Characteristics Collocation Method of Compressible Miscible Displacement with Dispersion

DOI: 10.4236/jamp.2015.31012   PDF   HTML   XML   3,230 Downloads   3,595 Views  

Abstract

The compressible miscible displacement in a porous media is considered in this paper. The problem is a nonlinear system with dispersion in non-periodic space. The concentration is treated by a characteristics collocation method, and the pressure is treated by an orthogonal collocation method. Optimal order estimates are derived.

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Ma, N. and Lu, X. (2015) Characteristics Collocation Method of Compressible Miscible Displacement with Dispersion. Journal of Applied Mathematics and Physics, 3, 86-91. doi: 10.4236/jamp.2015.31012.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Douglas Jr., J. and Roberts, J.E. (1983) Numerical Methods for a Model for Compressible Miscible Displacement in Porous Media. Math. Comp., 41, 441-459. http://dx.doi.org/10.1090/S0025-5718-1983-0717695-3
[2] Russell, T.F. (1985) Time Stepping along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Dis-placement in Porous Media. SIAM. J Numer. Anal., 17, 970-1013. http://dx.doi.org/10.1137/0722059
[3] Dougals, J. and Dupont, T. (1974) Lecture Notes in Math. Vol. 385, Springer-Verlag, Berlin.
[4] Fernandes, R.L. and Fairweather, G. (1993) Analysis of Alternating Direction Collocation Methods for Parabolic and Hyperbolic Problems in Two Space Variables. Numerical Methods for Partial Differential Equations, 9, 191-211. http://dx.doi.org/10.1002/num.1690090207
[5] Bialecki, B. and Cai, X. (1994) H1-Norm Error Bounds for Piecewise Hermite Bicubic Orthogonal Space Collocation Schemes for Elliptic Boundary Value Problems. SIAM. J Numer.Anal., 31, 1128-1146. http://dx.doi.org/10.1137/0731059
[6] Ma, N., Lu, T. and Yang, D. (2006) Analysis of Incompressible Miscible Dis-placement in Porous Media by a Characteristics Collation Method. Numer. Methods for Partial Differential Eq., 22, 797-814.
[7] Yuan, Y. (1992) Time Stepping along Characteristics for the Finite Element Approximation of Com-pressible Miscible Displacement in Porous Media. Mathematica Numerica Sinica, 14, 385-400.
[8] Ma, N. (1906) Orthogonal Collocation Method for Miscible Displacement with Dispersion. Journal of Shandong University (Natural Science), 46, 78-81.
[9] Douglas Jr., J. and Roberts, J.E. (1983) Numerical Methods for a Model for Compressible Miscible Displacement in Porous Media. Math. Comp., 41, 441-459. http://dx.doi.org/10.1090/S0025-5718-1983-0717695-3
[10] Russell, T.F. (1985) Time Stepping along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Dis-placement in Porous Media. SIAM. J Numer. Anal., 17, 970-1013. http://dx.doi.org/10.1137/0722059
[11] Dougals, J. and Dupont, T. (1974) Lecture Notes in Math. Vol. 385, Springer-Verlag, Berlin.
[12] Fernandes, R.L. and Fairweather, G. (1993) Analysis of Alternating Direction Collocation Methods for Parabolic and Hyperbolic Problems in Two Space Variables. Numerical Methods for Partial Differential Equations, 9, 191-211. http://dx.doi.org/10.1002/num.1690090207
[13] Bialecki, B. and Cai, X. (1994) H1-Norm Error Bounds for Piecewise Hermite Bicubic Orthogonal Space Collocation Schemes for Elliptic Boundary Value Problems. SIAM. J Numer.Anal., 31, 1128-1146. http://dx.doi.org/10.1137/0731059
[14] Ma, N., Lu, T. and Yang, D. (2006) Analysis of Incompressible Miscible Dis-placement in Porous Media by a Characteristics Collation Method. Numer. Methods for Partial Differential Eq., 22, 797-814.
[15] Yuan, Y. (1992) Time Stepping along Characteristics for the Finite Element Approximation of Com-pressible Miscible Displacement in Porous Media. Mathematica Numerica Sinica, 14, 385-400.
[16] Ma, N. (1906) Orthogonal Collocation Method for Miscible Displacement with Dispersion. Journal of Shandong University (Natural Science), 46, 78-81.

  
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