HIGH-ORDER WENO SIMULATIONS OF THREE-DIMENSIONAL RESHOCKED RICHTMYER-MESHKOV INSTABILITY TO LATE TIMES:DYNAMICS,DEPENDENCE ON INITIAL CONDITIONS,AND COMPARISONS TO EXPERIMENTAL DATA

The dynamics of the reshocked multi-mode Richtmyer-Meshkov instability is investigated using 513 × 257^2 three-dimensional ninth-order weighted essentially nonoscil- latory shock-capturing simulations. A two-mode initial perturbation with superposed ran- dom noise is used to model the Mach 1.5 air/SF6 Vetter-Sturtevant shock tube experiment. The mass fraction and enstrophy isosurfaces, and density cross-sections are utilized to show the detailed flow structure before, during, and after reshock. It is shown that the mixing layer growth agrees well with the experimentally measured growth rate before and after reshock. The post-reshock growth rate is also in good agreement with the prediction of the Mikaelian model. A parametric study of the sensitivity of the layer growth to the choice of amplitudes of the short and long wavelength initial interfacial perturbation is also pre- sented. Finally, the amplification effects of reshock are quantified using the evolution of the turbulent kinetic energy and turbulent enstrophy spectra, as well as the evolution of the baroclinic enstrophy production, buoyancy production, and shear production terms in the enstrophy and turbulent kinetic transport equations.

Detonation initiation developing from the Richtmyer-Meshkov instability

Detonation initiation resulting from the Richtmyer-Meshkov instability is investigated numerically in the configuration of the shock/spark-induced-deflagration interaction in a combustive gas mixture. Two-dimensional multi-species Navier-Stokes equations implemented with the detailed chemical reaction model are solved with the dispersion-controlled dissipative scheme. Numerical results show that the spark can create a blast wave and ignite deflagrations. Then, the deflagration waves are enhanced due to the Richtmyer-Meshkov instability, which provides detonation initiations with local environment conditions. By examining the deflagration fronts, two kinds of the initiation mechanisms are identified. One is referred to as the deflagration front acceleration with the help of the weak shock wave, occurring on the convex surfaces, and the other is the hot spot explosion deriving from the deflagration front focusing, occurring on the concave surfaces.

Numerical investigation of Richtmyer-Meshkov instability driven by cylindrical shocks

In this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov（RM） instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied.

The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics

The interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field is numerically investigated within the framework of ideal magnetohydrodynamics.Three fluids of differing densities are initially separated by the two perturbed cylindrical interfaces.The initial incident converging shock is generated from a Riemann problem upstream of the first interface.The effect of the magnetic field on the instabilities is studied through varying the field strength.It shows that the Richtmyer-Meshkov and Rayleigh-Taylor instabilities are mitigated by the field,however,the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations.The degree of asymmetry of the interfacial growth rate is increased when the seed field strength is increased.

Multiple-Relaxation-Time Lattice Boltzmann Approach to Richtmyer-Meshkov Instability

The aims of the present paper are twofold. At first, we further study the Multiple-Relaxation-Time （MRT） Lattice Boltzmann （LB） model proposed in [Europhys. Lett. 90 （2010） 54003]. We discuss the reason why the Gram Schmidt orthogonalization procedure is not needed in the construction of transformation matrix M; point out a reason why the Kataoka-Tsutahara model [Phys. Rev. E 69 （2004） 035701（R）] is only valid in subsonic flows. The yon Neumann stability analysis is performed. Secondly, we carry out a preliminary quantitative study on the Richtmyer- Meshkov instability using the proposed MRT LB model. When a shock wave travels from a light medium to a heavy one, the simulated growth rate is in qualitative agreement with the perturbation model by Zhang-Sohn. It is about half of the predicted value by the impulsive model and is closer to the experimental result. When the shock wave travels from a heavy medium to a light one, our simulation results are also consistent with physical analysis.

The Growth of Richtmyer-Meshkov Instability under Multiple Impingements

The growth of multi-mode Richtmyer-Meshkov instability under multiple impingements and the effect of initial shock strength on the growth of RMI are numerically investigated. We obtain the time evolution of turbulent mixing zone width for initial shock with different strength. The results show that the turbulent mixing zone width grows in a different manner at different stage but strictly in a similar way for the initial shock with different strength. Also, the initial shock strength has a significant effect on the growth rate of turbulent mixing zone width, especially before reshock, but can not change the growth laws in the whole process.

