Implementation of a Robust Weighted Compact Nonlinear Scheme for Modeling of Hydrogen/Air Detonation

REFERENCES

• Asahara, A., Hayashi, A. K., Yamada, E., and Tsuboi, N. 2012. Generation and dynamics of sub-transverse wave of cylindrical detonation. Combust. Sci. Technol., 184, 1568.
   Web of Science ®Google Scholar
• Batten, P., Clarke, N., Lambert, C., and Causon, D. M. 1997. On the choice of wavespeeds for the HLLC Riemann solver. SIAM J. Sci. Comput., 18, 1553.
   Web of Science ®Google Scholar
• Deng, X. G., and Zhang, H. 2000. Developing high-order weighted compact nonlinear schemes. J. Comput. Phys., 165, 22.
   Web of Science ®Google Scholar
• Einfeldt, B. 1988. On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal., 25, 294.
   Web of Science ®Google Scholar
• Gamezo, V. N., Desbordes, D., and Oran, E. S. 1999. Two-dimensional reactive flow dynamics in cellular detonation waves. Shock Waves, 54, 11.
   Web of Science ®Google Scholar
• Godunov, S. K. 1959. A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations. Math. Sbornik, 43, 271.
   Google Scholar
• Gottlieb, S., and Shu, C. W. 1998. Total variation diminishing Runge–Kutta schemes. Math. Comput., 67, 73.
   Web of Science ®Google Scholar
• Henrick, A. K., Aslam, T. D., and Powers, J. M. 2006. Simulations of pulsating one-dimensional detonations with true fifth order accuracy. J. Comput. Phys., 213, 311.
   Web of Science ®Google Scholar
• Hu, X. Y., Zhang, D. L., Khoo, B. C., and Jiang, Z. L. 2005. The structure and evolution of a two-dimensional H2/O2/Ar cellular detonation. Shock Waves, 14, 37.
   Web of Science ®Google Scholar
• Jiang, G. S., and Shu, C. W. 1996. Efficient implementation of weighted ENO schemes. J. Comput. Phys., 126, 200.
   Web of Science ®Google Scholar
• Mahmoudi, Y., and Mazaheri, K. 2011. High resolution numerical simulation of the structure of 2-D gaseous detonations. Proc. Combust. Inst., 31, 2187.
   Web of Science ®Google Scholar
• Nonomura, T., and Fujii, K. 2009. Effects of difference scheme type in high-order weighted compact nonlinear schemes. J. Comput. Phys., 228, 3533.
   Web of Science ®Google Scholar
• Nonomura, T. and Fujii, K. 2013. Robust explicit formulation of weighted compact nonlinear scheme. Comput. Fluids, 85, 8.
   Web of Science ®Google Scholar
• Nonomura, T., Iizuka, N., and Fujii, K. 2010. Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids. Comput. Fluids, 39, 197.
   Web of Science ®Google Scholar
• Nonomura, T., Morizawa, S., Terashima, H., Obayashi, S., and Fujii, K. 2012. Numerical (error) issues on compressible multicomponent flows using a high-order differencing scheme: Weighted compact nonlinear scheme. J. Comput. Phys., 231, 3181.
   Web of Science ®Google Scholar
• Odlyzko, A. M. 1985. Discrete logarithms in finite fields and their cryptographic significance. Lect. Notes Comput. Sci., 209, 224.
   Google Scholar
• Petersen, E. L., and Hanson, R. K. 1999. Reduced kinetics mechanisms for ram accelerator combustion. J. Propul. Power, 15, 591.
   Web of Science ®Google Scholar
• Shu, C., and Osher, S. 1989. Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. J. Comput. Phys., 83, 32.
   Web of Science ®Google Scholar
• Sod, G. A. 1978. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys., 27, 1.
   Web of Science ®Google Scholar
• Strang, G. 1968. On the construction and composition of difference schemes. SIAM J. Numer. Anal., 5, 506.
   Web of Science ®Google Scholar
• Stull, D. R., and Prophet, H. 1971. JANAF Thermochemical Tables, 2nd ed. NSRDS-NBS, 37.
   Google Scholar
• Taylor, B. D., Kessler, V. N., Gamezo, V. N., and Oran, E. S. 2013. Numerical simulation of hydrogen detonations with detailed chemical kinetics. Proc. Combust. Inst., 34, 2009.
   Web of Science ®Google Scholar
• Togashi, F., Lohner, R., and Tsuboi, N. 2007. Numerical simulation of H₂/air detonation wave around obstacles using detailed reaction models. AIAA Paper 03‐3170.
   Google Scholar
• Wada, Y., and Liou, M. 1994. A flux splitting scheme with high resolution and robustness for discontinuities. AIAA Paper 94‐0083.
   Google Scholar
• Wintenberger, E., and Shepherd, J. E. 2003. A model for the performance of air-breathing pulse detonation engines. AIAA Paper 03‐4511.
   Google Scholar
• Woodward, P. R., and Colella, P. 1984. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys., 54, 115.
   Web of Science ®Google Scholar
• Yee, H. C. 1987. Upwind and symmetric shock-capturing schemes. NASA TM-89464.
   Google Scholar
• Zhang, S., Jiang, S., and Shu, C. W. 2008. Development of nonlinear weighted compact schemes with increasingly higher order accuracy. J. Comput. Phys., 227, 7294.
   Web of Science ®Google Scholar