References
- K. Aziz, A. Settari, Petroleum Reservoir Simulation, Applied Science Publisher, London, 1979.
- J. Bear, Hydraulics of Groundwater, McGraw-Hill, New York, 1978.
- Z. Chen, G. Huang and Y. Ma, Computational Methods for Multiphase Flows in Porous Media, Vol. Computational Science and Engineering Series, 2, SIAM, Philadelphia, 2006.
- P. Colella and P. Woodward, The piecewise parabolic method (PPM) for gas-dynamical simulations, J. Comput. Phys. 54 (1984), pp. 174–201.
- J. Douglas, C. Huang Jr. and F. Pereira, The modified method of characteristics with adjust advection, Numer. Math. 83 (1999), pp. 353–369.
- J. Douglas and T. Russell Jr., Numerical solution for convection-dominated diffusion problem based on combining the method of characteristics with finite element or differncen procedures, SIAM J. Numer Anal. 19 (1982), pp. 871–885.
- C. Du and D. Liang, An efficient S-DDM iterative approach for compressible contamination fluid flows in porous media, J. Comput. Phys. 229 (2010), pp. 4501–4521.
- R. Ewing, The mathmematics of reservior simulation, Front. Appl. Math. 1 (1988), pp. 294–318.
- K. Fu and D. Liang, The conservative characteristic FD methods for atmospheric aerosol transport problems, J. Comput. Phys. 305 (2016), pp. 494–520.
- K. Fu and D. Liang, The time second order mass conservative characteristic FDM for advection-diffusion equations in high dimensions, J. Sci. Comput. 73 (2017), pp. 26–49.
- X. Li and J. Shen, Rakkiyappan, Persistent impulsive effects on stability of functional differential equations with finite or infinite delay, Appl. Math. Comput. 329 (2018), pp. 14–22.
- C. Li and Y. Yuan, A modified upwind difference domain decomposition method for convection–diffusion equations, Appl. Numer. Math. 59 (2009), pp. 1584–1598.
- R. Li, Z. Zhou and L. Li, The mass-preserving domain decomposition scheme for solving three-dimensional convection-diffusion equations, Math. Comput. Simulat. 177 (2020), pp. 527–555.
- D. Liang, C. Du and H. Wang, A fractional step ELLAM approach to high-dimensional convection–diffusion problems with forward particle tracking, J. Comput. Phys. 221 (2007), pp. 198–225.
- D. Liang and Z. Zhou, The conservative splitting domain decomposition method for multicomponent contamination flows in porous media, J. Comput. Phys. 400 (2020), pp. 108974.
- H. Rui and M. Tabata, A mass-conservative characteristic finite element scheme for convection–diffusion problems, J. Sci. Comput. 43 (2010), pp. 416–432.
- J. Zhang, D. Yang, S. Shen and J. Zhu, A new MMOCAA-MFE method for compressible miscible displacement in porous media, Appl. Numer. Math. 80 (2014), pp. 65–80.
- S. Zheng and X. Fu, Chatter dynamic analysis for a planning model with the effect of pulse, J. Appl. Anal. Comput. 5 (2015), pp. 767–780.
- Z. Zhou and D. Liang, The mass-preserving and modified-upwind splitting DDM scheme for time-dependent convection-diffusion equations, J. Comput. Appl. Math. 317 (2017), pp. 247–273.
- Z. Zhou, X. Sun, H. Pan and Y. Wang, An efficient characteristic finite difference S-DDM scheme for convection–diffusion equations, Comput. Math. Appl. 80 (2020), pp. 3044–3065.
- L. Zhu, G. Yuan and Q. Du, An explicit-implicit predictor–corrector domain decomposition method for time dependent multi-dimensional convection–diffusion equations, Numer. Math. Theor. Meth. Appl.2 (2019), pp. 301–325.