Large-Eddy Simulation of the Three-Dimensional Experiment on Richtmyer-Meshkov Instability Induced Turbulence

A program MVFT3D of large-eddy simulation is developed and performed to solve the multi compressible Navier- Stokes equations. The SGS dissipation and molecular viscosity dissipation have been analyzed, and the former is much larger than the later. Our test shows that the SGS dissipation of Vreman model is smaller than the Smagorinsky model. We mainly simulate the experiment of fluid instability of shock-accelerated interface by Poggi in this paper. The decay of the turbulent kinetic energy before the first reflected shock wave–mixing zone interaction and its strong enhancement by re-shocks are presented in our numerical simulations. The computational mixing zone width under double re-shock agreement well with the experiment, and the decaying law of the turbulent kinetic energy is consistent with Mohamed and Larue’s investigation. Also, by using MVFT3D we give some simulation results of the inverse Chevron model from AWE. The numerical simulations presented in this paper allow us to characterize and better understand the Richtmyer-Meshkov instability induced turbulence, and the code MVFT3D is validated.

Investigation of coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles

This study investigates numerically the coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles.Five scenarios are considered,each with varying initial separations S/L(where L demotes the side length of the square)ranging from 0.125 to 1.0.Squares are filled with SF6gas,and are enclosed by N2gas.The simulations of shock-induced multispecies flow are performed by solving the two-dimensional compressible Euler equations with a higher-order explicit modal discontinuous Galerkin solver.The simulations demonstrate that the flow morphology resulting from the coupling effect is highly dependent on the separation between two squares.When the separation is large,the squares experience a weaker coupling effect and evolve independently.While,as the separation reduces,the coupling effect manifests earlier in the interaction and becomes more substantial.As a result,this phenomenon greatly intensifies the motion of inner upstream/downstream vortex rings towards the symmetry axis,leading to the emergence of multiple jets such as the twisted downward,upward,and coupled jets.A thorough exploration of the coupling effect of double squares is conducted by analyzing the vorticity production.Notably,a significant quantity of vorticity is produced along the squares interface for smaller separation.Further,these coupling effects result in various interface features(upstream/downstream movement,and height/width evolution),and temporal variations of various spatially integrated fields.Finally,the analysis of the flow structure also considers the interaction between two more flow parameters,the Mach and Atwood numbers,in order to evaluate the coupling effects.

Molecular dynamics simulation of cylindrical Richtmyer-Meshkov instability

The microscopic-scale Richtmyer-Meshkov(RM) instability of a single-mode Cu-He interface subjected to a cylindrically converging shock is studied through the classical molecular dynamics simulation. An unperturbed interface is first considered to examine the flow features in the convergent geometry, and notable distortions at the circular inhomogeneity are observed due to the atomic fluctuation. Detailed processes of the shock propagation and interface deformation for the single-mode interface impacted by a converging shock are clearly captured. Different from the macroscopic-scale situation, the intense molecular thermal motions in the present microscale flow introduce massive small wavelength perturbations at the single-mode interface, which later significantly impede the formation of the roll-up structure. Influences of the initial conditions including the initial amplitude,wave number and density ratio on the instability growth are carefully analyzed. It is found that the late-stage instability development for interfaces with a large perturbation does not depend on its initial amplitude any more. Surprisingly, as the wave number increases from 8 to 12, the growth rate after the reshock drops gradually. The distinct behaviors induced by the amplitude and wave number increments indicate that the present microscopic RM instability cannot be simply characterized by the amplitude over wavelength ratio(η). The pressure history at the convergence center shows that the first pressure peak caused by the shock focusing is insensitive to η, while the second one depends heavily on it.

Mode coupling in converging Richtmyer-Meshkov instability of dual-mode interface

The converging Richtmyer-Meshkov(RM)instability on single-and dual-mode N2/SF6 interfaces is studied by an upwind conservation element and solution element solver.An unperturbed case is first considered,and it is found that the shocked interface undergoes a long-term deceleration after a period of uniform motion.The evolution of single-mode interface at the early stage exhibits an evident nonlinearity,which can be reasonably predicted by the nonlinear model of Wang et al.(Phys Plasmas 22:082702,2015).During the deceleration stage,the perturbation amplitude drops quickly and even becomes a negative(phase inversion)before the reshock due to the Rayleigh-Taylor(RT)stabilization.After the reshock,the interface experiences a phase inversion again or does not,depending on the reshock time.The growth of the second-order harmonic in the deceleration stage clearly reveals the competition between the RT effect and the nonlinearity.For dual-mode interfaces,the growth of the first mode(wavenumber k1)relies heavily on the second mode(wavenumber k2)due to the mode coupling effect.Specifically,for cases where k2 is an even or odd multiple of k1,the growth of the first mode is inhibited or promoted depending on its initial amplitude sign and the phase difference between two basic waves,while for cases where k2 is a non-integer multiple of k1,the second mode has negligible influence on the first mode.Through a systematic study,signs of perturbation amplitudes of the generated k2−k1 and k2+k1 waves are obtained for all possible dual-mode configurations,which are reasonably predicted by a modified Haan model(Phys Fluids B 3:2349-2355,1991).

