Narrow Results

Artificial viscosity is often expressed as a superposition of linear and quadratic terms in the first derivative of the velocity field. In trying to find a continuous solution for the hydrodynamic equations, we propose an alternative one-term artificial viscosity which is a linear form of the derivative of the specific volume. It is shown that this artificial viscosity is able to capture the profile of the steady plane shock wave, largely removing the non-physical oscillations originated by the artificial viscosity of von Neumann and Richtmyer. Analytical and numerical calculations for one-dimensional shock using both artificial viscosities are compared.

We numerically study the evolution of a boost-invariant SYM medium using AdS/CFT. We consider a toy model for the collision of gravitational shock waves, finding that the energy density first increases, reaches a maximum and then starts to decrease, matching hydrodynamics for late times. For the initial conditions we consider, the hydrodynamic scale governing the late time behavior is to very good approximation determined by the area of the black hole horizon at initial times. Our results provide a toy model for the early time evolution of the bulk system in heavy-ion collisions at RHIC and the LHC.

We show that a hyperbolic system with a mathematical entropy can be discretized with vectorial lattice Boltzmann schemes using the methodology of kinetic representation of the dual entropy. We test this approach for the shallow water equations in one and two spatial dimensions. We obtain interesting results for a shock tube, reflection of a shock wave and nonstationary two-dimensional propagation. This contribution shows the ability of vectorial lattice Boltzmann schemes to simulate strong nonlinear waves in nonstationary situations.

The boundary layer correction method is applied to study asymptotic traveling wave solutions to anisotropic higher-order traffic flow model with viscous coefficient, which clearly indicates that the truncation error between the original and approximate equations is an equivalent infinitesimal of the coefficient. Therefore, the solution is exact in the case when the coefficient vanishes, which corresponds to a certain nonviscous model following the standard hyperbolic and viscous conservation laws. Numerical simulation is implemented to reproduce a typical traveling wave or wide moving jam consisting of a transitional layer (the downstream front) and a shock (the upstream front) profiles, of which the parameters converge not only for refined meshes but for refined viscous coefficient as well. These are highly in agreement with the analytical results.

In high-speed flow applications, increased aero-thermodynamic loads, localized turbulent regions, instability, excessive drag and pressure losses are among the negative effects of the interaction between shock waves and boundary layers and the subsequent separation of the boundary layer. These drawbacks emphasize how crucial it is to look into ways to control the boundary layer separation caused by shock waves. In order to determine whether using a pressure feedback technique to regulate boundary layer separation on a two-dimensional forward-facing step (FFS) is effective, a numerical study is conducted. The pressure feedback technique utilizes a channel to remove fluid from the separated area and reintroduce it into the mainstream flow, by leveraging the pressure contrast as the motivating factor. Ansys Fluent 2021 simulation software is used to conduct a numerical study investigating shock wave boundary layer interaction over a FFS at a supersonic Mach number of 2.5. The present study aims to explore the effectiveness of implementing a pressure feedback channel near the FFS as a strategy for controlling flow separation induced by the step. Turbulence effects are simulated using a k-omega model, and the study employs a finite-volume method with upwind flux difference splitting and second-order upwind flow discretization. The simulation results indicate the efficacy of the pressure feedback mechanism in reducing flow separation, thus enhancing its role in separation control. Integration of an 80mm channel results in a notable 42.85% decrease in separation bubble size, while the longer 90mm channel yields an even more substantial 52.38% reduction.

Usual uniformly accelerated frame, in Dray–’t Hooft spacetime, does not see the any quantum imprint on Unruh effect due to localized shock wave in Minkowski spacetime. Here, we argue that such non-appearance of quantum memory is specific to those particular observers which do not incorporate the presence of wave in their trajectory. In fact, a detector, associated with a frame which is affected by the shock, cannot be trivial in terms of its response. We explicitly show that the later type of frame detects particle in the shock wave Minkowski vacuum which is the effect of shock. Therefore, this quantum memory is very special to specific class of observers as far as Dray–’t Hooft spacetime is concerned. We analyze for a null like trajectory along which the detector is moving.

The 28 October 2003 flare gave us the unique opportunity to compare the acceleration time of high-energy protons with the escaping time of those particles which have been measured onboard spacecraft and by neutron monitors network as GLE event. High-energy emission time scale and shock wave height and velocity time dependencies were also studied.

The radial variation of the ~ 0.5 – 2 MeV proton background is estimated at 20 – 80 AU during low solar activity periods using Voyager 1 LECP data. The estimation of proton radial gradient suggest an intensity drop between about 30 and 60 AU and a change of the gradient sign from negative to positive beyond about of 70 AU.

