Showing papers on "Rarefaction published in 2016"
TL;DR: It is shown that the Coulomb-like friction term make waves (including rarefaction, shock and delta shock) bend into parabolic shapes for the Riemann solutions.
52 citations
TL;DR: In this paper, it was shown that energy transport proceeds by the formation of an instantaneous shock wave and a broadening rarefaction wave on either side of the interface, and not by two shock waves as previously proposed.
Abstract: We reexamine the emergence of a universal nonequilibrium steady state following a local quench between quantum critical heat baths in spatial dimensions greater than one. We show that energy transport proceeds by the formation of an instantaneous shock wave and a broadening rarefaction wave on either side of the interface, and not by two shock waves as previously proposed. For small temperature differences the universal steady state energy currents of the two-shock and rarefaction-shock solutions coincide. Over a broad range of parameters, the difference in the energy flow across the interface between these two solutions is at the level of 2%. The properties of the energy flow remain fully universal and independent of the microscopic theory. We briefly discuss the width of the shock wave in a viscous fluid, the effects of momentum relaxation, and the generalization to charged fluids.
51 citations
TL;DR: In this paper, the authors apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation with steplike initial data leading to a rarefaction wave.
49 citations
TL;DR: In this article, the role of collisional coupling between a proton-electron, charge-neutral fluid and a neutral hydrogen fluid for the 1D Riemann problem initiated in a constant pressure and density background state by a discontinuity in the magnetic field is investigated.
Abstract: The role of slow-mode magnetohydrodynamic (MHD) shocks in magnetic reconnection is of great importance for energy conversion and transport, but in many astrophysical plasmas the plasma is not fully ionised. In this paper, we use numerical simulations to investigate the role of collisional coupling between a proton-electron, charge-neutral fluid and a neutral hydrogen fluid for the one-dimensional (1D) Riemann problem initiated in a constant pressure and density background state by a discontinuity in the magnetic field. This system, in the MHD limit, is characterised by two waves. The first is a fast-mode rarefaction wave that drives a flow towards a slow-mode MHD shock wave. The system evolves through four stages: initiation, weak coupling, intermediate coupling, and a quasi-steady state. The initial stages are characterised by an over-pressured neutral region that expands with characteristics of a blast wave. In the later stages, the system tends towards a self-similar solution where the main drift velocity is concentrated in the thin region of the shock front. Because of the nature of the system, the neutral fluid is overpressured by the shock when compared to a purely hydrodynamic shock, which results in the neutral fluid expanding to form the shock precursor. Once it has formed, the thickness of the shock front is proportional to ξ i -1.2 , which is a smaller exponent than would be naively expected from simple scaling arguments. One interesting result is that the shock front is a continuous transition of the physical variables of subsonic velocity upstream of the shock front (a c-shock) to a sharp jump in the physical variables followed by a relaxation to the downstream values for supersonic upstream velocity (a j-shock). The frictional heating that results from the velocity drift across the shock front can amount to ~2 per cent of the reference magnetic energy.
45 citations
TL;DR: In this paper, a methodology is developed to measure solar-wind compression and rarefaction using the orientations of solar wind current sheets, based on the current-sheet orientations, on magnetic field strength, on the intensity of the electron strahl, and on the negative vorticity, an inflection point is taken as the best indicator of the trailing-edge stream interface.
Abstract: The trailing-edge rarefactions of 54 high-speed streams at 1AU are analyzed. The temporal durations of the trailing-edge rarefactions agree with ballistic calculations based on the observed speeds of the fast and slow wind bounding the rarefactions. A methodology is developed to measure solar-wind compression and rarefaction using the orientations of solar-wind current sheets. One focus is to determine the signature that best describes the location of the trailing-edge stream interface between coronal-hole-origin plasma and streamer-belt-origin plasma; based on the current-sheet orientations, on the magnetic-field strength, on the intensity of the electron strahl, and on the intensity of the negative vorticity, an inflection point in the temporal profile of the solar-wind velocity is taken as the best indicator of the trailing-edge stream interface. Computer simulations support this choice. Using superposed-epoch analysis, the plasma properties and turbulence properties of trailing-edge rarefactions are surveyed. Whereas the signatures of the coronalhole/streamer-belt (slow-wind/fast-wind) boundary in the leading edge (corotating interaction region) stream interface are simultaneous, they are not simultaneous in the trailing edge, with ion-charge-state signatures occurring on average 13.7h prior to the proton entropy signature. It is suggested that differences in the leading and trailing edges of coronal holes on the Sunmight account for the differences in the leading and trailing edges of high-speed streams at 1AU: the formation timescales, heating timescales, and charge-state-equilibration timescales of closed flux loops in the corona might be involved.
