Implicit large eddy simulations of anisotropic weakly compressible turbulence with application to core-collapse supernovae
Tóm tắt
In the implicit large eddy simulation (ILES) paradigm, the dissipative nature of high-resolution shock-capturing schemes is exploited to provide an implicit model of turbulence. The ILES approach has been applied to different contexts, with varying degrees of success. It is the de-facto standard in many astrophysical simulations and in particular in studies of core-collapse supernovae (CCSN). Recent 3D simulations suggest that turbulence might play a crucial role in core-collapse supernova explosions, however the fidelity with which turbulence is simulated in these studies is unclear. Especially considering that the accuracy of ILES for the regime of interest in CCSN, weakly compressible and strongly anisotropic, has not been systematically assessed before. Anisotropy, in particular, could impact the dissipative properties of the flow and enhance the turbulent pressure in the radial direction, favouring the explosion. In this paper we assess the accuracy of ILES using numerical methods most commonly employed in computational astrophysics by means of a number of local simulations of driven, weakly compressible, anisotropic turbulence. Our simulations employ several different methods and span a wide range of resolutions. We report a detailed analysis of the way in which the turbulent cascade is influenced by the numerics. Our results suggest that anisotropy and compressibility in CCSN turbulence have little effect on the turbulent kinetic energy spectrum and a Kolmogorov
$k^{-5/3}$
scaling is obtained in the inertial range. We find that, on the one hand, the kinetic energy dissipation rate at large scales is correctly captured even at low resolutions, suggesting that very high “effective Reynolds number” can be achieved at the largest scales of the simulation. On the other hand, the dynamics at intermediate scales appears to be completely dominated by the so-called bottleneck effect, i.e., the pile up of kinetic energy close to the dissipation range due to the partial suppression of the energy cascade by numerical viscosity. An inertial range is not recovered until the point where high resolution ∼5123, which would be difficult to realize in global simulations, is reached. We discuss the consequences for CCSN simulations.
Tài liệu tham khảo
Abdikamalov, E, Ott, CD, Radice, D, Roberts, LF, Haas, R, Reisswig, C, Moesta, P, Klion, H, Schnetter, E: Neutrino-driven turbulent convection and standing accretion shock instability in three-dimensional core-collapse supernovae Astrophys. J. 808, 70 (2015). doi:10.1088/0004-637X/808/1/70
Arnett, D, Meakin, C, Young, PA: Turbulent convection in stellar interiors. II. The velocity field. Astrophys. J. 690, 1715-1729 (2009). doi:10.1088/0004-637X/690/2/1715
Aspden, A, Nikiforakis, N, Dalziel, S, Bell, J: Analysis of implicit LES methods. Commun. Appl. Math. Comput. Sci. 3(1), 103-126 (2009). doi:10.2140/camcos.2008.3.103
Benzi, R, Biferale, L, Fisher, RT, Kadanoff, LP, Lamb, DQ, Toschi, F: Intermittency and universality in fully developed inviscid and weakly compressible turbulent flows. Phys. Rev. Lett. 100(23), 234503 (2008). doi:10.1103/PhysRevLett.100.234503
Bethe, HA: Supernova mechanisms. Rev. Mod. Phys. 62, 801-867 (1990)
Biferale, L, Procaccia, I: Anisotropy in turbulent flows and in turbulent transport. Phys. Rep. 414(2-3), 43-164 (2005). doi:10.1016/j.physrep.2005.04.001
Biferale, L, Daumont, I, Lanotte, A, Toschi, F: Anomalous and dimensional scaling in anisotropic turbulence. Phys. Rev. E 66(5), 056306 (2002). doi:10.1103/PhysRevE.66.056306
Biferale, L, Calzavarini, E, Toschi, F, Tripiccione, R: Universality of anisotropic fluctuations from numerical simulations of turbulent flows. Europhys. Lett. 64(4), 461-467 (2003). doi:10.1209/epl/i2003-00233-9
