Data-driven prediction of growth rate for a shocked heavy gas layer

Numerical investigation on the evolution of a heavy gas layer is performed over a wide range of parameters. Neural networks and curve fitting techniques are employed to predict the growth rate of downstream interface based on 2688 simulated cases. Significant amounts of observable data are generated by considering four primary variables: shock wave intensity, density difference between the inside and outside of the gas layer, gas layer thickness, and initial interface shape. The neural network model maps the growth rate directly to the initial parameters, while the curve fitting approach provides an explicit formula. The neural network model has high accuracy and a certain extrapolation capability. The explicit formula provides a more intuitive understanding compared to the neural network model and has a stronger extrapolation. Furthermore, to thoroughly examine the evolution of the gas layer, the numerical investigation is conducted on the shocked single interface. It is discovered that there is a range of parameters in which the growth rate of gas layer is lower than that of the single interface. Meanwhile, a modified model that includes an attenuation factor is proposed to replace the impulsive model of the single interface. In summary, these methods can significantly reduce simulation time by quickly identifying desirable cases.

[1]  Xisheng Luo,et al.  Hydrodynamic instabilities of two successive slow/fast interfaces induced by a weak shock , 2023, Journal of Fluid Mechanics.

[2]  Xisheng Luo,et al.  Interaction of a planar shock wave with two heavy/light interfaces , 2022, Acta Mechanica Sinica.

[3]  Xisheng Luo,et al.  Instability of a heavy gas layer induced by a cylindrical convergent shock , 2022, Physics of Fluids.

[4]  Xisheng Luo,et al.  On shock-induced light-fluid-layer evolution , 2021, Journal of Fluid Mechanics.

[5]  Xisheng Luo,et al.  On shock-induced heavy-fluid-layer evolution , 2021, Journal of Fluid Mechanics.

[6]  K. Lan,et al.  Novel Target Designs to Mitigate Hydrodynamic Instabilities Growth in Inertial Confinement Fusion. , 2021, Physical review letters.

[7]  T. Si,et al.  Evolution of shock-accelerated heavy gas layer , 2020, Journal of Fluid Mechanics.

[8]  Baoyue Chai,et al.  Fast estimation of ion temperature from EAST charge exchange recombination spectroscopy using neural network , 2019, Plasma Science and Technology.

[9]  Gilbert W. Collins,et al.  Tripled yield in direct-drive laser fusion through statistical modelling , 2019, Nature.

[10]  Man Long Wong,et al.  High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with reshock , 2018, Physical Review Fluids.

[11]  Prakash Vedula,et al.  Data-driven deconvolution for large eddy simulations of Kraichnan turbulence , 2018, Physics of Fluids.

[12]  R. P. Drake,et al.  How high energy fluxes may affect Rayleigh–Taylor instability growth in young supernova remnants , 2018, Nature Communications.

[13]  T. Si,et al.  On the interaction of a planar shock with a three-dimensional light gas cylinder , 2017, Journal of Fluid Mechanics.

[14]  Sanjiva K. Lele,et al.  High-order localized dissipation weighted compact nonlinear scheme for shock- and interface-capturing in compressible flows , 2017, J. Comput. Phys..

[15]  Demis Hassabis,et al.  Mastering the game of Go with deep neural networks and tree search , 2016, Nature.

[16]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[17]  A. Ng,et al.  Deep Speech 2 : End-to-End Speech Recognition in English and Mandarin , 2015, ICML.

[18]  E. Johnsen,et al.  Numerical simulations of a shock interacting with successive interfaces using the Discontinuous Galerkin method: the multilayered Richtmyer–Meshkov and Rayleigh–Taylor instabilities , 2015 .

[19]  John Lindl,et al.  Review of the National Ignition Campaign 2009-2012 , 2014 .

[20]  Jay D. Salmonson,et al.  Optimized beryllium target design for indirectly driven inertial confinement fusion experiments on the National Ignition Facility , 2014 .

[21]  Taku Nonomura,et al.  Robust explicit formulation of weighted compact nonlinear scheme , 2013 .

[22]  R. Bonazza,et al.  Shock-Bubble Interactions , 2011 .

[23]  F. Grinstein,et al.  Numerical simulation of Richtmyer–Meshkov instabilities in shocked gas curtains , 2011 .

[24]  L. J. Atherton,et al.  Point design targets, specifications, and requirements for the 2010 ignition campaign on the National Ignition Facility , 2010 .

[25]  G. Jourdan,et al.  Investigation of the Richtmyer-Meshkov instability with stereolithographed interfaces. , 2008, Physical review letters.

[26]  Mark H. Anderson,et al.  A computational parameter study for the three-dimensional shock–bubble interaction , 2007, Journal of Fluid Mechanics.

[27]  K. Mikaelian,et al.  Rayleigh-Taylor and Richtmyer-Meshkov Instabilities and Mixing in Stratified Cylindrical Shells , 2005 .

[28]  Peter A. Amendt,et al.  Multimode short-wavelength perturbation growth studies for the National Ignition Facility double-shell ignition target designs , 2004 .

[29]  Guang-Bin Huang,et al.  Learning capability and storage capacity of two-hidden-layer feedforward networks , 2003, IEEE Trans. Neural Networks.

[30]  J. Jacobs,et al.  PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF6 interface , 2002, Journal of Fluid Mechanics.

[31]  Rémi Abgrall,et al.  Computations of compressible multifluids , 2001 .

[32]  R. P. Drake,et al.  An Evaluation of the Richtmyer-Meshkov Instability in Supernova Remnant Formation , 1998 .

[33]  K. Nishihara,et al.  Asymptotic growth in the linear Richtmyer–Meshkov instability , 1997 .

[34]  Robert F. Benjamin,et al.  Simulation of shock-generated instabilities , 1996 .

[35]  K. Mikaelian.  NUMERICAL SIMULATIONS OF RICHTMYER-MESHKOV INSTABILITIES IN FINITE-THICKNESS FLUID LAYERS , 1996 .

[36]  Robert F. Benjamin,et al.  Nonlinear growth of the shock-accelerated instability of a thin fluid layer , 1995, Journal of Fluid Mechanics.

[37]  K. Mikaelian.  Rayleigh--Taylor and Richtmyer--Meshkov instabilities in finite-thickness fluid layers , 1995 .

[38]  Mikaelian.  Rayleigh-Taylor and Richtmyer-Meshkov instabilities in multilayer fluids with surface tension. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[39]  R. D. Richtmyer.  Taylor instability in shock acceleration of compressible fluids , 1960 .

[40]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[41]  Luo Xishen.  Experimental study on the interfacial instability induced by shock waves , 2014 .

[42]  M. Aghbashlo,et al.  Original paper: Optimization of an artificial neural network topology using coupled response surface methodology and genetic algorithm for fluidized bed drying , 2011 .

[43]  Sun Quan,et al.  The Theory of Canonical Correlation Analysis and Its Application to Feature Fusion , 2005 .

[44]  M. Brouillette.  THE RICHTMYER-MESHKOV INSTABILITY , 2002 .

[45]  Norman J. Zabusky,et al.  VORTEX PARADIGM FOR ACCELERATED INHOMOGENEOUS FLOWS: Visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov Environments , 1999 .

[46]  K. Burrell,et al.  A neural network for the analysis of DIII-D charge exchange recombination data , 1994 .

[47]  K. Brecher.  Will Supernova 1987A , 1987 .

[48]  Mikaelian.  Richtmyer-Meshkov instabilities in stratified fluids. , 1985, Physical review. A, General physics.

[49]  E. Meshkov.  Instability of the interface of two gases accelerated by a shock wave , 1969 .