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1.
This paper deals with the non-stationary incompressible Navier--Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H1 for the velocity, as in most current numerical schemes relying on spatial discretizations of local type. 相似文献
2.
A primitive-variable Riemann method for solution of the shallow water equations with wetting and drying 总被引:1,自引:0,他引:1
P. Sivakumar D.G. Hyams L.K. Taylor W.R. Briley 《Journal of computational physics》2009,228(19):7452-7472
A Riemann flux that uses primitive variables rather than conserved variables is developed for the shallow water equations with nonuniform bathymetry. This primitive-variable flux is both conservative and well behaved at zero depth. The unstructured finite-volume discretization used is suitable for highly nonuniform grids that provide resolution of complex geometries and localized flow structures. A source-term discretization is derived for nonuniform bottom that balances the discrete flux integral both for still water and in dry regions. This primitive-variable formulation is uniformly valid in wet and dry regions with embedded wetting and drying fronts. A fully nonlinear implicit scheme and both nonlinear and time-linearized explicit schemes are developed for the time integration. The implicit scheme is solved by a parallel Newton-iterative algorithm with numerically computed flux Jacobians. A concise treatment of characteristic-variable boundary conditions with source terms is also given. Computed results obtained for the one-dimensional dam break on wet and dry beds and for normal-mode oscillations in a circular parabolic basin are in very close agreement with the analytical solutions. Other results for a forced breaking wave with friction interacting with a sloped bottom demonstrate a complex wave motion with wetting, drying and multiple interacting wave fronts. Finally, a highly nonuniform, coastline-conforming unstructured grid is used to demonstrate an unsteady simulation that models an artificial coastal flooding due to a forced wave entering the Gulf of Mexico. 相似文献
3.
Richard Massy 《Journal of Number Theory》2005,113(2):244-275
In this paper, we introduce a notion of “Galois average” which allows us to give a suitable answer to the question: how can one extend a finite Galois extension E/F by a prime degree extension N/E to get a Galois extension N/F? Here, N/E is not necessarily a Kummer extension. 相似文献
4.
Enea Pagliano Claudio Broglia Miguel Molero Casado Francesco Malatesta 《Journal of solution chemistry》2008,37(10):1393-1409
Activity coefficients of the highly charged electrolytes Mgds, La2ds3, and [Co(en)3]2ds3 (en = ethylenediamine, ds2−=1,5-naphthalenedisulfonate anion), were determined at 298.15 K using liquid-membrane cells. These salts are found not to
display large negative deviations from the Debye-Hückel limiting slope in the dilute regions, which characterize the corresponding
sulfate salts. Theoretical calculations based on the primitive model (charged hard spheres in an unstructured dielectric medium)
reproduce the behavior of these salts correctly up to concentrations of 0.01 mol⋅kg−1 or more (0.1 mol⋅kg−1 for Mgds), although ds2−, far from resembling a charged sphere, is a planar ion with charges distant from one another. The Pitzer model parameter
values are reported for the activity and osmotic coefficients. 相似文献
5.
6.
In this paper we prove that the language of all primitive (strongly primitive) words over a nontrivial alphabet can be generated by certain types of Marcus contextual grammars. 相似文献
7.
A decomposition of the complete 7-partite graph on 28 vertices where each set in the partition has four vertices is given. Several unusual properties of this decomposition are discussed, giving rise to several natural questions. 相似文献
8.
The present paper reports on a modified pressure implicit predictor corrector type scheme for solving the flow governing equations, in which a consistent formulation is combined with a multi-grid solver for the pressure correction. In addition a parabolic sublayer (PSL) approach for the treatment of the flow in the vicinity of solid walls is critically evaluated in terms of accuracy and computational efficiency. The lid-driven cavity flow is chosen as the test case and results are presented for Reynolds numbers ranging from 100 to 1000. Predictions with the proposed scheme indicate substantial computational savings and fairly good agreement when compared with previous work. The PSL approach reduces the computing time, but with increasing Reynolds numbers the accuracy of the solutions tends to deteriorate. 相似文献
10.
Abstract We identify ℝ7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for
the unit sphere S6. It is known that a cone over a surface M in S6 is an associative submanifold of ℝ7 if and only if M is almost complex in S6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S6 are the equation for primitive maps associated to the 6-symmetric space G2=T2, and use this to explain some of the known results. Moreover, the equation for S1-symmetric almost complex curves in S6 is the periodic Toda lattice, and a discussion of periodic solutions is given.
(Dedicated to the memory of Shiing-Shen Chern)
* Partially supported by NSF grant DMS-0529756. 相似文献