Steinberg-Guinan constitutive model is widely used in impact engineering simulations. Shock wave profile measurements of Al, Cu, and W under shock pressures ranging from 4 GPa to 200 GPa were analyzed, and shear modulus G and yield strength Y of these materials were obtained by using the high-pressure sonic velocities and rate independent Lagrange analysis results. Then values of derivatives of G and Y with respect to pressure or temperature at the reference state of these three metals were determined. By analyzing the pressure and temperature dependence of shear modulus and yield strength, we conclude that the relations of Steinberg-Guinan constitutive model, Y/G=constant, are approximately correct on Hugoniot state for these materials. So this is a probable approach to solve the difficulty of measurement of Y under high-pressure and high-temperature directly.

In order to study the protection behavior of brittle materials against a shaped charge jet, the jet penetration and the fracture behavior have been investigated by the series of photographs taken by the IMACON high speed camera. The examined materials were glass, fused silica, and single crystalline quartz. The trend of crack growth in BK7 glass and fused silica indicated conical shape. In the case of the single crystalline quartz, it was observed that the crack grows fast along the axis of crystal growth. The velocity of shock wave (~ 6km/sec) into glass and fused silica was faster than the sonic velocity. However, the velocity of shock wave in the single crystalline quartz showed to be similar to its sonic velocity. The ballistic protection capability of single crystalline quartz showing fast crack growth has been evaluated to be lower than that of fused silica which has relatively slow crack growth, although the quartz has higher physical and mechanical properties.

The nonlinear increase of the lift of the double swept waverider at high angles of attack is of vital interest. The aerodynamic performance of the double swept waverider is calculated and compared with that of single swept waveriders. Results suggest that the lift nonlinearity of the double swept waverider is stronger than that of equal-planform-area single swept one, and the nonlinearity increases as Mach number increases. Some scholars have proposed the “vortex lift” to explain the nonlinear lift increase, but it is questionable as the main lift of the waverider comes from the lower surface rather than the upper surface. This paper proposes another explanation that the nonlinear lift increase is related to the attachment of shock wave, influenced by the leading-edge sweep angle. The shock wave is more inclined to attach under the lower surface with smaller swept than that of larger swept as angle of attack increases. When the shock wave attaches, the pressure increase via angle of attack is nonlinear, leading to the nonlinearity of lift increase.

Under the propagating limitation-conditions and based on the pulsed-laser-induced plasma shock wave theory,¹ the propagating rules in the global free space (including close areas and mid-far areas) of pulsed-laser-induced shock waves are established for the first time. Compared with the previous work by Bian et al.,² our theoretical model can directly lead to the relationship of the initial Mach number M₀ of plasma shock waves and the whole energy E released into plasma shock waves from a pulsed laser without any approximations or any unnecessary experimental parameters. Here, M₀ is also related to the pulse duration τ₀ and the sound velocity υ₀ in the atmosphere; the variation of attenuation index τ, as a function of laser parameters (especial τ₀), is also obtained, and our theoretical predictions of mid-far propagating rules of plasma shock waves are in good agreement with experimental results. In addition, it should be noted that Sedov–Taylor solutions to the ideal shock wave in a point explosion are only the approximations of the propagating rules in the mid-far area of pulsed-laser plasma shock waves that we obtained.

A new analytic model of the intense shock-wave decay is deduced in the paper based on self-consistent and well-defined assumptions. The shock wave attenuation in PMMA can be divided into two stages. In the initial decay, a spherical wave model is adopted because the dimension of the wave origin is too small to be neglected in comparison with the dimension of target. Due to overdamp at initial stage, the pressure gradient along the radial direction is expressed as dp/dr=f(∂p/∂t, du/dp) with the term (du/dp) deduced from the transient equation of wave front and the linear relation between the wave velocity and particle velocity at the wave rear. A temporal equicrural trapezoidal pressure profile applied to the target surface is used as the initial condition in order to obtain the pressure of ∂p/∂t. This pressure profile induces three stages of shock wave evolution: (1) The formation stage of "pressure increase"; (2) The plateau of "maximum pressure"; (3) The decay stage of "pressure decreases". According to the relation between the surge pressure of shock wave and laser power density, the character of laser-induced shock wave is described in detail. The above assumptions could not be applied in the final stage of propagation because the distorted "negative" pressure caused by the overdamp assumption would appear. In the final stage, the famous Taylor's equations of shock wave attenuation based on underdamp assumption are adopted. The theoretical model and the numerical results are in good agreement with the experiment.