32 citations
TL;DR: In this paper, the authors explore the behavior of the Rayleigh-Taylor instability initiated with a diffuse interface and perform experiments in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave.
Abstract: Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order of , where is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duff et al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duff et al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a decay in growth rates as for large-wavenumber perturbations.
32 citations
TL;DR: In this article, the relativistic Riemannian problem is used to generate a non-equilibrium steady state in a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime.
Abstract: We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under consideration, the initial conditions consist of a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime. The new double shock solutions are in contrast with older solutions that involve one shock and one rarefaction wave. We use numerical simulations to show that the older solutions are preferred. Briefly we discuss the effects of a conserved charge. Finally, we discuss deforming the relativistic equations with a nonlinear term and how that deformation affects the temperature and velocity in the region connecting the asymptotic fluids.
31 citations
TL;DR: In this article, the authors investigate the self-consistent excitation of slow magneto-acoustic body waves (slow modes) in a magnetic flux concentration, and conclude that this process of "magnetic pumping" is a most plausible mechanism for direct generation of longitudinal chromospheric and coronal compressive waves within magnetic flux concentrations, and it may provide an important heat source in the chromosphere.
Abstract: Using radiation magnetohydrodynamic simulations of the solar atmospheric layers from the upper convection zone to the lower corona, we investigate the self-consistent excitation of slow magneto-acoustic body waves (slow modes) in a magnetic flux concentration. We find that the convective downdrafts in the close surroundings of a two-dimensional flux slab "pump" the plasma inside it in the downward direction. This action produces a downflow inside the flux slab, which encompasses ever higher layers, causing an upwardly propagating rarefaction wave. The slow mode, excited by the adiabatic compression of the downflow near the optical surface, travels along the magnetic field in the upward direction at the tube speed. It develops into a shock wave at chromospheric heights, where it dissipates, lifts the transition region, and produces an offspring in the form of a compressive wave that propagates further into the corona. In the wake of downflows and propagating shock waves, the atmosphere inside the flux slab in the chromosphere and higher tends to oscillate with a period of $
u\approx 4$~mHz. We conclude that this process of "magnetic pumping" is a most plausible mechanism for the direct generation of longitudinal chromospheric and coronal compressive waves within magnetic flux concentrations, and it may provide an important heat source in the chromosphere. It may also be responsible for certain types of dynamic fibrils.
25 citations
TL;DR: In this paper, the authors studied the stability of superposition of boundary layer and rarefaction wave on the two-fluid Navier-Stokes-Poisson system in the half line R + = : ( 0, + ∞ ).
Abstract: This paper is concerned with the study of nonlinear stability of superposition of boundary layer and rarefaction wave on the two-fluid Navier–Stokes–Poisson system in the half line R + = : ( 0 , + ∞ ) . On account of the quasineutral assumption and the absence of the electric field for the large time behavior, we successfully construct the boundary layer and rarefaction wave, and then we give the rigorous proofs of the stability theorems on the superposition of boundary layer and rarefaction wave under small perturbations for the corresponding initial boundary value problem of the Navier–Stokes–Poisson system, only provided the strength of boundary layer is small while the strength of rarefaction wave can be arbitrarily large. The complexity of nonlinear composite wave leads to many complicated terms in the course of establishing the a priori estimates. The proofs are given by an elementary L 2 energy method.
23 citations
TL;DR: In this article, the authors dealt with a theoretical investigation of steady fully developed MHD natural convection flow of viscous, incompressible, electrically conducting fluid in micro-concntric-annuli in the presence of radial magnetic field and derived exact solutions for energy and momentum equations under relevant boundary conditions.
22 citations
TL;DR: In this article, the authors studied the nonlinear stability of rarefaction waves to the Cauchy problem of one-dimensional compressible Navier-Stokes equations for a viscous and heat conducting ideal polytropic gas when the transport coefficients depend on both temperature and density.
