[1] J. Joshi, "Computational flow modelling and design of bubble column reactors," Chemical Engineering Science, vol. 56, pp. 5893-5933, 2001.
[2] N. Kantarci, F. Borak, and K. O. Ulgen, "Bubble column reactors," Process Biochemistry, vol. 40, pp. 2263-2283, 2005.
[3] D. Zhang, N. G. Deen, and J. Kuipers, "Euler− Euler Modeling of Flow, Mass Transfer, and Chemical Reaction in a Bubble Column," Industrial & engineering chemistry research, vol. 48, pp. 47-57, 2008.
[4] V. V. Ranade, Computational flow modeling for chemical reactor engineering vol. 5: Academic press, 2001.
[5] P. Chen, J. Sanyal, and M. Dudukovic, "CFD modeling of bubble columns flows: implementation of population balance," Chemical Engineering Science, vol. 59, pp. 5201-5207, 2004.
[6] D. Zhang, N. Deen, and J. Kuipers, "Numerical modeling of hydrodynamics, mass transfer and chemical reaction in bubble columns," 2007.
[7] D. Darmana, N. Deen, and J. Kuipers, "Detailed modeling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model," Chemical Engineering Science, vol. 60, pp. 3383-3404, 2005.
[8] S.-C. Chang, "The method of space-time conservation element and solution element—a new approach for solving the Navier-Stokes and Euler equations," Journal of computational Physics, vol. 119, pp. 295-324, 1995.
[9] S.-C. Chang, X.-Y. Wang, and C.-Y. Chow, "The space-time conservation element and solution element method: a new high-resolution and genuinely multidimensional paradigm for solving conservation laws," Journal of Computational Physics, vol. 156, pp. 89-136, 1999.
[10] X.-Y. Wang and S.-C. Chang, "A 2D non-splitting unstructured triangular mesh Euler solver based on the space-time conservation element and solution element method," Computational Fluid Dynamics Journal, vol. 8, pp. 309-325, 1999.
[11] X.-Y. Wang and S.-C. Chang, "A 3D Non-Splitting Structured/Unstructured Euler Solver Based on the Space-Time Conservation Element and Solution Element Method," AIAA Paper, pp. 99-3278, 1999.
[12] Z.-C. Zhang, S. J. Yu, and S.-C. Chang, "A space-time conservation element and solution element method for solving the two-and three-dimensional unsteady Euler equations using quadrilateral and hexahedral meshes," Journal of Computational Physics, vol. 175, pp. 168-199, 2002.
[13] S.-C. Chang, "Courant number insensitive CE/SE schemes," AIAA paper, vol. 3890, p. 2002, 2002.
[14] S.-C. Chang, Y. Wu, V. Yang, and X.-Y. Wang, "Local time-stepping procedures for the space-time conservation element and solution element method," International Journal of Computational Fluid Dynamics, vol. 19, pp. 359-380, 2005.
[15] J. Wang, K. Liu, and D. Zhang, "An improved CE/SE scheme for multi-material elastic–plastic flows and its applications," Computers & Fluids, vol. 38, pp. 544-551, 2009.
[16] S.-C. Chang, A new approach for constructing highly stable high order CESE schemes: National Aeronautics and Space Administration, Glenn Research Center, 2010.
[17] C.-L. Chang, B. Venkatachari, and G. Cheng, "Time-Accurate Local Time Stepping and High-Order Space-Time CESE Methods for Multi-Dimensional Flows with Unstructured Meshes," AIAA paper, vol. 3069, p. 2013, 2013.
[18] D. L. Bilyeu, S.-T. J. Yu, Y.-Y. Chen, and J.-L. Cambier, "A two-dimensional fourth-order unstructured-meshed Euler solver based on the CESE method," Journal of Computational Physics, vol. 257, pp. 981-999, 2014.
[19] H. Shen and C.-Y. Wen, "A characteristic space–time conservation element and solution element method for conservation laws II. Multidimensional extension," Journal of Computational Physics, vol. 305, pp. 775-792, 2016.
[20] X.-Y. Wang, S.-C. Chang, and P. C. Jorgenson, "Prediction of sound waves propagating through a nozzle without/with a shock wave using the space-time CE/SE method," 2000.
[21] Y. Guo, A. T. Hsu, J. Wu, Z. Yang, and A. Oyediran, "Extension of CE/SE method to 2D viscous flows," Computers & fluids, vol. 33, pp. 1349-1361, 2004.
[22] H. He, S.-T. J. Yu, and Z.-C. Zhang, "Direct calculations of one-, two-, and three-dimensional detonations by the CESE method," AIAA Paper, vol. 229, p. 2005, 2005.
[23] G. Wang, D. Zhang, K. Liu, and J. Wang, "An improved CE/SE scheme for numerical simulation of gaseous and two-phase detonations," Computers & Fluids, vol. 39, pp. 168-177, 2010.
[24] H. Shen, G. Wang, K. Liu, and D. Zhang, "Numerical simulation of liquid-fueled detonations by an Eulerian–Lagrangian model," International Journal of Nonlinear Sciences and Numerical Simulation, vol. 13, pp. 177-188, 2012.
[25] M. Liu, J. B. Wang, and K.-Q. Wu, "The direct aero-acoustics simulation of flow around a square cylinder using the CE/SE scheme," Journal of Algorithms & Computational Technology, vol. 1, pp. 525-538, 2007.
[26] G. Wang, H. Zhu, Q. Sun, D. Zhang, and K. Liu, "An improved CE/SE scheme and its application to dilute gas–particle flows," Computer Physics Communications, vol. 182, pp. 1589-1601, 2011.
[27] S. Qamar and M. Yousaf, "The space–time CESE method for solving special relativistic hydrodynamic equations," Journal of Computational Physics, vol. 231, pp. 3928-3945, 2012.
[28] H. Shen, C.-Y. Wen, M. Parsani, and C.-W. Shu, "Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids," Journal of Computational Physics, vol. 330, pp. 668-692, 2017.
[29] D. A. Drew and S. L. Passman, Theory of multicomponent fluids vol. 135: Springer Science & Business Media, 2006.
[30] U. S. G. FLUENT, "Release 6.1," Fluent Inc., Centerra Resource Park, Lebanon, January, 2003.
[31] H. Zheng, C. Shu, Y. Chew, and N. Qin, "A solution adaptive simulation of compressible multi‐fluid flows with general equation of state," International Journal for Numerical Methods in Fluids, vol. 67, pp. 616-637, 2011.
[32] C. Jiang, S. Cui, and X. Feng, "Solving the Euler and Navier–Stokes equations by the AMR–CESE method," Computers & Fluids, vol. 54, pp. 105-117, 2012.