Burgers equation is a fundamental partial differential equation of second order to describe the integrated process of convection-diffusion in physics. It occurs in various areas of applied mathematics and physics, such as modeling of turbulence, boundary layer behavior, shock wave formation, and mass transport. The convective and diffusive terms in Navier-Stokes equation are included in Burgers equation while the pressure term is neglected. A least-square point collocation meshless formula is proposed to discretize the Burgers equation. To verify the present meshless approach, the distributions of velocity for Burgers equation under different Reynolds numbers are investigated. Numerical results show that the proposed approach presents a good simulation of shock wave for Burgers equation with large Reynolds number.

The interaction of shock wave and turbulence for transonic flow over a circular cylinder is investigated using detached-eddy simulation (DES). Several typical cases are calculated for free-stream Mach number M_∞ from 0.85 to 0.95, and the physical mechanisms relevant to the shock wave and turbulence interaction are discussed. Results show that there exist two flow states. One is unsteady flow state with moving shock waves interacting with turbulent flow for M_∞ < 0.9 approximately, and the other is quasi-steady flow with stationary shocks standing over the wake of the cylinder for M_∞ > 0.9, suppressing the vortex shedding from the cylinder. Moreover, local supersonic zones are identified in the wake of the cylinder and generated by two processes, i.e., reverse flow and shock wave distortion induced the supersonic zone. Turbulent shear layer instabilities are revealed and associated with moving shock wave and traveling pressure wave.

The immersed boundary method (IBM) is an innovative approach for modeling flow with complex geometries and is more efficient than traditional method. In the present investigation, the shock wave propagation over one circular cylinder is simulated numerically with the Ghost-Body Immersed Boundary Method and high-resolution Roe scheme. To validate the IBM, a plane incident shock wave passing through a square cylinder is predicted and good agreement with previous experiments was obtained. Then based on our calculation, the reflection and diffraction processes of a shock wave passing through a circular cylinder were visualized and discussed in detail.

In order to carry out blast response of curtain wall, the first step is to understand the complex flow of the air blasts around the structures and predict the blast loads acting on the structures. But in earlier studies related to blast resistant design of glass curtain wall, blast flow induced by condensed explosive is not taken into account due to expensively computational resources required. Based on high performance computing, this paper presents a new three-dimensional numerical simulation method of condensed explosive-induced flow propagation and impact on a complex glass curtain wall, where the fluid is represented by solving Navier–Stokes equations with a multimaterial arbitrary Lagrangian–Eulerian (ALE) formulation. In particular, the whole analytical model consists of condensed explosive, air, detailed curtain wall system, and ground, which comprehensively represents the real fluid–structure interaction environment. Final calculation has been performed on the Dawning 4000A supercomputer based on the domain decomposition method. The flow mechanisms of blast wave rounding curtain wall is visualized and the simulated pressure history of gauge is in good agreement with the experimental result which validates this method. The present method is shown to be a useful tool for blast resistance design of curtain wall in the future.

A supersonic flow past a hemispherical nose with an opposing jet placed on its axis has been investigated using large eddy simulation. We find that the flow behaviors depend mainly on the jet total pressure ratio and can be classified into three typical flow regimes of unstable, stable and transition. The unstable flow regime is characterized by an oscillatory bow shock with a multi-jet-cell structure and the stable flow regime by a steady bow shock with a single jet cell. The transition regime lies between the unstable and stable ones with a complex flow evolution. Turbulence statistics are further analyzed to reveal the relevant turbulent behaviors in the three flow regimes. The results obtained in this study provide a physical insight into the understanding of the mechanisms underlying this complex flow.

This paper presents an analytical investigation into the propagation of a normal shock wave in Van der Waals gas flow, employing the Buongiorno model. It explores the dynamics of this flow type under a shock wave, considering modified Rankine–Hugoniot (RH) jump conditions within the Buongiorno model framework. By solving the RH conditions, this study provides a solution for gas flows with varying nanoparticle concentrations, facilitating an examination of parameter variations under discontinuity. The abstract further emphasizes the graphical representation of velocity coefficient and pressure in adiabatic gas flow during a shock wave, considering compressive and exponential waves. The analysis accounts for nanoparticle concentration and non-ideal parameters.

Artificial viscosity is widely used in numerical calculations of stellar core collapse. The failure or success of the prompt mechanism explosion of type-II supernovae is strongly dependent on the numerical code, and the study of a suitable and efficient method of capturing the shock front is a current problem. We present a novel one-term artificial viscosity which is dependent on the velocity field along the shock front. We show that this form of artificial viscosity is able to capture the profile of a plane shock wave, removing the non-physical oscillations originated by the artificial viscosity of von Neumann and Richtmyer type.