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References (81)
-
A. Beck, T. Bolemann, David Flad, Hannes Frank, G. Gassner, F. Hindenlang, C. Munz (2014)
High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulationsInternational Journal for Numerical Methods in Fluids, 76
-
Y. Lv (2015)
Discontinuous Galerkin scheme for turbulent flow simulations -
Xiangxiong Zhang, Chi-Wang Shu (2010)
On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshesJ. Comput. Phys., 229
-
A. Klöckner, T. Warburton, J. Bridge, J. Hesthaven (2009)
Nodal discontinuous Galerkin methods on graphics processorsJ. Comput. Phys., 228
-
F. Bassi (2000)
GMRES discontinuous Galerkin solution of the compressible Navier–Stokes equations. In: CockburnCockburn
-
W.H. Reed (1973)
Triangular mesh methods for the neutron transport equation. Los Alamos Report LA-UR-73-479 -
PL Roe (1981)
Approximate Riemann solvers, parameter vectors, and difference schemesJ. Comput. Phys., 43
-
Xiangxiong Zhang, Chi-Wang Shu (2011)
A minimum entropy principle of high order schemes for gas dynamics equationsNumerische Mathematik, 121
-
Liñán Amable, F. Williams (1963)
Fundamental Aspects of CombustionNature, 200
-
F. Hu, M. Hussaini, P. Rasetarinera (1999)
An Analysis of the Discontinuous Galerkin Method for Wave Propagation ProblemsJournal of Computational Physics, 151
-
C. Wiart, K. Hillewaert, L. Bricteux, G. Winckelmans (2015)
Implicit LES of free and wall‐bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty methodInternational Journal for Numerical Methods in Fluids, 78
-
Jun Zhu, Xinghui Zhong, Chi-Wang Shu, J. Qiu (2013)
Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshesJ. Comput. Phys., 248
-
(1991)
Validation rig—a tool for flame studies -
Bernardo Cockburn, Chi-Wang Shu (1998)
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion SystemsSIAM Journal on Numerical Analysis, 35
-
R. Hartmann (2006)
Adaptive discontinuous Galerkin methods with shock‐capturing for the compressible Navier–Stokes equationsInternational Journal for Numerical Methods in Fluids, 51
-
Y. Lv, M. Ihme (2014)
Entropy-bounded discontinuous Galerkin scheme for Euler equationsJ. Comput. Phys., 295
-
L. Maley, R. Bhattacharjee, S. Lau-Chapdelaine, M. Radulescu (2013)
Influence of hydrodynamic instabilities on the propagation mechanism of fast flamesarXiv: Fluid Dynamics
-
(1991)
LDA measurements of velocities and turbulence in a bluff body stabilized flame -
J. Peraire, P. Persson (2007)
The Compact Discontinuous Galerkin (CDG) Method for Elliptic ProblemsSIAM J. Sci. Comput., 30
-
D. Arnold, F. Brezzi, Bernardo Cockburn, L. Marini (2001)
Unified Analysis of Discontinuous Galerkin Methods for Elliptic ProblemsSIAM J. Numer. Anal., 39
-
P.C. Ma (2017)
An entropy-stable hybrid scheme for simulations of transcritical real-fluid flows. J. Comput. Phys. 340 -
(1975)
Turbulence, 2nd edn -
T. Lu, C. Law (2009)
Toward accommodating realistic fuel chemistry in large-scale computationsProgress in Energy and Combustion Science, 35
-
P. Roe (1997)
Approximate Riemann Solvers, Parameter Vectors, and Difference SchemesJournal of Computational Physics, 135
-
E. Tadmor (1986)
A minimum entropy principle in the gas dynamics equationsApplied Numerical Mathematics, 2
-
E. Toro, M. Spruce, W. Speares (1994)
Restoration of the contact surface in the HLL-Riemann solverShock Waves, 4
-
Bernardo Cockburn, Chi-Wang Shu (1998)
The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws VJournal of Computational Physics, 141
-
Bernardo Cockburn, Chi-Wang Shu (1989)
TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General frameworkMathematics of Computation, 52
-
H. Luo, J. Baum, R. Löhner (2007)
A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured gridsJ. Comput. Phys., 225
-
V. Gamezo, D. Desbordes, E. Oran (1999)
Formation and evolution of two-dimensional cellular detonationsCombustion and Flame, 116
-
M. Vuik, J. Ryan (2014)
Multiwavelet troubled-cell indicator for discontinuity detection of discontinuous Galerkin schemesJ. Comput. Phys., 270
-
Y. Lv, Y. See, M. Ihme (2016)
An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methodsJ. Comput. Phys., 322
-
S. Ohyagi, T. Obara, S. Hoshi, P. Cai, Teruo Yoshihashi (2002)
Diffraction and re-initiation of detonations behind a backward-facing stepShock Waves, 12
-
J. Haas, B. Sturtevant (1987)
Interaction of weak shock waves with cylindrical and spherical gas inhomogeneitiesJournal of Fluid Mechanics, 181
-
G. Gassner, F. Lörcher, C. Munz (2008)
A Discontinuous Galerkin Scheme based on a Space-Time Expansion II. Viscous Flow Equations in Multi DimensionsJournal of Scientific Computing, 34
-
W. Reed, T. Hill (1973)
Triangular mesh methods for the neutron transport equation -
L. Krivodonova, J. Xin, J. Remacle, N. Chevaugeon, J. Flaherty (2004)
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation lawsApplied Numerical Mathematics, 48
-
R. Hartmann, P. Houston (2008)
An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equationsJ. Comput. Phys., 227
-
F. Pintgen, C. Eckett, J. Austin, J. Shepherd (2003)
Direct observations of reaction zone structure in propagating detonationsCombustion and Flame, 133
-
J.J. Quirk (1996)
On the dynamics of a shock–bubble interaction. J. Fluid Mech. 381 -
J. Guermond, R. Pasquetti (2008)
Entropy-based nonlinear viscosity for Fourier approximations of conservation lawsComptes Rendus Mathematique, 346
-
Y. Zel’dovich, Y. Raizer, W. Hayes, R. Probstein, S. Gill (2002)
Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena -
A. Sjunnesson (1991)
Validation rig—a tool for flame studies. In: 10th International Symposium on Air Breathing Engines. Nottingham10th International Symposium on Air Breathing Engines
-
L. Krivodonova (2007)
Limiters for high-order discontinuous Galerkin methodsJ. Comput. Phys., 226
-
N. Nguyen, P. Persson, J. Peraire (2007)
RANS Solutions Using High Order Discontinuous Galerkin Methods -
J. Quirk, S. Karni (1994)
On the dynamics of a shock–bubble interactionJournal of Fluid Mechanics, 318
-
V. Gamezo, D. Desbordes, E. Oran (1999)
Two-dimensional reactive flow dynamics in cellular detonation wavesShock Waves, 9
-
R. Abgrall, S. Karni (2001)
Computations of compressible multifluidsJournal of Computational Physics, 169
-
J Pitkäranta C Johnson (1986)
An analysis of the discontinuous Galerkin method for a scalar hyperbolic equationMath. Comput., 46
-
G. Gassner, A. Beck (2013)
On the accuracy of high-order discretizations for underresolved turbulence simulationsTheoretical and Computational Fluid Dynamics, 27
-
E. Toro (1997)
Riemann Solvers and Numerical Methods for Fluid Dynamics -
J. Shepherd (2009)
Detonation in gases, 32
-
Claes Johnson, J. Pitkäranta (1986)
An analysis of the discontinuous Galerkin method for a scalar hyperbolic equationMathematics of Computation, 46
-
P. Lax (1971)
Shock Waves and Entropy -
F. Bassi, S. Rebay (1997)
A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes EquationsJournal of Computational Physics, 131
-
Garrett Barter, D. Darmofal (2010)
Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. FormulationJ. Comput. Phys., 229
-
N.C. Nguyen (2007)
RANS solutions using high order discontinuous Galerkin methods. AIAA 2007-914 -
Bernardo Cockburn, San-Yih Lin, Chi-Wang Shu (1989)
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systemsJournal of Computational Physics, 84
-
EF Toro (2013)
Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction -
S. Kanner, P. Persson (2016)
Validation of a High-Order Large-Eddy Simulation Solver Using a Vertical-Axis Wind TurbineAIAA Journal, 54
-
E. Johnsen, T. Colonius (2005)
Implementation of WENO schemes in compressible multicomponent flow problemsJ. Comput. Phys., 219
-
P.C. Ma (2015)
Discontinuous Galerkin scheme for turbulent flow simulations. Annual Research Briefs -
P.D. Lax (1971)
Shock waves and entropy. In: Zarantonello E.H.Zarantonello E
-
Y. Lv, M. Ihme (2015)
Computational analysis of re-ignition and re-initiation mechanisms of quenched detonation waves behind a backward facing step, 35
-
John Lee (2008)
The Detonation Phenomenon -
C-W Shu B Cockburn (1989)
TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general frameworkJ. Sci. Comp., 52
-
P. Persson, J. Peraire (2006)
Sub-Cell Shock Capturing for Discontinuous Galerkin Methods -
Cheng Wang, Xiangxiong Zhang, Chi-Wang Shu, J. Ning (2012)
Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonationsJ. Comput. Phys., 231
-
Y. Lv, M. Ihme (2014)
Discontinuous Galerkin method for multicomponent chemically reacting flows and combustionJ. Comput. Phys., 270
-
Carton C. de Wiart (2015)
Implicit LES of free and wall-bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method. Int. J. Numer. Methods Fluids 78 -
P.-O. Persson (2006)
Sub-cell shock capturing for discontinuous Galerkin methods. AIAA 2006-112 -
P. Ma, Y. Lv, M. Ihme (2017)
An entropy-stable hybrid scheme for simulations of transcritical real-fluid flowsJ. Comput. Phys., 340
-
F. Bassi, S. Rebay (2000)
GMRES Discontinuous Galerkin Solution of the Compressible Navier-Stokes Equations -
JO Hinze (1975)
Turbulence -
Zhijian Wang, K. Fidkowski, R. Abgrall, F. Bassi, D. Caraeni, A. Cary, H. Deconinck, R. Hartmann, K. Hillewaert, H. Huynh, N. Kroll, G. May, P. Persson, B. Leer, M. Visbal (2013)
High‐order CFD methods: current status and perspectiveInternational Journal for Numerical Methods in Fluids, 72
-
Devesh Ranjan, J. Oakley, R. Bonazza (2011)
Shock-Bubble InteractionsAnnual Review of Fluid Mechanics, 43
-
Bernardo Cockburn, Chi-Wang Shu (2001)
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated ProblemsJournal of Scientific Computing, 16
-
M. Burke, M. Chaos, Y. Ju, F. Dryer, S. Klippenstein (2012)
Comprehensive H2/O2 kinetic model for high‐pressure combustionInternational Journal of Chemical Kinetics, 44
-
T. Peterson (1991)
A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equationSIAM Journal on Numerical Analysis, 28
-
A. Ghani, T. Poinsot, L. Gicquel, G. Staffelbach (2015)
LES of longitudinal and transverse self-excited combustion instabilities in a bluff-body stabilized turbulent premixed flameCombustion and Flame, 162
-
(1961)
Calculation of intersection of non-steady shock waves with obstacles
- Publisher
- Springer Journals
- Copyright
- 2017 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
- ISSN
- 0567-7718
- eISSN
- 1614-3116
- DOI
- 10.1007/s10409-017-0664-9
- Publisher site
- See Article on Publisher Site
Abstract
Abstract 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 entropy-residual 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.
Journal
"Acta Mechanica Sinica" – Springer Journals
Published: Jun 1, 2017