Blondin, JM, Mezzacappa, A, DeMarino, C: Stability of standing accretion shocks, with an eye toward core-collapse supernovae. Astrophys. J. 584, 971-980 (2003). doi:10.1086/345812
Borges, R, Carmona, M, Costa, B, Don, WS: An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws. J. Comput. Phys. 227, 3191-3211 (2008). doi:10.1016/j.jcp.2007.11.038
Burrows, A: Colloquium: perspectives on core-collapse supernova theory. Rev. Mod. Phys. 85, 245 (2013). doi:10.1103/RevModPhys.85.245
Burrows, A, Hayes, J, Fryxell, BA: On the nature of core-collapse supernova explosions. Astrophys. J. 450, 830-850 (1995)
Calzavarini, E, Toschi, F, Tripiccione, R: Evidences of bolgiano-obhukhov scaling in three-dimensional Rayleigh-Bénard convection. Phys. Rev. E 66, 016304 (2002). doi:10.1103/PhysRevE.66.016304
Casciola, CM, Gualtieri, P, Jacob, B, Piva, R: The residual anisotropy at small scales in high shear turbulence. Phys. Fluids 19(10), 101704 (2007). doi:10.1063/1.2800043
Clausen, D, Piro, AL, Ott, CD: The black hole formation probability. Astrophys. J. 799, 190 (2015). doi:10.1088/0004-637X/799/2/190
Colella, P: Multidimensional upwind methods for hyperbolic conservation laws. J. Comput. Phys. 87, 171-200 (1990). doi:10.1016/0021-9991(90)90233-Q
Colella, P, Woodward, PR: The Piecewise Parabolic Method (PPM) for gas-dynamical simulations. J. Comp. Physiol. 54, 174-201 (1984)
Couch, SM, O’Connor, EP: High-resolution three-dimensional simulations of core-collapse supernovae in multiple progenitors. Astrophys. J. 785, 123 (2014). doi:10.1088/0004-637X/785/2/123
Couch, SM, Ott, CD: Revival of the stalled core-collapse supernova shock triggered by precollapse asphericity in the progenitor star. Astrophys. J. Lett. 778, L7 (2013). doi:10.1088/2041-8205/778/1/L7
Couch, SM, Ott, CD: The role of turbulence in neutrino-driven core-collapse supernova explosions. Astrophys. J. 799, 5 (2015). doi:10.1088/0004-637X/799/1/5
Dolence, JC, Burrows, A, Murphy, JW, Nordhaus, J: Dimensional dependence of the hydrodynamics of core-collapse supernovae. Astrophys. J. 765, 110 (2013). doi:10.1088/0004-637X/765/2/110
Donzis, DA, Yeung, PK, Sreenivasan, KR: Dissipation and enstrophy in isotropic turbulence: resolution effects and scaling in direct numerical simulations. Phys. Fluids 20(4), 045108 (2008). doi:10.1063/1.2907227
Dubey, A, Antypas, K, Ganapathy, MK, Reid, LB, Riley, K, Sheeler, D, Siegel, A, Weide, K: Extensible component-based architecture for flash, a massively parallel, multiphysics simulation code. Parallel Comput. 35, 512-522 (2009). doi:10.1016/j.parco.2009.08.001
Einfeldt, B: On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25, 294-318 (1988). doi:10.1137/0725021
Eswaran, V, Pope, S: An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16(3), 257-278 (1988)
Falkovich, G: Bottleneck phenomenon in developed turbulence. Phys. Fluids 6(4), 1411-1414 (1994)
Federrath, C: On the universality of supersonic turbulence. Mon. Not. R. Astron. Soc. Lett. 436(2), 1245-1257 (2013). doi:10.1093/mnras/stt1644
Federrath, C, Roman-Duval, J, Klessen, RS, Schmidt, W, Mac Low, M-M: Comparing the statistics of interstellar turbulence in simulations and observations. Astron. Astrophys. 512, A81 (2010). doi:10.1051/0004-6361/200912437
Foglizzo, T, Scheck, L, Janka, H-T: Neutrino-driven convection versus advection in core-collapse supernovae. Astrophys. J. 652, 1436-1450 (2006). doi:10.1086/508443
Foglizzo, T, Galletti, P, Scheck, L, Janka, H-T: Instability of a stalled accretion shock: evidence for the advective-acoustic cycle. Astrophys. J. 654, 1006-1021 (2007). doi:10.1086/509612
Foglizzo, T, Kazeroni, R, Guilet, J, Masset, F, González, M, et al.: The explosion mechanism of core-collapse supernovae: progress in supernova theory and experiments. Publ. Astron. Soc. Aust. 32, e009 (2015). doi:10.1017/pasa.2015.9
Frisch, U: Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge (1996)
Frisch, U, Kurien, S, Pandit, R, Pauls, W, Ray, S, Wirth, A, Zhu, J-Z: Hyperviscosity, Galerkin truncation, and bottlenecks in turbulence. Phys. Rev. Lett. 101(14), 144501 (2008). doi:10.1103/PhysRevLett.101.144501
Fryxell, B, Olson, K, Ricker, P, Timmes, FX, Zingale, M, Lamb, DQ, MacNeice, P, Rosner, R, Truran, JW, Tufo, H: FLASH: an adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. Astrophys. J. Suppl. Ser. 131, 273-334 (2000). doi:10.1086/317361
Fureby, C, Grinstein, FF: Monotonically integrated large eddy simulation of free shear flows. AIAA J. 37(5), 544-556 (1999). doi:10.2514/2.772
Garnier, E, Mossi, M, Sagaut, P: On the use of shock-capturing schemes for large-eddy simulation. J. Comput. Phys. 311, 273-311 (1999)
Garnier, E, Adams, N, Sagaut, P: Large Eddy Simulation for Compressible Flows. Springer, Berlin (2000)
Gotoh, T, Fukayama, D, Nakano, T: Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation. Phys. Fluids 14(3), 1065-1081 (2002)
Grinstein, FF, Margolin, LG, Rider, WJ: Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics Cambridge University Press, Cambridge (2011)
Handy, T, Plewa, T, Odrzywołek, A: Toward connecting core-collapse supernova theory with observations. I. Shock revival in a 15 M⊙ blue supergiant progenitor with SN 1987A energetics. Astrophys. J. 783, 125 (2014). doi:10.1088/0004-637X/783/2/125
Herant, M: The convective engine paradigm for the supernova explosion mechanism and its consequences. Phys. Rep. 256, 117-133 (1995). doi:10.1016/0370-1573(94)00105-C
Hickel, S, Adams, NA, Domaradzki, JA: An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213(1), 413-436 (2006). doi:10.1016/j.jcp.2005.08.017
Ishihara, T, Kaneda, Y, Yokokawa, M, Itakura, K, Uno, A: Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592, 335-366 (2007). doi:10.1017/S0022112007008531
Janka, H-T: Explosion mechanisms of core-collapse supernovae. Annu. Rev. Nucl. Part. Sci. 62, 407 (2012). doi:10.1146/annurev-nucl-102711-094901
Janka, H-T, Müller, E: Neutrino heating, convection, and the mechanism of Type-II supernova explosions. Astron. Astrophys. 306, 167-198 (1996)
Janka, H-T, Hanke, F, Hüdepohl, L, Marek, A, Müller, B, Obergaulinger, M: Core-collapse supernovae: reflections and directions. Prog. Theor. Exp. Phys. 2012(1), 010000 (2012). doi:10.1093/ptep/pts067
Johnsen, E, Larsson, J, Bhagatwala, AV, Cabot, WH, Moin, P, Olson, BJ, Rawat, PS, Shankar, SK, Sjögreen, B, Yee, HC, Zhong, X, Lele, SK: Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves. J. Comput. Phys. 229(4), 1213-1237 (2010). doi:10.1016/j.jcp.2009.10.028
Kaneda, Y, Ishihara, T, Yokokawa, M, Itakura, K, Uno, A: Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids 15, L21 (2003). doi:10.1063/1.1539855
Kaneda, Y, Yoshino, J, Ishihara, T: Examination of Kolmogorov’s 4/5 law by high-resolution direct numerical simulation data of turbulence. J. Phys. Soc. Jpn. 77(6), 064401 (2008). doi:10.1143/JPSJ.77.064401
Lee, D: A solution accurate, efficient and stable unsplit staggered mesh scheme for three dimensional magnetohydrodynamics. J. Comp. Physiol. 243, 269-292 (2013). doi:10.1016/j.jcp.2013.02.049
Lee, D, Deane, AE: An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics. J. Comput. Phys. 228, 952-975 (2009). doi:10.1016/j.jcp.2008.08.026
Lee, D, Tzeferacos, P, Couch, SM, Bachan, J, Daley, C, Fatenejad, M, Flocke, N, Lamb, D, Weide, K, Dubey, A: FLASH: a multi-physics code for adaptive mesh computational fluid dynamics in astrophysics. Astrophys. J. Suppl. Ser. (2014, to be submitted)
Lohse, D, Xia, K-Q: Small-scale properties of turbulent Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 42(1), 335-364 (2010). doi:10.1146/annurev.fluid.010908.165152
Martín, MP, Taylor, EM, Wu, M, Weirs, VG: A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence. J. Comput. Phys. 220(1), 270-289 (2006). doi:10.1016/j.jcp.2006.05.009
Müller, B, Janka, H-T: Non-radial instabilities and progenitor asphericities in core-collapse supernovae. Mon. Not. R. Astron. Soc. Lett. 448, 2141-2174 (2015). doi:10.1093/mnras/stv101
Murphy, JW, Meakin, C: A global turbulence model for neutrino-driven convection in core-collapse supernovae. Astrophys. J. 742, 74 (2011). doi:10.1088/0004-637X/742/2/74
Murphy, JW, Dolence, JC, Burrows, A: The dominance of neutrino-driven convection in core-collapse supernovae. Astrophys. J. 771, 52 (2013). doi:10.1088/0004-637X/771/1/52
O’Connor, E, Ott, CD: Black hole formation in failing core-collapse supernovae. Astrophys. J. 730, 70 (2011). doi:10.1088/0004-637X/730/2/70
Ott, CD, Abdikamalov, E, Mösta, P, Haas, R, Drasco, S, O’Connor, EP, Reisswig, C, Meakin, CA, Schnetter, E: General-relativistic simulations of three-dimensional core-collapse supernovae. Astrophys. J. 768, 115 (2013). doi:10.1088/0004-637X/768/2/115
Pejcha, O, Thompson, TA: The physics of the neutrino mechanism of core-collapse supernovae. Astrophys. J. 746, 106 (2012). doi:10.1088/0004-637X/746/1/106
Porter, D, Pouquet, A, Woodward, P: Measures of intermittency in driven supersonic flows. Phys. Rev. E 66(2), 1-12 (2002). doi:10.1103/PhysRevE.66.026301
Porter, DH, Woodward, PR: High-resolution simulations of compressible convection using the piecewise-parabolic method. Astrophys. J. Suppl. Ser. 93, 309-349 (1994). doi:10.1086/192057
Schmidt, W, Hillebrandt, W, Niemeyer, JC: Numerical dissipation and the bottleneck effect in simulations of compressible isotropic turbulence. Comput. Fluids 35(4), 353-371 (2006)
She, Z, Jackson, E: On the universal form of energy spectra in fully developed turbulence. Phys. Fluids 5(7), 1526-1528 (1993)
Sytine, IV, Porter, DH, Woodward, PR, Hodson, SW, Winkler, K-H: Convergence tests for the piecewise parabolic method and Navier-Stokes solutions for homogeneous compressible turbulence. J. Comp. Physiol. 158, 225-238 (2000). doi:10.1006/jcph.1999.6416
Thornber, B, Mosedale, A, Drikakis, D: On the implicit large eddy simulations of homogeneous decaying turbulence. J. Comput. Phys. 226(2), 1902-1929 (2007). doi:10.1016/j.jcp.2007.06.030
Thornber, B, Mosedale, A, Drikakis, D, Youngs, D, Williams, RJR: An improved reconstruction method for compressible flows with low Mach number features. J. Comput. Phys. 227(10), 4873-4894 (2008). doi:10.1016/j.jcp.2008.01.036
Toro, EF: Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin (1999)
Toro, EF, Spruce, M, Speares, W: Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4, 25-34 (1994). doi:10.1007/BF01414629
Uhlenbeck, G, Ornstein, L: On the theory of the Brownian motion. Phys. Rev. 36, 823-841 (1930). doi:10.1103/PhysRev.36.823
Verhoeven, J, Wiesehöfer, T, Stellmach, S: Anelastic versus fully compressible turbulent Rayleigh-Bénard convection. Astrophys. J. 805, 62 (2015). doi:10.1088/0004-637X/805/1/62
Verma, MK, Donzis, D: Energy transfer and bottleneck effect in turbulence. J. Phys. A 40(16), 4401-4412 (2007)
Vincent, A, Meneguzzi, M: The satial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1-20 (1991). doi:10.1017/S0022112091001957
Woosley, SE, Janka, H-T: The physics of core-collapse supernovae. Nat. Phys. 1, 147-154 (2005). doi:10.1038/nphys172
Yakhot, V, Zakharov, V: Hidden conservation laws in hydrodynamics; energy and dissipation rate fluctuation spectra in strong turbulence. Physica D 64(4), 379-394 (1993)
Zhou, Y, Grinstein, FF, Wachtor, AJ, Haines, BM: Estimating the effective Reynolds number in implicit large-eddy simulation. Phys. Rev. E 89(1), 013303 (2014). doi:10.1103/PhysRevE.89.013303