Special finite-difference approximations of flow equations in terms of stream function, vorticity and velocity components for viscous incompressible liquid in curvilinear orthogonal coordinates
Kalis, Harijs
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 165-174 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

The Navier-Stokes equations written in general orthogonal curvilinear coordinates are reformulated with the use of the stream function, vorticity and velocity components. The resulting system id discretized on general irregular meshes and special monotone finite-difference schemes are derived.

Publié le : 1993-01-01
Classification:  65M06,  76D05,  76E99,  76M20 
@article{118566,
     author = {Harijs Kalis},
     title = {Special finite-difference approximations of flow equations  in terms of stream function, vorticity  and velocity components for viscous incompressible liquid in curvilinear orthogonal coordinates},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {165-174},
     zbl = {0783.76060},
     mrnumber = {1240214},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118566}
}

Kalis, Harijs. Special finite-difference approximations of flow equations  in terms of stream function, vorticity  and velocity components for viscous incompressible liquid in curvilinear orthogonal coordinates. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 165-174. http://gdmltest.u-ga.fr/item/118566/

Doolan E.P.; Miller J.J.H.; Schilders W.H.A. Uniform Numerical Methods for Problems with Initial and Boundary Layers, Dublin, 1980. | MR 0610605 | Zbl 0527.65058

Allen D.N.; Southwell R.V. Relaxation methods to determine the motion in two dimensions of viscous fluid past a fixed cylinder, Quart. J. Mech. and Appl. Math. VIII (1955), 129-145. (1955) | MR 0070367

Buleev N.Y. Three Dimensional Model of Turbulent Exchange (in Russian), Moscow, Nauka, 1989. | MR 1007137

Samarsky A.A. Theory of Difference Schemes (in Russian), Moscow, Nauka, 1977. | MR 0483271

Milne L.M.; Thomson C.B.E. Theoretical Hydrodynamics, London-New York, 1960. | MR 0112435 | Zbl 0164.55802

Kochin N.E. Vector Calculus and the Introduction to Tensor Calculus (in Russian), Moscow, Nauka, 1965.

Angot A. Complements des mathématiques. A l'usage des ingenieurs de l'electrotechnique et des telecommunications, Paris, 1957.

Kalis H. Special difference schemes for solving boundary value problems of mathematical physics (in Russian), J. Electronical Modelling, Vol. 8, No. 3, Kiev, 1986, pp. 78-83.

Kalis H. Some special schemes for solving boundary value problems of hydrodynamics and magneto-hydrodynamics in a wide range of changing parameters, Latvia Mathematical Annual, Vol. 31, Riga, 1988, pp. 160-166. | MR 0942126

Gantmacher J.R. Theory of Matrices (in Russian), Moscow, Nauka, 1967.

Ilhyn A.M. Difference scheme for differential equations with small parameter at highest derivative (in Russian), Mathematical Notes 6 (1969), 234-248. (1969)