Back
 AM  Vol.6 No.5 , May 2015
Numerical Modelling and Simulation of Sand Dune Formation in an Incompressible Out-Flow
Yahaya Mahamane Nourialassanenouri@yahoo.fr, Saley Bisso
Abstract: In this paper, we are concerned with computation of a mathematical model of sand dune formation in a water of surface to incompressible out-flows in two space dimensions by using Chebyshev projection scheme. The mathematical model is formulate by coupling Navier-Stokes equations for the incompressible out-flows in 2D fluid domain and Prigozhin’s equation which describes the dynamic of sand dune in strong parameterized domain in such a way which is a subset of the fluid domain. In order to verify consistency of our approach, a relevant test problem is considered which will be compared with the numerical results given by our method.
Cite this paper: Nouri, Y. and Bisso, S. (2015) Numerical Modelling and Simulation of Sand Dune Formation in an Incompressible Out-Flow. Applied Mathematics, 6, 864-876. doi: 10.4236/am.2015.65080.
References

[1]   Prigozhin, L. (1994) Sandpiles and River Networks: Extended Systems with Nonlocal Interactions. Physical Review E, 49, 1161.
http://dx.doi.org/10.1103/physreve.49.1161

[2]   Igbida, N. (2012) Mathematical Models for Sandpile Problems. XLIM-DMI, UMR-CNRS 6172, Workshop MathEnv, Essaouira.

[3]   Nouri, Y.M. and Bisso, S. (2013) Numerical Approach for Solving a Mathematical Model of Sand Dune Formation. Pioneer Journal of Advances in Applied Mathematics, 9, 1-15.

[4]   R?nquist, E.M. (1990) Optimal Spectral Element Methods for the Unsteady 3-Dimensionnal Incompressible Navier-Stokes Equations. Ph.D. Thesis, Mass, Cambridge.

[5]   Azaez, M. (1990) Computation of the Pressure in the Stokes Problem for Incompressible Viscous Fluids by a Spectral Method Collocation. Thesis of Doctorate, Paris-Sud University, Orsay.

[6]   Botella, O. (1996) Resolution des equations de Navier-Stokes par des schemas de Projection Tchebychev. Rapport de recherche No. 3018 de L’Institut national de rechercheen informatique et en automatique (inria).

[7]   Maday, Y., Patera, A.T. and R?nquist, E.M. (1992) The Method for the Approximation of the Stokes Problem. Laboratoire d’Analyse Numerique, Paris VI, 11, fasc.4.

[8]   Chorin, A. (1968) Numerical Simulation of the Navier-Stokes Equations. Mathematics of Computation, 22, 745-762.
http://dx.doi.org/10.1090/S0025-5718-1968-0242392-2

[9]   Temam, R. (1969) On the Approximation of the Solution of Navier-Stokes Equations by the Fractional Steps Method II. Archive for Rational Mechanics and Analysis, 32, 377-385.

[10]   Azaez, M., Bernardi, C. and Grundmann, M. (1994) Spectral Methods Applied to Porous Media Equations. East-West Journal of Numerical Mathematics, 2, 91-105.

[11]   Brezzi, F. (1974) On the Existence, Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrangian Multipliers. R.A.I.R.O, R2, 129-151.

[12]   Hesthaven, J.S., Gottlieb, S. and Gottlieb, D. (2007) Spectral Methods for Time-Dependent Problems. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511618352

[13]   Trefethen, L.N. (2000) Spectral Methods in MATLAB.
http://dx.doi.org/10.1137/1.9780898719598

[14]   Canuto, C., Bernardi, C. and Maday, Y. (1986) Generalized Inf-Sup Condition for Chebyshev Approximation of the Navier-Stokes Equations. Technical Report, No. 86-61, ICASE.

[15]   Canuto, C., Hussaini, M.Y., Quarteroni, A. and Zang, T.A. (1988) Spectral Methods in Fluid Dynamics. Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-3-642-84108-8

[16]   Ehrenstein, U. and Peyret, R. (1989) A Chebyshev-Collocation Method for the Navier-Stokes Equations with Application to Double-Diffusive Convection. International Journal for Numerical Methods in Fluids, 9, 427-452.
http://dx.doi.org/10.1002/fld.1650090405

[17]   Azaez, M., Fikri, A. and Labrosse, G. (1994) A Unique Grid Spectral Solver of the nd Cartesian Unsteady Stokes System. Illustrative Numerical Results. Finite Elements in Analysis and Design, 16, 247-260.
http://dx.doi.org/10.1016/0168-874X(94)90068-X

 
 
Top