Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations

Journal of Computational Physics

Volumn 231, Issue 2, 2012, Pages 653-665

  Wang, Cheng ^a   Zhang, Xiangxiong ^b   Shu, Chi Wang ^b   Ning, Jianguo ^a  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

^b BROWN UNIVERSITY   (United States)

Author keywords

Discontinuous Galerkin method; Gaseous detonations; High order accuracy; Positivity preserving

Indexed keywords

DETONATION; GALERKIN METHODS;

DISCONTINOUS GALERKIN METHODS; DISCONTINUOUS GALERKIN SCHEMES; EULER'S EQUATION; GASEOUS DETONATION; HIGH-ORDER; HIGHER ORDER ACCURACY; HIGHER-ORDER; POSITIVITY PRESERVING; POSITIVITY PRESERVING SCHEME; SIMPLE++;

EULER EQUATIONS;

EID: 81455124786     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.10.002     Document Type: Article

References (24)

1. Cockburn B., Lin S.-Y., Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems. Journal of Computational Physics 1989, 84:90-113.
2. Cockburn B., Shu C.-W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. Journal of Computational Physics 1998, 141:199-224.
3. Clarke J.F., Karni S., Quirk J.J., Roe P.L., Simmonds L.G., Toro E.F. Numerical computation of two-dimensional unsteady detonation waves in high energy solids. Journal of Computational Physics 1993, 106:215-233.
4. Dou H.-S., Khoo B.C. Effect of initial disturbance on the detonation front structure of a narrow duct. Shock Waves 2010, 20:163-173.
5. Dou H.-S., Tsai H.M., Khoo B.C., Qiu J. Simulations of detonation wave propagation in rectangular ducts using a three-dimensional WENO scheme. Combustion and Flame 2008, 154:644-659.
6. Einfeldt B., Munz C.D., Roe P.L., Sjögreen B. On Godunov-type methods near low densities. Journal of Computational Physics 1991, 92:273-295.
7. Harten A., Engquist B., Osher S., Chakravarthy S. Uniformly high order essentially non-oscillatory schemes, III. Journal of Computational Physics 1987, 71:231-303.
8. Jiang G.-S., Shu C.-W. Efficient implementation of weighted ENO schemes. Journal of Computational Physics 1996, 126:202-228.
9. LeVeque R.J., Yee H.C. A study of numerical methods for hyperbolic conservation laws with stiff source terms. Journal of Computational Physics 1990, 86:187-210.
10. T. Linde, P.L. Roe, Robust Euler codes, in: Thirteenth Computational Fluid Dynamics Conference, AIAA Paper-97-2098.
11. Liu X.-D., Osher S., Chan T. Weighted essentially non-oscillatory schemes. Journal of Computational Physics 1994, 115:200-212.
12. Ma T.-B., Wang C., Ning J.-G. Multi-material Eulerian formulation and hydrocode for the simulation of explosions. Computer Modeling in Engineering & Sciences 2008, 33:155-178.
13. Ning J.-G., Chen L.-W. Fuzzy interface treatment in Eulerian method. Science in China Series E: Technological Sciences 2004, 47:550-568.
14. Perthame B. Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions. SIAM Journal on Numerical Analysis 1992, 29:1-19.
15. Perthame B., Shu C.-W. On positivity preserving finite volume schemes for Euler equations. Numerische Mathematik 1996, 73:119-130.
16. Qu Q., Khoo B.C., Dou H.-S., Tsai H.M. The evolution of a detonation wave in a variable cross-sectional chamber. Shock Waves 2008, 18:213-233.
17. Shu C.-W. Total-Variation-Diminishing time discretizations. SIAM Journal on Scientific and Statistical Computing 1988, 9:1073-1084.
18. Shu C.-W., Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics 1988, 77:439-471.
19. Wang C., Ma T.-B., Lu J. Influence of obstacle disturbance in a duct on explosion characteristics of coal gas. Science China: Physics, Mechanics & Astronomy 2010, 53:269-278.
20. Wescott B.L., Scott Stewart D., Bdzil J.B. On self-similarity of detonation diffraction. Physics of Fluids 2004, 16:373-384.
21. Zhang X., Shu C.-W. On maximum-principle-satisfying high order schemes for scalar conservation laws. Journal of Computational Physics 2010, 229:3091-3120.
22. Zhang X., Shu C.-W. On positivity preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. Journal of Computational Physics 2010, 229:8918-8934.
23. Zhang X., Shu C.-W. Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms. Journal of Computational Physics 2011, 230:1238-1248.
24. X. Zhang, Y. Xia, C.-W. Shu, Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes, Journal of Scientific Computing, to appear, doi:. doi:10.1007/s10915-011-9472-8.