References
- Deng, X.G., and Maekawa, H. 1997. Compact high-order accurate nonlinear schemes. J. Comput. Phys., 130, 77.
- Deng, X.G., Mao, M., Tu, G., Liu, H., and Zhang, H. 2011. Geometric conservation law and applications to high-order finite difference schemes with stationary grids. J. Comput. Phys., 230, 1100.
- Deng, X.G., and Zhang, H. 2000. Developing high-order weighted compact nonlinear schemes. J. Comput. Phys., 165, 22.
- Gamezo, V.N., Desborder, D., and Oran, E.S. 1999. Two-dimensional reactive flow dynamics in cellular detonation waves. Shock Waves, 9, 11–17.
- Gottlieb, S., and Shu, C.W. 1998. Total variation diminishing Runge-Kutta schemes. Math. Comput., 67, 73–85.
- Iida, R., Asahara, M., Hayashi, A.K., Tsuboi, N., and Nonomura, T. 2014. Implementation of a robust weighted compact nonlinear scheme for modeling of hydrogen/air detonation. Combust. Sci. Technol., 186, 1736.
- Jiang, G.S., and Shu, C.W. 1996. Efficient implementation of weighted ENO schemes. J. Comput. Phys., 126, 202.
- Liu, X., Osher, S., and Chan, T. 1994. Weighted essentially non-oscillatory schemes. J. Comput. Phys., 115, 200.
- Nonomura, T., and Fujii, K. 2009. Effects of difference scheme type in high-order weighted compact nonlinear schemes. J. Comput. Phys., 228, 3533.
- Nonomura, T., and Fujii, K. 2013. Robust explicit formulation of weighted compact nonlinear scheme. Comput. Fluids, 85, 8.
- 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, 197–214.
- Nonomura, T., Morizawa, S., Terashima, H., Obayashi, S., and Fujii, K. 2012. Numerical issues on compressible multicomponent flows using a high-order differencing scheme: Weighted compact nonlinear scheme. J. Comput. Phys., 231, 3181.
- Nuclear and Industrial Safety Agency and Ministry of Economy, Trade and Industry JAPAN. 2002. Investigation report on pipe rupture incident at Hamaoka Nuclear Power Station Unit-1.
- Oppenheim, A.K., Manson, N., and Wagner, H.G. 1963. Recent progress in detonation research. AIAA J., 1(10), 2243–2252.
- Roe, P.L. 1981. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys., 43, 276–299.
- Shepherd, J.E. 2010. Thirty years of research on hydrogen explosion hazards in the nuclear industry. Presented at the ANS 2010 Annual Meeting.
- Shimizu, K., Hibi, A., Koshi, M., Morii, Y., and Tsuboi, N. 2011. Updated kinetic mechanism for high-pressure hydrogen combustion. J. Propul. Power, 27, 383–395.
- Steger, J.L., and Warming, R.F. 1981. Flux vector splitting of the inviscid gasdynamics equations with applications to finite difference methods. J. Comput. Phys., 40, 263–293.
- Tsuboi, N., Daimon, Y., and Hayashi, A.K. 2008. Three-dimensional numerical simulation of detonations in coaxial tubes. Shock Waves, 18, 379–392.
- Wada, Y., and Liou, M. 1994. A flux splitting scheme with high resolution and robustness for discontinuities. AIAA Paper 94–0083.
- Wada, Y., and Liou, M.S. 1997. An accurate and robust flux splitting scheme for shock and contact discontinuities. SIAM J. Sci. Comput., 18, 633–657.
- Watt, S.D., and Sharpe, G.J. 2005. Linear and nonlinear dynamics of cylindrically and spherically expanding detonation waves. J. Fluid Mech., 522, 329–356.
- 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.