ABSTRACT This paper describes a numerical solution for two dimensional partial differential equations modeling (or arising from) a fluid flow and transport phenomena. The diffusion equation is discretized by the Nodal methods. The saturation equation is solved by a finite volume method. We start with incompressible single-phase flow and move step-by-step to the black-oil model and compressible two phase flow. Numerical results are presented to see the performance of the method, and seem to be interesting by comparing them with other recent results.
Cite this paper
nullA. Elakkad, A. Elkhalfi and N. Guessous, "Combined Nodal Method and Finite Volume Method for Flow in Porous Media," Wireless Sensor Network, Vol. 2 No. 3, 2010, pp. 227-232. doi: 10.4236/wsn.2010.23030.
 J. W. Song and J. K. Kim, “An efficient nodal method for transient calculations in light water reactors,” Nuclear Technology, Vol. 103, pp. 157–167, 1993.
N. K. Gupta, “Nodal methods for three-dimensional simulators,” Progress in Nuclear Energy, Vol. 7, pp. 127–149, 1981.
R. D. Lawrence, “Progress in nodal methods for the solution of the neutron diffusion and transport equations,” Progress in Nuclear Energy, Vol. 17, pp. 271–301, 1986.
R. Eymard, T. Gallouet, and R. Herbin, “Finite volume methods,” In: P. G. Ciarlet and J. L. Lions, Ed., Hand- book of Numerical Analysis, Elsevier Science B.V., Amsterdam, Vol. 7, pp. 713–1020, 1997.
A. Shamsai and H. R. Vosoughifar, “Finite volume discretization of flow in porous media by the MATLAB system,” Scientia Iranica, Vol. 11, No. 1–2, pp. 146–153, 2004.
H. Finnemann, F. Bennewitz, and M. R. Wagner, “Interface current techniques for multidimensional reactor calculations,” Atomkernenergie, Vol. 30, pp. 123–128, 1977.
H. D. F. Fisher and H. Finnemann, “The nodal integration method—A diverse solver for neutron diffusion pro- blems,” Atomkernenergie-Kerntechnik, Vol. 39, pp. 229– 236, 1981.
R. D. Lawrence and J. J. Dorning, “A nodal Green's function method for mutidimensional neutron diffusion calculations,” Nuclear Science and Engineering, Vol. 76, pp. 218–231, 1980.
B. Montagnini, P. Soraperra, C. Trantavizi, M. Sumini, and D. M. Zardini, “A well-balanced coarse-mesh flux expansion method,” Annals of Nuclear Energy, Vol. 21, pp. 45–53, 1994.
G. J. E. Aarnes, T. Gimse, and K.-A. Lie, “An introduction to the numerics of flow in porous media using Matlab,” In: G. Hasle, K.-A. Lie, and E. Quak, Ed., Geometrical Modeling, Numerical Simulation and opti- mization: Industrial Mathematics at SINTEF, Springer Verlag, pp. 265–306, 2007.
D. Burkle and M. Ohlberger, “Adaptive finite volume methods for displacement problems in porous media,” Computing and Visualization in Science, Vol. 5, No. 2, 2002.