Abstract: We study the nonlinear stability of rarefaction waves to the Cauchy problem of one-dimensional compressible Navier-Stokes equations for a viscous and heat conducting ideal polytropic gas when the transport coefficients depend on both temperature and density. When the strength of the rarefaction waves is small or the rarefaction waves of different families are separated far enough initially, we show that rarefaction waves are nonlinear stable provided that $(\gamma- 1)\cdot H^3(\mathbb{R})$-norm of the initial perturbation is suitably small with $\gamma>1$ being the adiabatic gas constant.
TL;DR: In this article, a direct approach is used to solve the Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady planar flow of an isentropic, inviscid compressible fluid in the presence of dust particles.
Abstract: A direct approach is used to solve the Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady planar flow of an isentropic, inviscid compressible fluid in the presence of dust particles. The elementary wave solutions of the Riemann problem, that is, shock waves, rarefaction waves and contact discontinuities are derived and their properties are discussed for a dusty gas. The generalised Riemann invariants are used to find the solution between rarefaction wave and the contact discontinuity and also inside rarefaction fan. Unlike the ordinary gasdynamic case, the solution inside the rarefaction waves in dusty gas cannot be obtained directly and explicitly; indeed, it requires an extra iteration procedure. Although the case of dusty gas is more complex than the ordinary gas dynamics case, all the parallel results for compressive waves remain identical. We also compare/contrast the nature of the solution in an ordinary gasdynamics and the dusty gas flow case.
TL;DR: In this article, the authors investigate the self-consistent excitation of slow magneto-acoustic body waves (slow modes) in a magnetic flux concentration, and conclude that this process of "magnetic pumping" is a most plausible mechanism for direct generation of longitudinal chromospheric and coronal compressive waves within magnetic flux concentrations, and it may provide an important heat source in the chromosphere.
Abstract: Using radiation magnetohydrodynamic simulations of the solar atmospheric layers from the upper convection zone to the lower corona, we investigate the self-consistent excitation of slow magneto-acoustic body waves (slow modes) in a magnetic flux concentration. We find that the convective downdrafts in the close surroundings of a two-dimensional flux slab "pump" the plasma inside it in the downward direction. This action produces a downflow inside the flux slab, which encompasses ever higher layers, causing an upwardly propagating rarefaction wave. The slow mode, excited by the adiabatic compression of the downflow near the optical surface, travels along the magnetic field in the upward direction at the tube speed. It develops into a shock wave at chromospheric heights, where it dissipates, lifts the transition region, and produces an offspring in the form of a compressive wave that propagates further into the corona. In the wake of downflows and propagating shock waves, the atmosphere inside the flux slab in the chromosphere and higher tends to oscillate with a period of $
u\approx 4$~mHz. We conclude that this process of "magnetic pumping" is a most plausible mechanism for the direct generation of longitudinal chromospheric and coronal compressive waves within magnetic flux concentrations, and it may provide an important heat source in the chromosphere. It may also be responsible for certain types of dynamic fibrils.
TL;DR: In this article, a p-system with relaxation is considered and two possible classes of exact solutions of the governing model both parameterized by one arbitrary function are determined within the theoretical framework of the differential constraints method.
Abstract: In this paper a p-system with relaxation is considered. Within the theoretical framework of the differential constraints method, we determine two possible classes of exact solutions of the governing model both parameterized by one arbitrary function. This allows to solve classes of initial value problems of interest in nonlinear wave propagation. In fact a generalized Riemann problem is solved by determining a smooth solution which plays the role of the well known rarefaction wave of the homogeneous case.
TL;DR: In this article, the authors examined the same situation for an undular bore represented by a modulated periodic wave train and showed that the leading solitary waves in the undular bearing are destroyed and replaced by a developing rarefaction wave supporting emerging solitary waves of the opposite polarity.
TL;DR: In this article, an analytical correlation is developed for stagnation-point heat flux on spherical objects travelling at high velocity which is accurate for conditions ranging from the continuum to the free-molecular flow regime.
