Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Acta Mechanica Sinica
Erschienen in: Acta Mechanica Sinica 4/2018

15.03.2018 | Research Paper

An efficient unstructured WENO method for supersonic reactive flows

verfasst von: Wen-Geng Zhao, Hong-Wei Zheng, Feng-Jun Liu, Xiao-Tian Shi, Jun Gao, Ning Hu, Meng Lv, Si-Cong Chen, Hong-Da Zhao

Erschienen in: Acta Mechanica Sinica | Ausgabe 4/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

An efficient high-order numerical method for supersonic reactive flows is proposed in this article. The reactive source term and convection term are solved separately by splitting scheme. In the reaction step, an adaptive time-step method is presented, which can improve the efficiency greatly. In the convection step, a third-order accurate weighted essentially non-oscillatory (WENO) method is adopted to reconstruct the solution in the unstructured grids. Numerical results show that our new method can capture the correct propagation speed of the detonation wave exactly even in coarse grids, while high order accuracy can be achieved in the smooth region. In addition, the proposed adaptive splitting method can reduce the computational cost greatly compared with the traditional splitting method.
Vorheriger Artikel Theoretical analysis for the mechanical behavior caused by an electromagnetic cycle in ITER cable-in-conduit conductors
Nächster Artikel Study of droplet flow in a T-shape microchannel with bottom wall fluctuation

