Numerical solution of Navier stokes equation using control volume and finite element method

Authors

  • Musa Adam Aigo Umm Al-Qura University College Al-QunfudahMathematics department, Macca, KSA

DOI:

https://doi.org/10.14419/ijamr.v5i1.5616

Keywords:

Navier stokes equation, Finite element, control volume, Projection.

Abstract

The aim of this paper is twofold first we will  provide a numerical solution of the Navier Stokes equation using the Projection technique and finite element method. The problem will be introduced in weak formulation and a Finite Element method will be developed, then solve in a fast way the sparse system derived. Second, the projection method with Control volume approach will be applied to get a fast solution, in iterations count.

References

[1] Galdi, Giovanni P. An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Springer Monographs in Mathematics 2011.

[2] Temam, Roger. Navier-Stokes equations and nonlinear functional analysis. CBMS-NSF regional conference series in applied mathematics, publisher Society for Industrial and Applied Mathematics, Philadelphia, ISBN 0-89871-183-5, year = 1983.

[3] A.J. Chorin. On the convergence of discrete approximations to the Navier-Stokes equations. Math. Comp, 23 (1969), pp. 341-353..

[4] R. Temam. Sur l'approximation de la solution des equations de Navier-Stokes par la methode des pas fractionnaires II. Arch. Rat. Mech. Anal, 33 (1969), pp. 377-385..

[5] Chorin, A. J. The numerical solution of the Navier-Stokes equations for an incompressible fluid. Bull. Am. Math. Soc. 73 (1967) 928-931..

[6] Chorin, A. J.; J. E. Marsden. A Mathematical Introduction to Fluid Mechanics (3rd ed.). Springer-Verlag. (1993) ISBN 0-387-97918-2.

[7] Chorin, A. J. A numarical method for solving imcompressible viscous flow problems. Journal of computational physics 135, 118-125 1997..

[8] F.H. Harlow and J.E. Welch. Phys. Fluids 8, 2182 1965 .8

[9] Francis H Harlow, Anthony A Amsden. A numerical fluid dynamics calculation method for all flow speeds. Journal of Computational physics. Volume 8, Issue 2,(1971) 197-213.

[10]Claude Brezinski. Projection methods for systems of equations Studies in computational mathematics 7. ISBN 0444 82 7773.

[11]J.N. Reddy. An introduction to the finite element method. Third edition. McGraw Hill Newyork 2005.

[12]Klaus Jurgen Bathe. Finite element procedures. Prentice hall Pearson Education,Inc. ISBN 978 0979004902.

[13]E. M.Ronquist. A Domain Decomposition Solver for the Steady Navier-Stokes Equation. ICOSAHOM'95 Proceedings of the Third International Conference on Spectral and High Order Methods. 1996 Houston Journal of Mathematics, University of Houston:

[14]X.C. Cai and O.B. Widlund, Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. SIAM J. Numer. Anal. , 30(4), pp. 936-952 , 1993.

Downloads

Additional Files

Published

2016-02-23

Issue

Section

Articles