Abstract: An analytical correlation is developed for stagnation-point heat flux on spherical objects travelling at high velocity which is accurate for conditions ranging from the continuum to the free-molecular flow regime. Theoretical analysis of the Burnett and super-Burnett equations is performed using simplifications from shock-wave and boundary-layer theory to determine the relative contribution of higher-order heat flux terms compared with the Fourier heat flux (assumed in the Navier–Stokes equations). A rarefaction parameter ( ), based on the free-stream Mach number ( ), the Reynolds number ( ) and the viscosity–temperature index ( ), is identified as a better correlating parameter than the Knudsen number in the transition regime. By studying both the Burnett and super-Burnett equations, a general form for the entire series of higher-order heat flux contributions is obtained. The resulting heat flux expression includes terms with dependence on gas properties, stagnation to wall-temperature ratio and a main dependence on powers of the rarefaction parameter . The expression is applied as a correction to the Fourier heat flux and therefore can be combined with any continuum-based correlation of choice. In the free-molecular limit, a bridging function is used to ensure consistency with well-established free-molecular flow theory. The correlation is then fitted to direct simulation Monte Carlo (DSMC) solutions for stagnation-point heat flux in high-speed nitrogen flows. The correlation is shown to accurately capture the variation in heat flux predicted by the DSMC method in the transition flow regime, while limiting to both continuum and free-molecular values.
TL;DR: In this article, a model has been derived that predicts compressive/rarefaction, supersonic/supersonic solitary waves, varying the level of compression and the support type (guided or pinned).
TL;DR: In this paper, a hybrid type Riemann solver is proposed to compute numerical fluxes across the interfaces of gas-gas, liquid-liquid and gas-liquid flows in the considered flow fields.
TL;DR: In this article, a quasi-one-dimensional inviscid flow approximation for a single-phase fluid expanding from a reservoir into a stationary atmosphere through a conventional converging-diverging nozzle is derived.
Abstract: Steady nozzle flows of Bethe–Zel’dovich–Thompson fluids – substances exhibiting non-classical gasdynamic behaviour in a finite vapour-phase thermodynamic region in close proximity to the liquid–vapour saturation curve – are examined. Non-classical flow features include rarefaction shock waves, shock waves with either upstream or downstream sonic states and split shocks. Exact solutions for a mono-component single-phase fluid expanding from a reservoir into a stationary atmosphere through a conventional converging–diverging nozzle are determined within the quasi-one-dimensional inviscid flow approximation. The novel analytical approach makes it possible to elucidate the connection between the adiabatic, possibly non-isentropic flow field and the underlying local isentropic-flow features, including the possible qualitative alterations in passing through shock waves. Contrary to previous predictions based on isentropic-flow inspection, shock disintegration is found to occur also from reservoir states corresponding to a single sonic point. The global layout of the flow configurations produced by a monotonic decrease in the ambient pressure, namely the functioning regime, is examined for reservoir conditions resulting in single-phase flows. Accordingly, a classification of steady nozzle flows into 10 different functioning regimes is proposed. Flow conditions determining the transition between the different classes of flow are investigated and each functioning regime is associated with the corresponding thermodynamic region of reservoir states.
TL;DR: In this article, a sequence of solutions to the one-dimensional motion of a radiating gas are constructed, and when the absorption coefficient α tends to ∞, the above solutions converge to the rarefaction wave, which is an elementary wave pattern of gas dynamics, with a convergence rate
Abstract: In this paper, a sequence of solutions to the one-dimensional motion of a radiating gas are constructed. Furthermore, when the absorption coefficient α tends to ∞, the above solutions converge to the rarefaction wave, which is an elementary wave pattern of gas dynamics, with a convergence rate \(\alpha ^{ - \tfrac{1} {3}} \left| {\ln \alpha } \right|^2\).
TL;DR: In this paper, the role of collisional coupling between a proton-electron charge-neutral fluid and a neutral hydrogen fluid for the 1D Riemann problem initiated in a constant pressure and density background state by a discontinuity in the magnetic field was investigated.