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Roy, G.D.: Pulse detonation propulsion: challenges, current status, and future perspective. Prog. Energy Combust. 30, 545–672 (2004)CrossRef
2.
Geßner, T.: Dynamic mesh adaption for supersonic combustion waves modeled with detailed reaction mechanisms. [Ph.D. Thesis], Technical University Dresden, German (2001)
3.
Fedkiw, R.P., Merriman, B., Osher, S.: High accuracy numerical methods for thermally perfect gas flows with chemistry. J. Comput. Phys. 132, 175–190 (1997)MathSciNetCrossRefMATH
4.
Togashi, F., Löhner, R., Tsuboi, N.: Numerical simulation of H\(_2\)/air detonation using unstructured mesh. Shock Waves 192, 151–162 (2009)CrossRefMATH
5.
Ju, Y.: Recent progress and challenges in fundamental combustion research. Adv. Mech. 44, 1142–1157 (2014)
6.
Chapman, D.L.V.I.: On the rate of explosion in gases. Lond. Edinb. Dublin Philos. Mag. J. Sci. 47, 90–104 (1899)CrossRefMATH
7.
Jouguet, E.: On the propagation of chemical reactions in gases. J. Math. Pureset Appl. 1, 347–425 (1905)MATH
8.
Zeldovich, Y.B.: On the theory of the propagation of detonation in gaseous systems. Tech. Memos. Nat. Adv. Comm. Aeronaut. 1950, 1261 (1950)MathSciNet
9.
Von Neuman, J.: Theory of Detonation Waves. Institute for Advanced Study, Princeton (1942)
10.
Döring, W.: On detonation processes in gases. Ann. Phys. 43, 421–436 (1943)CrossRef
11.
Bao, W., Jin, S.: The random projection method for hyperbolic conservation laws with stiff reaction terms. J. Comput. Phys. 163, 216–248 (2000)MathSciNetCrossRefMATH
12.
13.
Bao, W., Jin, S.: The random projection method for stiff multispecies detonation capturing. J. Comput. Phys. 178, 37–57 (2002)MathSciNetCrossRefMATH
14.
Helzel, C., Leveque, R.J., Warnecke, G.: A modified fractional step method for the accurate approximation of detonation waves. SIAM J. Sci. Comput. 22, 1489–1510 (2000)MathSciNetCrossRefMATH
15.
16.
Dumbser, M., Enaux, C., Toro, E.F.: Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. J. Comput. Phys. 227, 3971–4001 (2008)MathSciNetCrossRefMATH
17.
Wang, W., Shu, C.W., Yee, H.C., et al.: High order finite difference methods with subcell resolution for advection equations with stiff source terms. J. Comput. Phys. 231, 190–214 (2012)MathSciNetCrossRefMATH
18.
Zhang, B., Liu, H., Chen, F.: The equilibrium state method for hyperbolic conservation laws with stiff reaction terms. J. Comput. Phys. 263, 151–176 (2014)MathSciNetCrossRefMATH
19.
Taki, S., Fujiwara, T.: Numerical analysis of two-dimensional non-steady detonations. AIAA J. 16, 73–77 (1978)CrossRef
20.
Lefebvre, M.H., Oran, E.S., Kailasanath, K.: Computations of Detonation Structure: The Influence of Model Input Parameters. Naval Research Lab, Washington, DC (1992)
21.
Sichel, M., Tonello, N.A., Oran, E.S., et al.: A two-step kinetics model for numerical simulation of explosions and detonations in H\(_2\)–O\(_2\) mixtures. R. Soc. 458, 49–82 (2002)CrossRefMATH
22.
Colella, P., Majda, A., Roytburd, V.: Theoretical and numerical structure for reacting shock waves. SIAM J. Sci. Comput. 7, 1059–1080 (1986)MathSciNetCrossRefMATH
23.
LeVeque, R.J., Yee, H.C.: A study of numerical methods for hyperbolic conservation laws with stiff source terms. J. Comput. Phys. 86, 187–210 (1990)MathSciNetCrossRefMATH
24.
Bussing, T.R.A., Murman, E.M.: Finite-volume method for the calculation of compressible chemically reacting flows. AIAA J. 26, 1070–1078 (1988)MathSciNetCrossRefMATH
25.
Gnoffo, P.A.: An upwind-biased, point-implicit relaxation algorithm for viscous, compressible perfect-gas flows. NASA Tech. Rep. 90, 17–42 (1990)
26.
Zhong X.: New high-order semi-implicit Runge–Kutta schemes for computing transient nonequilibrium hypersonic flow. In: 30th Thermophysics Conference, New York, August 4–14 (1995)
27.
Oran, E.S., Weber, J.W., Stefaniw, E.I., et al.: A numerical study of a two-dimensional H\(_2\)–O\(_2\)–Ar detonation using a detailed chemical reaction model. Combust. Flame 113, 147–163 (1998)CrossRef
28.
Xiao, X., Edwards, J.R., Hassan, H.A., et al.: Inflow boundary conditions for hybrid large eddy/Reynolds averaged Navier–Stokes simulations. AIAA J. 41, 1481–1489 (2003)CrossRef
29.
Shen, Y., Zha, G.: Application of low diffusion E-CUSP scheme with high order WENO scheme for chemical reacting flows. In: The 40th Fluid Dynamics Conference and Exhibit, Chicago, June 28–30 (2010)
30.
Taylor, B.D., Kessler, D.A., Gamezo, V.N., et al.: Numerical simulations of hydrogen detonations with detailed chemical kinetics. Proc. Combust. Inst. 34, 2009–2016 (2013)CrossRef
31.
Billet, G., Ryan, J., Borrel, M.: A Runge Kutta discontinuous Galerkin approach to solve reactive flows on conforming hybrid grids: the parabolic and source operators. Comput. Fluids 95, 98–115 (2014)MathSciNetCrossRefMATH
32.
Lv, Y., Ihme, M.: Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion. J. Comput. Phys. 270, 105–137 (2014)MathSciNetCrossRefMATH
33.
Dumbser, M., Castro, M., Parés, C., et al.: ADER schemes on unstructured meshes for non-conservative hyperbolic systems: applications to geophysical flows. Comput. Fluids 38, 1731–1748 (2009)MathSciNetCrossRefMATH
34.
Dumbser, M., Zanotti, O.: Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations. J. Comput. Phys. 228, 6991–7006 (2009)MathSciNetCrossRefMATH
35.
Titarev, V.A., Tsoutsanis, P., Drikakis, D.: WENO schemes for mixed-element unstructured meshes. Commun. Comput. Phys. 8, 585–609 (2010)MathSciNetMATH
36.
Zhang, Y.T., Shu, C.W.: Third order WENO scheme on three dimensional tetrahedral meshes. Commun. Comput. Phys. 5, 836–848 (2009)MathSciNetMATH
37.
