Advertisement

Unsteady Two-Dimensional Problems

  • Akpofure E. Taigbenu
Chapter

Abstract

The additional dimension of time which is incorporated into the two-dimensional steady problems addressed in the earlier chapter allows for solutions that provide information on the time history of the behaviour of the primary scalar or vector variable. Such solutions do, in most cases, give better representation of the behaviour of engineering systems which are usually under dynamic forces that alter equilibrium states from time to time.

Keywords

Green Element Transient Problem Early Chapter Semianalytic Solution Uniform Time Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Morse, P.M. and H. Feshbach, Methods of Theoretical Physics, Vol. 1, McGraw-Hill, NY., 1953.Google Scholar
  2. 2.
    Shaw, R.P., “An Integral Equation Approach to Diffusion”, Int. J. Heat and mass Transfer, 17, 693–699, 1974.Google Scholar
  3. 3.
    Banerjee, P.K. and R. Butterfield, Boundary Element Methods in Engineering Science, McGraw- Hill, London UK, 1981.Google Scholar
  4. 4.
    Taigbenu, A.E. and J.A. Liggett, “Boundary Element calculations of Diffusion Equation”, J. Engineering Mech., 111 (3), pp. 311–328, 1985.CrossRefGoogle Scholar
  5. 5.
    Abramowitz, M. and I.A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, 1970.Google Scholar
  6. Theis, C.V., “The relation between the lowering of the Piezometric surface and the rate and duration of discharge of a well using groundwater storage”, Trans. Amer. Geophysical Union,16 pp. 519524,1935.Google Scholar
  7. 7.
    Jacob„ C.E., “Radial flow in a leaky artesian aquifer”, Trans. Amer. Geophysical Union, 27 (2), pp. 198–208, 1946.CrossRefGoogle Scholar
  8. 8.
    Bear, J., Hydraulics of Groundwater, McGraw-Hill, 1979.Google Scholar
  9. 9.
    Cleary, R.W., Groundwater Pollution and Hydrology: Mathematical models and computer programs, Report No. 78-WR-15, Water resources Program, Princeton University, 1978.Google Scholar
  10. 10.
    Yeh, G.T., “Solution of groundwater flow equations using an orthogonal finite element scheme”, Proc. of Int. AMSE Conf. on modelling and Simulations, Tassin, France, pp. 219–351, 1983.Google Scholar
  11. 11.
    Warrick, A.W. and D.O. Lomen, Time-dependent linearized infiltration: III. Strip and Disc sources, Soil Sci. Soc. Am. J, 40, pp. 639–643, 1976.CrossRefGoogle Scholar
  12. 12.
    Tsai, W.F., C-I. Chen and H-C. Tien, Finite analytic numerical solutions for unsaturated flow with irregular boundaries, ASCE J. Hydr. Eng., 119 (11), pp. 1274–1298, 1993.CrossRefGoogle Scholar
  13. 13.
    Yeh, G.T., FEMWATER: A Finite-element model of water flow through saturated-unsaturated porous media, 1st. Rev. Rep. ONRL-5567/R1, Oak Ridge Mat. Lab, Oak Ridge, TN, 1987.Google Scholar
  14. 14.
    Taigbenu, A.E., and O.O.Onyejekwe, “Green Element simulations of the Transient Unsaturated Flow Equation,” Applied Mathematical Modelling, 19, pp. 675–684, 1995.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Akpofure E. Taigbenu
    • 1
  1. 1.Department of Civil and Water EngineeringNational University of Science and TechnologyBulawayoZimbabwe

Personalised recommendations