Effect of Atwood number on convergent Richtmyer-Meshkov instability

Developments of two-dimensional single-mode light/heavy interfaces driven by convergent shock waves are numerically investigated,focusing on the effect of the Atwood number on the Rayleigh-Taylor stabilization,the compressibility and the nonlinearity.Five different test gases,including C〇2,Kr,R22,R12 and SF6,are considered with air as the ambient gas.It is clarified for the first time that the unperturbed interface begins to decelerate when the shock focuses at the convergence center,and the acceleration during the deceleration phase is proportional to the Atwood number.During the first reshock,the interface moves outwards with a deceleration until it starts moving inwards.When the initial interface is weakly disturbed,a more obvious amplitude reduction is observed for the case with a larger Atwood number before the reshock,which means that the Rayleigh-Taylor stabilization is stronger.To assess the effect of the Atwood number on the compressibility and the nonlinearity,three models,including a linear incompressible model,a nonlinear incompressible model and a linear compressible model,are adopted to predict the amplitude growth before the reshock.The results show that the nonlinearity is weak,and is almost not influenced by the Atwood number before the reshock.The compressibility,however,greatly changes the amplitude growth.As the Atwood number increases,the compressibility plays a less significant role in the amplitude growth because a heavier gas is harder to be compressed.Although a gas with a larger specific heat ratio is also difficult to be compressed,the specific heat ratio plays a minor role to the compressibility relative to the Atwood number.During the reshock,the amplitude grows linearly until the nonlinearity in the cases with large Atwood numbers is strong enough to reduce the amplitude growth rate.

Numerical Simulations of the Richtmyer-Meshkov Instability of Solid-Vacuum Interface

The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum is investigated by numerical simulation using a multi-material solid mechanics algorithm based on an Eulerian framework.The research efforts are directed to reveal the influence of the initial perturbation and material strength on the deformation of the perturbed interface impacted by an initial shock.By varying the initial amplitude(kx0)of the perturbed interface and the yield stress(sY),three typical modes of interface deformation have been identified as the broken mode,the stable mode and the oscillating mode.For the broken mode,the interface width(i.e.,the bubble position with respect to that of the spike)increases continuously resulting in a final separation of the spike from the perturbed interface.For the stable mode,the interface width grows to saturation and then maintains a nearly constant value in the long term.For the oscillating mode,the wavy-like interface moving forward obtains an aperiodic oscillation of small amplitude,namely,the interface width varies in time slightly around zero.The intriguing difference of the typical modes is interpreted qualitatively by comparing the early-stage wave motion and the commensurate pressure and effective stress.Further,the subsequent interface deformation is illustrated quantitatively via the time series of the interface positions and velocities of these three typical modes.

Numerical study on Rayleigh-Taylor effect on cylindrically converging Richtmyer-Meshkov instability

Evolution of a two-dimensional air/SF6 single-mode interface is numerically investigated by an upwind CE/SE method under a cylindrically converging circumstance. The Rayleigh-Taylor effect caused by the flow deceleration on the phase inversion(RTPI)is highlighted. The RTPI was firstly observed in our previous experiment, but the related mechanism remains unclear. By isolating the three-dimensional effect, it is found here that the initial amplitude(a0), the azimuthal mode number(k0) and the re-shocking moment are the three major parameters which determine the RTPI occurrence. In the variable space of(k0, a0), a critical a0 for the RTPI occurrence is solved for each k0, and there exists a threshold value of k0 below which the RTPI will not occur no matter what a0 is. There exists a special k0 corresponding to the largest critical a0, and the reduction rule of critical a0 with k0 can be well described by an exponential decay function. The results show that the occurrence of the RTPI requires a small a0 which should be less than a critical value, a large k0 which should exceed a threshold, and a right impinging moment of the re-shock which should be later than the RTPI occurrence. Finally, the effects of the incident shock strength, the density ratio and the initial position of the interface on the threshold value of k0 and on the maximum critical a0 are examined. These new findings would facilitate the understanding of the converging Richtmyer-Meshkov instability and would be helpful for designing an optimal structure of the inertia confinement fusion capsule.