Abstract: The role of slow-mode MHD shocks in magnetic reconnection is one of great importance for energy conversion and transport, but in many astrophysical plasmas the plasma is not fully ionised. In this paper, we investigate, using numerical simulations, the role of collisional coupling between a proton-electron charge-neutral fluid and a neutral hydrogen fluid for the 1D Riemann problem initiated in a constant pressure and density background state by a discontinuity in the magnetic field. This system, in the MHD limit, is characterised by two waves: a fast-mode rarefaction wave that drives a flow towards a slow-mode MHD shock. The system evolves through four stage: initiation, weak coupling, intermediate coupling and a quasi steady state. The initial stages are characterised by an over-pressured neutral region that expands with characteristics of a blast wave. In the later stages, the system tends towards a self-similar solution where the main drift velocity is concentrated in the thin region of the shock front. Due to the nature of the system, the neutral fluid is overpressured by the shock when compared to a purely hydrodynamic shock which results in the neutral fluid expanding to form the shock precursor. The thickness of the shockfront once it has formed proportional to the ionisation fraction to the power -1.2, which is a smaller exponent than would be naively expected from simple scaling arguments. One interesting result is that the shock front is a continuous transition of the physical variables for sub-sonic velocity upstream of the shock front (a c-shock) to a sharp jump in the physical variables followed by a relaxation to the downstream values for supersonic upstream velocity (a j-shock). The frictional heating that results from the velocity drift across the shock front can amount to approximately two per cent of the reference magnetic energy.
TL;DR: In this paper, the authors studied the zero viscosity and capillarity limit problem for the one-dimensional compressible isentropic Navier-Stokes-Korteweg equations when the corresponding Euler equations have rarefaction wave solutions.
Abstract: In this paper, we study the zero viscosity and capillarity limit problem for the one-dimensional compressible isentropic Navier–Stokes–Korteweg equations when the corresponding Euler equations have rarefaction wave solutions. In the case that either the effects of initial layer are ignored or the rarefaction waves are smooth, we prove that the solutions of the Navier–Stokes–Korteweg equation with centered rarefaction wave data exist for all time and converge to the centered rarefaction waves as the viscosity and capillarity number vanish, and we also obtain a rate of convergence, which is valid uniformly for all time. These results are showed by a scaling argument and elementary energy analysis. Copyright © 2016 John Wiley & Sons, Ltd.
01 Mar 2016
TL;DR: In this article, the unbalance response of micro gas bearing-rotor system is calculated using the fourth-order Runge-Kutta method based on the motion equation of the rotor, in which the nonlinear gas film force is obtained from solving the modified Reynolds equation using the alternating direction implication algorithm.
Abstract: The unbalance response of micro gas bearing-rotor system is calculated using the fourth-order Runge–Kutta method based on the motion equation of the rotor, in which the nonlinear gas film force is obtained from solving the modified Reynolds equation using the alternating direction implication algorithm. The study shows that the proper eccentric mass of the rotor can improve the stability of micro gas bearing-rotor system. Compared with the result without considering the gas rarefaction effect, the stability threshold speed of micro rotor system considering the gas rarefaction effect is increased. Meanwhile for the same mass eccentricity, the peak value emerges at the lower rotation speed, which shows that the unbalance eccentric mass will influence the motion of micro rotor system more greatly when the gas rarefaction effect is taken into account.
TL;DR: In this article, a modified equation of Burgers with a quadratically cubic (QC) nonlinear term was recently pointed out as a new exactly solvable model of mathematical physics and its derivation, analytical solution, computer modeling, as well as its physical applications and analysis of corresponding nonlinear wave phenomena have not been published up to now.
Abstract: A modified equation of Burgers type with a quadratically cubic (QC) nonlinear term was recently pointed out as a new exactly solvable model of mathematical physics. However, its derivation, analytical solution, computer modeling, as well as its physical applications and analysis of corresponding nonlinear wave phenomena have not been published up to now. The physical meaning and generality of this QC nonlinearity are illustrated here by several examples and experimental results. The QC equation can be linearized and it describes the experimentally observed phenomena. Some of its exact solutions are given. It is shown that in a QC medium not only shocks of compression can be stable, but shocks of rarefaction as well. The formation of stationary waves with finite width of shock front resulting from the competition between nonlinearity and dissipation is traced. Single-pulse propagation is studied by computer modeling. The nonlinear evolutions of N- and S-waves in a dissipative QC medium are described, and the transformation of a harmonic wave to a sawtooth-shaped wave with periodically recurring trapezoidal teeth is analyzed.
TL;DR: The numerical model offers a computationally efficient way of understanding the complex phenomena involving the interplay of a bubble, a shock wave, and a nearby bio-material.
