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111.
A numerical technique for the modelling of shallow water flow in one and two dimensions is presented in this work along with the results obtained in different applications involving unsteady flows in complex geometries. A cell‐centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured cells is presented. The discretization of the bed slope source terms is done following an upwind approach. In some applications a problem arises when the flow propagates over adverse dry bed slopes, so a special procedure has been introduced to model the advancing front. It is shown that this modification reproduces exactly steady state of still water in configurations with strong variations in bed slope and contour. The applications presented are mainly related with unsteady flow problems. The scheme is capable of handling complex flow domains as will be shown in the simulations corresponding to the test cases that are going to be presented. Comparisons of experimental and numerical results are shown for some of the tests. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
112.
Let f be the function which maps conformally a given doubly-connected domain Ω onto a circular annulus, and let . In this paper we consider the problem of determining the main singularities of the function H in compl(). Our purpose is to provide information regarding the location and nature of such singularities, and to explain how this information can be used to improve the efficiency of certain expansion methods for numerical conformal mapping. 相似文献
113.
114.
D.E. Edmunds R. Hurri-Syrjnen 《Journal of Mathematical Analysis and Applications》2005,310(2):424-435
For bounded Lipschitz domains D in it is known that if 1<p<∞, then for all β[0,β0), where β0=p−1>0, there is a constant c<∞ with for all . We show that if D is merely assumed to be a bounded domain in that satisfies a Whitney cube-counting condition with exponent λ and has plump complement, then the same inequality holds with β0 now taken to be . Further, we extend the known results (see [H. Brezis, M. Marcus, Hardy's inequalities revisited, Dedicated to Ennio De Giorgi, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997–1998) 217–237; M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, A. Laptev, A geometrical version of Hardy's inequality, J. Funct. Anal. 189 (2002) 537–548; J. Tidblom, A geometrical version of Hardy's inequality for W1,p(Ω), Proc. Amer. Math. Soc. 132 (2004) 2265–2271]) concerning the improved Hardy inequality c=c(n,p), by showing that the class of domains for which the inequality holds is larger than that of all bounded convex domains. 相似文献
115.
Thomas Bartsch Anna Maria Micheletti Angela Pistoia 《Calculus of Variations and Partial Differential Equations》2006,26(3):265-282
We study the existence of sign changing solutions to the slightly subcritical problem
where ω is a smooth bounded domain in ℝ
N
, N ≥ 3, p = (N + 2)/(N − 2) and ɛ > 0. We prove that, for ɛ small enough, there exist N pairs of solutions which change sign exactly once. Moreover, the nodal surface of these solutions intersects the boundary of ω, provided some suitable conditions are satisfied.The second and the third authors are supported by M.U.R.S.T. project “Metodi variazionali e topologici nello studio di fenomeni non lineari”
Mathematics Subject Classification (2000) 35J20, 35J65 相似文献
116.
Zdzislaw Brzezniak Yuhong Li 《Transactions of the American Mathematical Society》2006,358(12):5587-5629
We introduce a notion of an asymptotically compact (AC) random dynamical system (RDS). We prove that for an AC RDS the -limit set of any bounded set is nonempty, compact, strictly invariant and attracts the set . We establish that the D Navier Stokes Equations (NSEs) in a domain satisfying the Poincaré inequality perturbed by an additive irregular noise generate an AC RDS in the energy space . As a consequence we deduce existence of an invariant measure for such NSEs. Our study generalizes on the one hand the earlier results by Flandoli-Crauel (1994) and Schmalfuss (1992) obtained in the case of bounded domains and regular noise, and on the other hand the results by Rosa (1998) for the deterministic NSEs.
117.
Belhachmi Zakaria; Bucur Dorin; Sac-Epee Jean-Marc 《IMA Journal of Numerical Analysis》2006,26(4):790-810
** Email: belhach{at}poncelet.univ-metz.fr*** Email: bucur{at}math.univ-metz.fr**** Email: jmse{at}math.univ-metz.fr We study the NeumannLaplacian eigenvalue problem in domainswith multiple cracks. We derive a mixed variational formulationwhich holds on the whole geometric domain (including the cracks)and implements efficient finite-element discretizations forthe computation of eigenvalues. Optimal error estimates aregiven and several numerical examples are presented, confirmingthe efficiency of the method. As applications, we numericallyinvestigate the behaviour of the low eigenvalues in domainswith a large number of cracks. 相似文献
118.
Considered as a geophysical fluid, the polluted atmosphere shares the shallow domain characteristics with other natural large-scale fluids such as seas and oceans. This means that its domain is excessively greater horizontally than in the vertical dimension, leading to the classic hydrostatic approximation of the Navier–Stokes equations. In the past there has been proved a convergence theorem for this model with respect to the ocean, without considering pollution effects. The novelty of this present work is to provide a generalization of their result translated to the atmosphere, extending the fluid velocity equations with an additional convection–diffusion equation representing pollutants in the atmosphere. 相似文献
119.
120.
Alain DAMLAMIAN 《数学年刊B辑(英文版)》2018,39(2):335-344
A recent joint paper with Doina Cioranescu and Julia Orlik was concerned with the homogenization of a linearized elasticity problem with inclusions and cracks(see[Cioranescu, D., Damlamian, A. and Orlik, J., Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymptotic Analysis, 82, 2013, 201–232]). It required uniform estimates with respect to the homogenization parameter. A Korn inequality was used which involves unilateral terms on the boundaries where a nopenetration condition is imposed. In this paper, the author presents a general method to obtain many diverse Korn inequalities including the unilateral inequalities used in [Cioranescu, D., Damlamian, A. and Orlik, J., Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymptotic Analysis, 82, 2013, 201–232]. A preliminary version was presented in [Damlamian, A., Some unilateral Korn inequalities with application to a contact problem with inclusions, C. R. Acad. Sci. Paris, Ser. I,350, 2012, 861–865]. 相似文献