Large-eddy simulations of the Richtmyer-Meshkov instability of rectangular interfaces accelerated by shock waves

A parallel algorithm and code MVFT(multi-viscous-fluid and turbulence) of large-eddy simulation(LES) is developed from our MVPPM(multi-viscous-fluid piecewise parabolic method),and performed to solve the multi compressible Navier-Stokes(N-S) equations.The effect of the unresolved subgrid-scale(SGS) motions on the large scales is represented by different SGS stress models in LES.A Richtmyer-Meshkov instability experiment of the evolution of a rectangular block of SF6,which occupies half of the height of the shock tube test section,following the interaction with a planar shock wave,is numerically and exhaustively simulated by this code.The comparison between experimental and simulated images of the evolving SF6 block shows that they are consistent.The numerical simulations reproduce the complex developing process of SF6 block,which grows overturningly.The geometric quantities that characterize the extents of SF6 block are also compared in detail between numerical simulations and experiment with good agreements between them,a quantitative demonstration of the developing law of SF6 block.There is an evident discrepancy between the three numerical simulations for the maximum position of the right edge of block at the late stage,because the right interface grows complicated and the dissipation is different for different SGS models.The SGS turbulent dissipation,molecular viscosity dissipation and SGS turbulent kinetic energy have been studied and analyzed.They have a similar distribution to the large eddy structures.The SGS turbulent dissipation is much greater than the molecular viscosity dissipation;the SGS turbulent dissipation of Vreman model is smaller than the Smagorinsky model.In general,the simulated results of Vreman SGS model are better compared with the dynamic viscosity and Smagorinsky SGS model.The vorticity and circulation deposition on the block interface have also been investigated.

Numerical simulation of Richtmyer-Meshkov instability

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.

高马赫数激波作用下单模界面的Richtmyer-Meshkov不稳定性数值模拟

为了研究高马赫数激波冲击下的单模界面Richtmyer-Meshkov(RM)不稳定性,特别是高马赫数激波带来的热化学非平衡效应的影响,采用基于有限体积方法的二维高温非平衡流动程序,利用自适应非结构网格模拟了空气中高马赫数激波冲击两侧温度不同的单模界面导致的RM不稳定现象。研究中涵盖了轻/重界面和重/轻界面2种情况,涉及的激波马赫数范围分别为6~9和8~11。对比了冻结流、热非平衡流和热化学非平衡流3种气体模式下的流场演化过程,揭示了扰动增长和增长率的变化规律。通过对比扰动增长的线性理论和非线性理论,分析了初始激波马赫数和初始扰动尺度的变化对RM不稳定性的影响,同时讨论了涡量场分布和环量的演化规律。结果表明,与冻结流相比,热化学非平衡流中透射激波、反射波及界面速度明显不同,扰动振幅增长率峰值降低,界面增长率脉动减弱,界面不稳定性增长速度变慢。通过对比多种理论模型和本文的数值模拟结果,发现Zhang-Sohn模型相对于其他模型更适用于高马赫数激波作用下的单模界面RM不稳定性问题。对涡量场的研究发现,有2个较强的涡量生成区域,一个位于界面上,另一个位于透射激波波后,这同低马赫数下涡量主要在界面上生成的结论显著不同。此外,热化学非平衡流中环量的幅值大小低于冻结流中的结果,这与热化学非平衡流中扰动的增长低于冻结流的结论对应。

Construction and validation of somatic mutation-derived long noncoding RNAs signatures of genomic instability to predict prognosis of hepatocellular carcinoma

BACKGROUND Long non-coding RNAs(LncRNAs)have been found to be a potential prognostic factor for cancers,including hepatocellular carcinoma(HCC).Some LncRNAs have been confirmed as potential indicators to quantify genomic instability(GI).Nevertheless,GI-LncRNAs remain largely unexplored.This study established a GI-derived LncRNA signature(GILncSig)that can predict the prognosis of HCC patients.AIM To establish a GILncSig that can predict the prognosis of HCC patients.METHODS Identification of GI-LncRNAs was conducted by combining LncRNA expression and somatic mutation profiles.The GI-LncRNAs were then analyzed for functional enrichment.The GILncSig was established in the training set by Cox regression analysis,and its predictive ability was verified in the testing set and TCGA set.In addition,we explored the effects of the GILncSig and TP53 on prognosis.RESULTS A total of 88 GI-LncRNAs were found,and functional enrichment analysis showed that their functions were mainly involved in small molecule metabolism and GI.The GILncSig was constructed by 5 LncRNAs(miR210HG,AC016735.1,AC116351.1,AC010643.1,LUCAT1).In the training set,the prognosis of high-risk patients was significantly worse than that of low-risk patients,and similar results were verified in the testing set and TCGA set.Multivariate Cox regression analysis and stratified analysis confirmed that the GILncSig could be used as an independent prognostic factor.Receiver operating characteristic curve analysis of the GILncSig showed that the area under the curve(0.773)was higher than the two LncRNA signatures published recently.Furthermore,the GILncSig may have a better predictive performance than TP53 mutation status alone.CONCLUSION We established a GILncSig that can predict the prognosis of HCC patients,which will help to guide prognostic evaluation and treatment decisions.

