Special finite-difference approximations of flow equations in terms of stream function, vorticity and velocity components for viscous incompressible liquid in curvilinear orthogonal coordinates

Harijs Kalis

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 1, page 165-174
  • ISSN: 0010-2628

Abstract

top
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.

How to cite

top

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 34.1 (1993): 165-174. <http://eudml.org/doc/247516>.

@article{Kalis1993,
abstract = {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.},
author = {Kalis, Harijs},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {finite-difference hydrodynamics},
language = {eng},
number = {1},
pages = {165-174},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
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},
url = {http://eudml.org/doc/247516},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Kalis, Harijs
TI - Special finite-difference approximations of flow equations in terms of stream function, vorticity and velocity components for viscous incompressible liquid in curvilinear orthogonal coordinates
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 1
SP - 165
EP - 174
AB - 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.
LA - eng
KW - finite-difference hydrodynamics
UR - http://eudml.org/doc/247516
ER -

References

top
  1. Doolan E.P., Miller J.J.H., Schilders W.H.A., Uniform Numerical Methods for Problems with Initial and Boundary Layers, Dublin, 1980. Zbl0527.65058MR0610605
  2. 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) MR0070367
  3. Buleev N.Y., Three Dimensional Model of Turbulent Exchange (in Russian), Moscow, Nauka, 1989. MR1007137
  4. Samarsky A.A., Theory of Difference Schemes (in Russian), Moscow, Nauka, 1977. MR0483271
  5. Milne L.M., Thomson C.B.E., Theoretical Hydrodynamics, London-New York, 1960. Zbl0164.55802MR0112435
  6. Kochin N.E., Vector Calculus and the Introduction to Tensor Calculus (in Russian), Moscow, Nauka, 1965. 
  7. Angot A., Complements des mathématiques. A l'usage des ingenieurs de l'electrotechnique et des telecommunications, Paris, 1957. 
  8. 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. 
  9. 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. MR0942126
  10. Gantmacher J.R., Theory of Matrices (in Russian), Moscow, Nauka, 1967. 
  11. Ilhyn A.M., Difference scheme for differential equations with small parameter at highest derivative (in Russian), Mathematical Notes 6 (1969), 234-248. (1969) 

NotesEmbed ?

top

You must be logged in to post comments.