Zhang, Y., Shu, C.: High-order WENO Sschemes for Hamilton–Jacobi equations on triangular meshes. SIAM J. Sci. Comput. 24, 1005–1030 (2003)CrossRefMATH
38.
Togashi, F., Löhner, R., Tsuboi, N.: Numerical simulation of H\(_2\)/air detonation using unstructured mesh. Shock Waves 19, 151–162 (2009)CrossRefMATH
39.
Wang, Z.J.: High-order methods for the Euler and Navier–Stokes equations on unstructured grids. Prog. Aerosp. Sci. 43, 1–41 (2007)CrossRef
40.
Ekaterinaris, J.A.: High-order accurate, low numerical diffusion methods for aerodynamics. Prog. Aerosp. Sci. 41, 192–300 (2005)CrossRef
41.
Harten, A., Engquist, B., Osher, S., et al.: Uniformly high order accurate essentially non-oscillatory schemesIII. J. Comput. Phys. 71, 231–303 (1987)MathSciNetCrossRefMATH
42.
43.
44.
Cockburn, B., Karniadakis, G.E., Shu, C.W.: The Development of Discontinuous Galerkin Methods. Springer, Berlin (2000)CrossRefMATH
45.
Wang, Z.J.: Spectral (finite) volume method for conservation laws on unstructured grids basic formulation. J. Comput. Phys. 178, 210–251 (2002)MathSciNetCrossRefMATH
46.
Zheng, H., Zhao, W.G.: An improved unstructured WENO method for compressible multi-fluids flow. In. J. Numer. Methods Fluids 82, 113–129 (2016)MathSciNetCrossRef
47.
Stull, D., Prophet, H.: JANAF Thermo Chemical Tables, 2nd edn. NSRDS-NBS37, Washington (1971)
48.
Kailasanath, K., Oran, E.S., Boris, J.P.: Determination of detonation cell size and the role of transverse waves in two-dimensional detonations. Combust. Flame 61, 199–209 (1985)CrossRef
49.
Hu, Z., Mu, Q., Zhang, D., et al.: Numerical simulation of gaseous detonation wave propagation through bends with a detailed chemical reaction model. Chin. J. Comput. Phys. 21, 408–414 (2004)
50.
Lv, Y., Ihme, M.: Development of discontinuous Galerkin method for detonation and supersonic combustion. In: 51st AIAA Aerospace Sciences Meeting, Grapevine, January 7–10 (2013)
51.
Deiterding, R., Bader, G.: High-Resolution Simulation of Detonations with Detailed Chemistry. In: Analysis and Numeric for Conservation Laws, Berlin Heidelberg, May 4–12 (2005)
52.
Eckett, C.A.: Numerical and Analytical Studies of the Dynamics of Gaseous Detonations [Ph.D. Thesis], California Institute of Technology, America (2000)
53.
Deiterding, R.: Parallel Adaptive Simulation of Multi-Dimensional Detonation Structures. [Ph.D. Thesis], Branderburg University of Technology Cottbus, German (2003)
54.
Li, J., Zhao, Z., Kazakov, A., et al.: An updated comprehensive kinetic model of hydrogen combustion. Int. J. Chem. Kinet. 36, 566–575 (2004)CrossRef
55.
Stull, D.R., Prophet, H.: JANAF thermo chemical tables. Technical report, U. S. Department of Commerce (1971)
56.
57.
Dumbser, M., Käser, M., Titarev, V.A., et al.: Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J. Comput. Phys. 226, 204–243 (2007)MathSciNetCrossRefMATH
58.
Ivan, L.: High-order central ENO finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids. J. Comput. Phys. 12, 157–182 (2015)MathSciNetCrossRefMATH
59.
Ivan, L., Clinton, P.T.: High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows. J. Comput. Phys. 11, 830–862 (2014)
60.
Billet, G., Ryan, J., Borrel, M.: A Runge Kutta discontinuous Galerkin approach to solve reactive flows on conforming hybrid grids: the parabolic and source operators. Comput. Fluids 1, 98–115 (2014)MathSciNetCrossRefMATH
61.
Billet, G., Ryan, J., Borrel, M.: A Runge Kutta discontinuous Galerkin approach to solve reactive flows on conforming hybrid grids: the parabolic and source operators. Comput. Fluids 23, 98–115 (2014)MathSciNetCrossRefMATH
62.
Ren, Z.: Dynamic adaptive chemistry with operator splitting schemes for reactive flow simulations. J. Comput. Phys. 263, 19–36 (2014)CrossRefMATH
63.
Cai, X., Liang, J., Lin, Z., et al.: Adaptive mesh refinement-based numerical simulation of detonation initiation in supersonic combustible mixtures using a hot jet. J. Aerosp. Eng. 28, 1–15 (2015)
64.
Florian, E., Klaus, G., Sattelmayer, T.: Numerical simulation of the deflagration to detonation transition in inhomogeneous mixtures. J. Combust. 31, 1–15 (2014)
65.
Zhou, R., Wu, D., Wang, J.: Progress of continuously rotating detonation engines. Chin. J. Aeronaut. 29, 15–29 (2016)CrossRef
66.
Qing, Y., Zhang, X.: Discontinuous Galerkin immersed finite element methods for parabolic interface problems. J. Comput. Appl. Math. 1, 127–139 (2016)MathSciNetMATH
67.
Assyr, A., Huber, M.E.: Discontinuous Galerkin finite element heterogeneous multiscale method for advection–diffusion problems with multiplescales. Numer. Math. 126, 589–633 (2014)MathSciNetCrossRef
Metadaten
Titel
An efficient unstructured WENO method for supersonic reactive flows
verfasst von
Wen-Geng Zhao
Hong-Wei Zheng
Feng-Jun Liu
Xiao-Tian Shi
Jun Gao
Ning Hu
Meng Lv
Si-Cong Chen
Hong-Da Zhao
Publikationsdatum
15.03.2018
Verlag
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Erschienen in
Acta Mechanica Sinica / Ausgabe 4/2018
Print ISSN: 0567-7718
Elektronische ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-018-0756-1

Weitere Artikel der Ausgabe 4/2018

Acta Mechanica Sinica 4/2018 Zur Ausgabe

Research Paper

Three-point bending of honeycomb sandwich beams with facesheet perforations

Review Paper

Review of deployment technology for tethered satellite systems

Research Paper

Reducing the anisotropy of a Brazilian disc generated in a bonded-particle model

Research Paper

Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

Research Paper

Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations

Research Paper

Structural eigenvalue analysis under the constraint of a fuzzy convex set model

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise