Coherent structures and wavepackets in subsonic transitional turbulent jets 
期刊名称Acta Mechanica Sinica
作者Yu Lv; Matthias Ihme
摘要This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications,in which DG methods have been successfully employed,DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness,combustion,heat release,compressibility effects,shocks,and variations in thermodynamic properties. To address these challenges,algorithms are developed, including an entropy-bounded DG method,an entropyresidual shock indicator,and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction,turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows.
关键词Discontinuous Galerkin method; High-order schemes; Reacting flows; Multicomponent flows
参考文献1. Zeldovich, Y.A., Raizer, Y.P.:Physics of Shock Waves and HighTemperature Hydrodynamic Phenomena. Dover, Mineola (2002)
2. Liñán, A., Williams, F.A.:Fundamental Aspects of Combustion. Oxford University Press, Oxford (1993)
3. Hinze, J.O.:Turbulence, 2nd edn. McGraw-Hill, New York (1975)
4. Lu, T., Law, C.K.:Toward accommodating realistic fuel chemistry in large-scale computations. Prog. Energy Combust. Sci. 35, 192- 215 (2009)
5. Ma, P.C., Lv, Y., Ihme, M.:An entropy-stable hybrid scheme for simulations of transcritical real-fluid flows. J. Comput. Phys. 340, 330-357 (2017)
6. Abgrall, R., Karni, S.:Computations of compressible multifluids. J. Comput. Phys. 169, 594-623 (2001)
7. Lee, J.H.S.:The Detonation Phenomenon. Cambridge University Press, Cambridge (2008)
8. Shepherd, J.E.:Detonation in gases. Proc. Combust. Inst. 32, 83-98 (2009)  
9. Pintgen, F., Eckett, C.A., Austin, J.M., et al.:Direct observations of reaction zone structure in propagating detonations. Combust. Flame 133, 211-229 (2003)  
10. Maley, L., Bhattacharjee, R., Lau-Chapdelaine, S.M., et al.:Influence of hydrodynamic instabilities on the propagation mechanism of fast flames. Proc. Combust. Inst. 35, 2117-2126 (2015)  
11. Gamezo, V.N., Desbordes, D., Oran, E.S.:Formation and evolution of two-dimensional cellular detonations. Combust. Flame 116, 154-165 (1999)  
12. Hu, F.Q., Hussaini, M.Y., Rasetarinera, P.:An analysis of the discontinuous Galerkin method for wave propagation problems. J. Comput. Phys. 151, 921-946 (1999)  
13. Lv, Y., Ihme, M.:Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion. J. Comput. Phys. 270, 105-137 (2014)  
14. Klöckner, A., Warburton, T., Bridge, J., et al.:Nodal discontinuous Galerkin methods on graphics processors. J. Comput. Phys. 228, 7863-7882 (2009)  
15. Reed, W.H., Hill, T.R.:Triangular mesh methods for the neutron transport equation. Los Alamos Report LA-UR-73-479, America (1973)
16. Johnson, C., Pitkäranta, J.:An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation. Math. Comput. 46, 1-26 (1986)  
17. Peterson, T.E.:A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. SIAM J. Numer. Anal. 28, 133-140 (1991)  
18. Cockburn, B., Shu, C.-W.:TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws Ⅱ:general framework. J. Sci. Comp. 52, 411-435 (1989)
19. Cockburn, B., Shu, C.-W.:TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws Ⅲ:one dimensional systems. J. Comput. Phys. 84, 90-113 (1989)  
20. Cockburn, B., Shu, C.-W.:The Runge-Kutta discontinuous Galerkin method for conservation laws V:multidimensional systems. J. Comput. Phys. 141, 199-224 (1998)  
21. Cockburn, B., Shu, C.-W.:Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16, 173-261 (2001)  
22. Arnold, D.N., Brezzi, F., Cockburn, B., et al.:Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749-1779 (2002)  
23. Cockburn, B., Shu, C.-W.:The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35, 2440-2463 (1998)  
24. Bassi, F., Rebay, S.:A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131, 267-279 (1997)  
25. Bassi, F., Rebay, S.:GMRES discontinuous Galerkin solution of the compressible Navier-Stokes equations. In:Cockburn, B., Shu, C.- W. (eds.) Discontinuous Galerkin Methods:Theory, Computation and Applications, Springer, Berlin, 197-208 (2000)
26. Peraire, J., Persson, P.-O.:The compact discontinuous Galerkin (CDG) method for elliptic problems. SIAM J. Sci. Comput. 30, 1806-1824 (2008)  
27. Hartmann, R., Houston, P.:An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier- Stokes equations. J. Comput. Phys. 227, 9670-9685 (2008)  
28. Gassner, G., Lörcher, F., Munz, C.-D.:A discontinuous Galerkin scheme based on a space-time expansion Ⅱ. Viscous flow equations in multi dimensions. J. Sci. Comput. 34, 260-286 (2008)
29. Toro, E.F.:Riemann Solvers and Numerical Methods for Fluid Dynamics:A Practical Introduction. Springer, Berlin (2013)
30. Roe, P.L.:Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43, 357-372 (1981)  
31. Toro, E.F., Spruce, M., Speares, W.:Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4, 25-34 (1994)  
32. Rusanov, V.V.:Calculation of intersection of non-steady shock waves with obstacles. J. Comput. Math. Phys. USSR 1, 267-279 (1961)
33. Ma, P.C., Lv, Y., Ihme, M.:Discontinuous Galerkin scheme for turbulent flow simulations. Annual Research Briefs, Center for Turbulence Research, 225-236 (2015)
34. Wang, Z.J., Fidkowski, K., Abgrall, R., et al.:High-order CFD methods:current status and perspective. Int. J. Numer. Methods Fluids 72, 811-845 (2013)  
35. Zhang, X., Shu, C.-W.:On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. J. Comput. Phys. 229, 8918-8934 (2010)  
36. Wang, C., Zhang, X., Shu, C.-W., et al.:Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. J. Comput. Phys. 231, 653-665 (2012)  
37. Zhang, X., Shu, C.-W.:A minimum entropy principle of high order schemes for gas dynamics equations. Numer. Math. 121, 545-563 (2012)  
38. Lv, Y., Ihme, M.:Entropy-bounded discontinuous Galerkin scheme for Euler equations. J. Comput. Phys. 295, 715-739 (2015)  
39. Persson, P.-O., Peraire, J.:Sub-cell shock capturing for discontinuous Galerkin methods. AIAA 2006-112 (2006)
40. Krivodonova, L., Xin, J., Remacle, J.-F., et al.:Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws. Appl. Numer. Math. 48, 323-338 (2004)  
41. Vuik, M.J., Ryan, J.K.:Multiwavelet troubled-cell indicator for discontinuity detection of discontinuous Galerkin schemes. J. Comput. Phys. 270, 138-160 (2014)  
42. Lv, Y., See, Y.C., Ihme, M.:An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methods. J. Comput. Phys. 322, 448-472 (2016)  
43. Tadmor, E.:A minimum entropy principle in the gas dynamics equations. Appl. Numer. Math. 2, 211-219 (1986)  
44. Guermond, J.-L., Pasquetti, R.:Entropy-based nonlinear viscosity for Fourier approximations of conservation laws. C. R. Acad. Sci. Paris, Ser. I 346, 801-806 (2008)
45. Lax, P.D.:Shock waves and entropy. In:Zarantonello E.H. (ed.) Contributions to Nonlinear Functional Analysis. Academic Press, New York and London, 603-634 (1971)
46. Krivodonova, L.:Limiters for high-order discontinuous Galerkin methods. J. Comput. Phys. 226, 879-896 (2007)  
47. Luo, H., Baum, J.D., Löhner, R.:A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids. J. Comput. Phys. 225, 686-713 (2007)  
48. Zhu, J., Zhong, X., Shu, C.-W., et al.:Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes. J. Comput. Phys. 248, 200-220 (2013)  
49. Hartmann, R.:Adaptive discontinuous Galerkin methods with shock-capturing for the compressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 51, 1131-1156 (2006)  
50. Nguyen, N.C., Persson, P.-O., Peraire, J.:RANS solutions using high order discontinuous Galerkin methods. AIAA 2007-914 (2007)
51. Barter, G.E., Darmofal, D.L.:Shock capturing with PDE-based artificial viscosity for DGFEM:part I formulation. J. Comput. Phys. 229, 1810-1827 (2010)  
52. Haas, J.F., Sturtevant, B.:Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 41-76 (1987)  
53. Quirk, J.J., Karni, S.:On the dynamics of a shock-bubble interaction. J. Fluid Mech. 381, 129-163 (1996)
54. Johnsen, E., Colonius, T.:Implementation of WENO schemes in compressible multicomponent flows. J. Comput. Phys. 219, 715- 732 (2006)  
55. Ranjan, D., Oakley, J., Bonazza, R.:Shock-bubble interactions. Annu. Rev. Fluid Mech. 43, 117-140 (2011)  
56. Sjunnesson, A., Nelsson, C., Max, E.:LDA measurements of velocities and turbulence in a bluff body stabilized flame. Laser Anemometry 3, 83-90 (1991)
57. Sjunnesson, A., Olovsson, S., Sjoblom, B.:Validation rig-a tool for flame studies. In:10th International Symposium on Air Breathing Engines. Nottingham, England, 385-393 (1991)
58. Ghani, A., Poinsot, T., Gicquel, L., et al.:LES of longitudinal and transverse self-excited combustion instabilities in a bluff-body stabilized turbulent premixed flame. Combust. Flame 162, 4075-4083 (2015)  
59. Gamezo, V.N., Desbords, D., Oran, E.S.:Two-dimensional reactive flow dynamics in cellular detonation. Shock Waves 9, 11-17 (1999)  
60. Ohyagi, S., Obara, T., Hoshi, S., et al.:Diffraction and re-initiation of detonations behind a backward-facing step. Shock Waves 12, 221-226 (2002)  
61. Burke, M.P., Chaos, M., Ju, Y., et al.:Comprehensive H2/O2 kinetic model for high-pressure combustion. Int. J. Chem. Kinet. 44, 444- 474 (2012)  
62. Lv, Y., Ihme, M.:Computational analysis of re-ignition and reinitiation mechanisms of quenched detonation waves behind a backward facing step. Proc. Combust. Inst. 35, 1963-1972 (2015)  
63. de Wiart, Carton C., Hillewaert, K., et al.:Implicit LES of free and wall-bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method. Int. J. Numer. Methods Fluids 78, 335-354 (2015)  
64. Kanner, S., Persson, P.-O.:Validation of a high-order large-eddy simulation solver using a vertical-axis wind turbine. AIAA J. 54, 101-112 (2015)
65. Beck, A.D., Bolemann, T., Flad, D., et al.:High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations. Int. J. Numer. Methods Fluids 76, 522- 548 (2014)  
66. Gassner,G.J.,Beck,A.D.:On the accuracy of high-order discretizations for underresolved turbulence simulations. Theor. Comput. Fluid Dyn. 27, 221-237 (2013)"  
基金项目This work was supported by an Early Career Faculty grant from NASA's Space Technology Research Grants Program. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center.
作者地址Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA

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