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
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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.
- Kenneth E. Barrett, Minimax principle for magnetohydrodynamic channel flow, Z. Angew. Math. Phys. 27 (1976), no. 5, 613–619 (English, with German summary). MR 434114, DOI https://doi.org/10.1007/BF01591173
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)
- 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
- 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
A. K. Didwania and G. M. Homsy, Rayleigh—Taylor instabilities in fluidized beds, Indust. Eng. Chem. Fundam. 20, 318–323 (1981)
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)
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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)
P. S. S. Rao, Unsteady flow of a dusty viscous liquid through circular cylinder, Defence Sci. J. 19, 135 (1969)
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D. M. Sloan, Extremum principles for magnetohydrodynamic channel flow, Z. Angew. Math. Phys. 24, 689–698 (1973)
P. Smith, Some applications of extremum principles to magneto-hydrodynamic pipe flow, Proc. Roy. Soc. Lond. A336, 211–222 (1974)
- Itiro Tani, Steady flow of conducting fluids in channels under transverse magnetic fields, with consideration of Hall effect, J. Aero/Space Sci. 29 (1962), 297–305. MR 135800
N. C. Wenger, A variational principle for magnetohydrodynamic channel flow, J. Fluid Mech. 43, 211–224 (1970)
K. E. Barrett, Minimax principle for magnetohydrodynamic channel flow, J. Appl. Math. Phys. (ZAMP) 27, 613–619 (1976)
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)
L. M. Delves and C. A. Hall, An implicit matching principle for global element calculations, J. Inst. Math. Applics. 23, 223–234 (1979)
L. M. Delves and C. Phillips, A fast implementation of the global element method, J. Inst. Math. Applics. 25, 177–197 (1980)
A. K. Didwania and G. M. Homsy, Rayleigh—Taylor instabilities in fluidized beds, Indust. Eng. Chem. Fundam. 20, 318–323 (1981)
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)
S. G. Mikhlin, The numerical performance of variational methods, Noordhoff, Amsterdam (1971)
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)
P. S. S. Rao, Unsteady flow of a dusty viscous liquid through circular cylinder, Defence Sci. J. 19, 135 (1969)
P. G. Saffman, On the stability of laminar flow of a dusty gas, J. Fluid Mech. 13, 120 (1962)
D. M. Sloan, Extremum principles for magnetohydrodynamic channel flow, Z. Angew. Math. Phys. 24, 689–698 (1973)
P. Smith, Some applications of extremum principles to magneto-hydrodynamic pipe flow, Proc. Roy. Soc. Lond. A336, 211–222 (1974)
I. Tani, Steady flow of conducting fluids in channels under transverse magnetic fields, with consideration of Hall effect, J. Aero. Sci. 29, 297–304 (1962)
N. C. Wenger, A variational principle for magnetohydrodynamic channel flow, J. Fluid Mech. 43, 211–224 (1970)
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© Copyright 1988
American Mathematical Society
