Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A variational formalism for steady flow of dusty fluid problems. I

Authors: Adnan A. Hajj and Elsayed F. Elshehawey
Journal: Quart. Appl. Math. 46 (1988), 275-283
MSC: Primary 76T05
DOI: https://doi.org/10.1090/qam/950602
MathSciNet review: 950602
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A general variational formalism for the solution of steady flow of dusty fluids is given. The associated boundary conditions are enforced by suitable terms in a functional which is stationary at the solution of the given problem and consequently the expansion functions used need not satisfy any of the boundary conditions.

References [Enhancements On Off] (What's this?)

  • [1] Kenneth E. Barrett, Minimax principle for magnetohydrodynamic channel flow, Z. Angew. Math. Phys. 27 (1976), no. 5, 613–619 (English, with German summary). MR 0434114, https://doi.org/10.1007/BF01591173
  • [2] K. E. Barrett and G. Demunshi, Finite element solutions of convective diffusion problems, International Journal for Numerical Methods in Engineering, Vol. 14, 1511-1524 (1979)
  • [3] L. M. Delves and C. A. Hall, An implicit matching principle for global element calculations, J. Inst. Math. Appl. 23 (1979), no. 2, 223–234. MR 529368
  • [4] L. M. Delves and C. Phillips, A fast implementation of the global element method, J. Inst. Math. Appl. 25 (1980), no. 2, 177–197. MR 571978
  • [5] A. K. Didwania and G. M. Homsy, Rayleigh--Taylor instabilities in fluidized beds, Indust. Eng. Chem. Fundam. 20, 318-323 (1981)
  • [6] A Haj, C. Phillips, and L. M. Delves, The global element method for stationary advective problems, Internat. J. Numer. Meth. Engng. 15, 167-175 (1980)
  • [7] S. G. Mikhlin, The numerical performance of variational methods, Translated from the Russian by R. S. Anderssen, Wolters-Noordhoff Publishing, Groningen, 1971. MR 0278506
  • [8] A. Moult, D. Burley and H. Rawson, The numerical solution of two-dimensional steady flow problems by the finite element method, Internat. J. Numer. Meth. Engng. 14, 11-35 (1979)
  • [9] P. S. S. Rao, Unsteady flow of a dusty viscous liquid through circular cylinder, Defence Sci. J. 19, 135 (1969)
  • [10] P. G. Saffman, On the stability of laminar flow of a dusty gas, J. Fluid Mech. 13 (1962), 120–128. MR 0137418, https://doi.org/10.1017/S0022112062000555
  • [11] D. M. Sloan, Extremum principles for magnetohydrodynamic channel flow, Z. Angew. Math. Phys. 24, 689-698 (1973)
  • [12] P. Smith, Some applications of extremum principles to magneto-hydrodynamic pipe flow, Proc. Roy. Soc. Lond. A336, 211-222 (1974)
  • [13] Itiro Tani, Steady flow of conducting fluids in channels under transverse magnetic fields, with consideration of Hall effect, J. Aerospace Sci. 29 (1962), 297–305. MR 0135800
  • [14] N. C. Wenger, A variational principle for magnetohydrodynamic channel flow, J. Fluid Mech. 43, 211-224 (1970)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 76T05

Retrieve articles in all journals with MSC: 76T05

Additional Information

DOI: https://doi.org/10.1090/qam/950602
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society