative results of the pressure distribution are obtained for an air-filled cavity. Lower bounding surfaces of different geometrical shapes can be inserted making it possible to get chambers with varying height. An electrical discharge across a pair of electrodes inside the cavity gives rise to the shock waves. Double pulsed holographic interferometry is used to study the propagation and focusing process of the waves. The results are quantitatively evaluated by using the method of two-reference-beam holography. The angular pressure distribution behind the converging wave front is presented for different geometries of an air-filled cavity. The pressure distribution is non-homogeneous but symmetric along the wave front. The pressure level is higher for the geometry where the height of the chamber decreases with the radial distance from the outgoing focus and lower for increasing height of the chamber. In addition, shock waves in a water-filled cavity are studied. In this case qualitative results are obtained. Received 3 November 1996 / Accepted 5 January 1997     

一种新型的固着磨料抛光片──WBN抛光片的制作工艺及其特性

本文描述了用冲击合成方法得到的超硬材料纤锌矿型氮化硼（ＷＢＮ）制作的一种新型抛光片。在光学玻璃抛光中的初步应用显示：这种新型的ＷＢＮ抛光片具有比传统的ＣｅＯ２。抛光片更大的切削力、更短的抛光时间和更好的表面粗糙度及更长寿命等优点。     

Vibrational excitation of molecules in a lattice due to shock induced molecular deformation

A simple formalism is developed to calculate the rate of internal vibrational excitation of a molecule in a lattice due to abrupt deformation of the bonds of the molecule as a result of the application of a shock pulse to the lattice. The excitation rate is calculated as a function of rise time of the pulse and peak pressure for the case of 1,3,5-trinitro, 1,3,5-triazocyclohexane. It is shown that large vibrational excitation rates can be achieved if the rise time of the shock pulse is in the order of the period of vibration of the bond. The possible role of this process in shock induced chemical reactions in solids is considered.     

Simulation of the starting flow in a wedge–like nozzle

The starting process of the flow in a wedge-like expansion nozzle of a shock tunnel is simulated by an unsplit 2-D GRP scheme on an unstructured grid. The scheme is briefly outlined and results are presented and discussed in comparison to the experimental (shadowgraph) findings obtained by Amann. The simulated pattern of reflected and transmitted shock waves in the nozzle inlet region and inside the nozzle is found to agree well with the experimental data. Received 5 April 1996 / Accepted 16 June 1997