Article Contents
Article Contents

# Two-Scale numerical simulation of sand transport problems

• In this paper we consider the model built in [3] for short term dynamics of dunes in tidal area. We construct a Two-Scale Numerical Method based on the fact that the solution of the equation which has oscillations Two-Scale converges to the solution of a well-posed problem. This numerical method uses on Fourier series.
Mathematics Subject Classification: Primary: 35K65, 35B25, 35B10; Secondary: 92F05, 86A60.

 Citation:

•  [1] G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal., 23 (1992), 1482-1518.doi: 10.1137/0523084. [2] P. Aillot, E. Frénod and V. Monbet, Long term object drift in the ocean with tide and wind, Multiscale Model. and Simul., 5 (2006), 514-531 (electronic).doi: 10.1137/050639727. [3] I. Faye, E. Frénod and D. Seck, Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment, Discrete Contin. Dyn. Syst., 29 (2011), 1001-1030.doi: 10.3934/dcds.2011.29.1001. [4] E. Frénod and A. Mouton, Two-dimensional finite Larmor radius approximation in canonical gyrokinetic coordinates, J. of Pure Appl. Math. Adv. Appl., 4 (2010), 135-169. [5] E. Frénod, A. Mouton and E. Sonnendrücker, Two-Scale numerical simulation of the weakly compressible 1D isentropic Euler equations, Numer. Math., 108 (2007), 263-293.doi: 10.1007/s00211-007-0116-8. [6] E. Frénod, F. Salvarani and E. Sonnendrücker, Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method, Math. Models Methods Appl. Sci., 19 (2009), 175-197.doi: 10.1142/S0218202509003395. [7] E. Frénod, P. A. Raviart and E. Sonnendrücker, Two scale expansion of a singularly perturbed convection equation, J. Math. Pures Appl. (9), 80 (2001), 815-843.doi: 10.1016/S0021-7824(01)01215-6. [8] O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and quasilinear equations of parabolic type, (Russian) Translated from the Russian by S. Smith, Translation of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, R.I., 1968. [9] A. Mouton, Approximation Multi-échelles de L'équation de Vlasov, Thèse de doctorat, Strasbourg, 2009. [10] A. Mouton, Two-Scale semi-Lagrangian simulation of a charged particule beam in a periodic focusing channel, Kinet. Relat. Models, 2 (2009), 251-274.doi: 10.3934/krm.2009.2.251. [11] G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20 (1989), 608-623.doi: 10.1137/0520043.