Abstract: Following previous work on the dynamics of an oscillating bubble near a bio-material (Ohl et al 2009 Phys. Med. Biol. 54 6313-36) and the interaction of a bubble with a shockwave (Klaseboer et al 2007 J. Fluid Mech. 593 33-56), the present work concerns the interaction of a gas bubble with a traveling shock wave (such as from a lithotripter) in the vicinity of bio-materials such as fat, skin, muscle, cornea, cartilage, and bone. The bubble is situated in water (to represent a water-like biofluid). The bubble collapses are not spherically symmetric, but tend to feature a high speed jet. A few simulations are performed and compared with available experimental observations from Sankin and Zhong (2006 Phys. Rev. E 74 046304). The collapses of cavitation bubbles (created by laser in the experiment) near an elastic membrane when hit by a lithotripter shock wave are correctly captured by the simulation. This is followed by a more systematic study of the effects involved concerning shockwave bubble biomaterial interactions. If a subsequent rarefaction wave hits the collapsed bubble, it will re-expand to a very large size straining the bio-materials nearby before collapsing once again. It is noted that, for hard bio-material like bone, reflection of the shock wave at the bone-water interface can affect the bubble dynamics. Also the initial size of the bubble has a significant effect. Large bubbles (∼1 mm) will split into smaller bubbles, while small bubbles collapse with a high speed jet in the travel direction of the shock wave. The numerical model offers a computationally efficient way of understanding the complex phenomena involving the interplay of a bubble, a shock wave, and a nearby bio-material.
TL;DR: In this paper, heat transfer in hydrodynamically developed, thermally developing gas flows in micro-slits at various flow conditions was studied. But the authors only considered the heat conduction in the axial direction and heat dissipation of viscous forces.
TL;DR: By means of molecular dynamics simulation, this article investigated the interaction of picosecond-duration compression pulses excited by a flat impactor with flat and nano-structured rear surfaces of copper and aluminum samples.
Abstract: By means of molecular dynamics simulation, we investigate the interaction of picosecond-duration compression pulses excited by a flat impactor with flat and nano-structured rear surfaces of copper and aluminum samples It is shown that protrusions on the rear surface can increase the threshold value of the impact velocity, leading to spallation As the shock wave reaches the perturbed rear surface, an unloading on the lateral surfaces of the protrusions begins; it leads to an intensive plastic deformation in the surface layer of metal A part of the compression pulse energy is spent on the plastic deformation that restricts the rarefaction wave amplitude and suppresses the spall fracture An increase in threshold velocity can be observed for all investigated thicknesses of the targets The increase is substantial with respect to comparability between the protrusion height and the compression pulse width (the impactor thickness) Another condition is the ratio of the protrusion cross-section to the total s
TL;DR: In this article, the authors used the kinetic S-model to study the rarefied gas flow through a plane channel between two parallel infinite plates, where the gas is at rest and is separated by the plane x = 0 with different pressure values on opposite sides.
Abstract: The kinetic S-model is used to study the unsteady rarefied gas flow through a plane channel between two parallel infinite plates. Initially, the gas is at rest and is separated by the plane x = 0 with different pressure values on opposite sides. The gas deceleration effect of the channel walls is studied depending on the degree of gas rarefaction and the initial pressure drop, assuming that the molecules are diffusely reflected from the boundary. The decay of the shock wave and the disappearance of the uniform flow region behind the shock wave are monitored. Special attention is given to the gas mass flux through the cross section at x = 0, which is computed as a function of time. The asymptotic behavior of the solution at unboundedly increasing time is analyzed. The kinetic equation is solved numerically by applying a conservative finite-difference method of second-order accuracy in space.
TL;DR: In this paper, a volume diffusion model is used as an extension to the standard Navier-Stokes-Fourier set for simulating the flows in a lid-driven cavity flow initiated by instantaneously heating and cooling opposite walls.
TL;DR: In this article, the authors investigated the large-time behavior of the radially symmetric solution for Burgers equation on the exterior of a small ball in multi-dimensional space, where the boundary data and the data at the far field are prescribed.
Abstract: We investigate the large-time behavior of the radially symmetric solution for Burgers equation on the exterior of a small ball in multi-dimensional space, where the boundary data and the data at the far field are prescribed. In a previous paper [1], we showed that, for the case in which the boundary data is equal to $0$ or negative, the asymptotic stability is the same as that for the viscous conservation law. In the present paper, it is proved that if the boundary data is positive, the asymptotic state is a superposition of the stationary wave and the rarefaction wave, which is a new wave phenomenon. The proof is given using a standard $L^{2}$ energy method and the characteristic curve method.