Wave nature of Rosensweig instability

The explicit analytical solution of Rosensweig instability spikes'shapes obtained by Navier-Stokes(NS)equation in diverse magnetic field H vertical to the flat free surface of ferrofluids are systematically studied experimentally and theoretically.After carefully analyzing and solving the NS equation in elliptic form,the force balanced surface equations of spikes in Rosensweig instability are expressed as cosine wave in perturbated magnetic field and hyperbolic tangent in large magnetic field,whose results both reveal the wave-like nature of Rosensweig instability.The results of hyperbolic tangent form are perfectly fitted to the experimental results in this paper,which indicates that the analytical solution is basically correct.Using the forementioned theoretical results,the total energy of the spike distribution pattern is calculated.By analyzing the energy components under different magnetic field intensities H,the hexagon-square transition of Rosensweig instability is systematically discussed and explained in an explicit way.

Theoretical analysis of the elastic Kelvin-Helmholtz instability in explosive weldings

By considering the joint effects of the Kelvin-Helmholtz(KH) and Rayleigh-Taylor(RT) instabilities, this paper presents an interpretation of the wavy patterns that occur in explosive welding. It is assumed that the elasticity of the material at the interface effectively determines the wavelength, because explosive welding is basically a solid-state welding process. To this end, an analytical model of elastic hydrodynamic instabilities is proposed, and the most unstable mode is selected in the solid phase. Similar approaches have been widely used to study the interfacial behavior of solid metals in high-energy-density physics. By comparing the experimental and theoretical results, it is concluded that thermal softening,which significantly reduces the shear modulus, is necessary and sufficient for successful welding. The thermal softening is verified by theoretical analysis of the increase in temperature due to the impacting and sliding of the flyer and base plates, and some experimental observations are qualitatively validated.In summary, the combined effect of the KH and RT instabilities in solids determines the wavy morphology, and our theoretical results are in good qualitative agreement with experimental and numerical observations.

Integrated chromosomal instability and tumor microbiome re define d prognosis-related subtypes of pancreatic cancer

Background:Pancreatic cancer is a common malignancy with poor prognosis and limited treatment.Here we aimed to investigate the role of host chromosomal instability(CIN)and tumor microbiome in the prognosis of pancreatic cancer patients.Methods:One hundred formalin-fixed paraffin-embedded(FFPE)pancreatic cancer samples were collected.DNA extracted from FFPE samples were analyzed by low-coverage whole-genome sequencing(WGS)via a customized bioinformatics workflow named ultrasensitive chromosomal aneuploidy detector.Results:Samples were tested according to the procedure of ultrasensitive chromosomal aneuploidy detector(UCAD).We excluded 2 samples with failed quality control,1 patient lost to follow-up and 6 dead in the perioperative period.The final 91 patients were admitted for the following analyses.Thirteen(14.3%)patients with higher CIN score had worse overall survival(OS)than those with lower CIN score.The top 20 microbes in pancreatic cancer samples included 15 species of bacteria and 5 species of viruses.Patients with high human herpesvirus(HHV)-7 and HHV-5 DNA reads exhibited worse OS.Furthermore,we classified 91 patients into 3 subtypes.Patients with higher CIN score(n=13)had the worst prognosis(median OS 6.9 mon);patients with lower CIN score but with HHV-7/5 DNA load(n=24)had worse prognosis(median OS 10.6 mon);while patients with lower CIN score and HHV-7/5 DNA negative(n=54)had the best prognosis(median OS 21.1 mon).Conclusions:High CIN and HHV-7/5 DNA load were associated with worse survival of pancreatic cancer.The novel molecular subtypes of pancreatic cancer based on CIN and microbiome had prognostic value.