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991.
A. Castro 《Advances in Mathematics》2008,219(6):1916-1936
In this paper we study a one-dimensional model equation with a nonlocal flux given by the Hilbert transform that is related with the complex inviscid Burgers equation. This equation arises in different contexts to characterize nonlocal and nonlinear behaviors. We show global existence, local existence, blow-up in finite time and ill-posedness depending on the sign of the initial data for classical solutions. 相似文献
992.
Spatial discretization of transport and transformation processes in porous media requires techniques that handle general geometry, discontinuous coefficients and are locally mass conservative. Multi‐point flux approximation (MPFA) methods are such techniques, and we will here discuss some formulations on triangular grids with further application to the nonlinear Richards equation. The MPFA methods will be rewritten to mixed form to derive stability conditions and error estimates. Several MPFA versions will be shown, and the versions will be discussed with respect to convergence, symmetry and robustness when the grids are rough. It will be shown that the behavior may be quite different for challenging cases of skewness and roughness of the simulation grids. Further, we apply the MPFA discretization approach for the Richards equation and derive new error estimates without extra regularity requirements. The analysis will be accompanied by numerical results for grids that are relevant for practical simulation. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
993.
This article looks at the hydrodynamic elastico-viscous fluid over a stretching surface. The equations governing the flow are reduced to ordinary differential equations, which are analytically solved by applying an efficient technique namely the homotopy analysis method (HAM). The solutions for the velocity components are computed. The numerical values of wall skin friction coefficients are also tabulated. The present HAM solution is compared with the known exact solution for the two-dimensional flow and an excellent agreement is found. 相似文献
994.
We develop a parallel computational algorithm for simulating models of gel dynamics where the gel is described by two phases, a networked polymer and a fluid solvent. The models consist of transport equations for the two phases, two coupled momentum equations, and a volume‐averaged incompressibility constraint. Multigrid with Vanka‐type box‐relaxation scheme is used as preconditioner for the Krylov subspace solver (GMRES) to solve the momentum and incompressibility equations. Through numerical experiments of a model problem, the efficiency, robustness and scalability of the algorithm are illustrated. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
995.
We study nonlinear resonance in viscous gravity-driven films flowing over undulated substrates. Numerical solution of the full, steady Navier–Stokes equations is used to follow the emergence of the first few free-surface harmonics with increasing wall amplitude, and to study their parametric dependence on film thickness, inertia and capillarity. Bistable resonance is computed for steep enough bottom undulations. As an analytic approach, we apply the integral boundary-layer method and derive an asymptotic equation valid for rather thin films. The analysis recovers the key numerical findings and provides qualitative understanding. It shows that higher harmonics are generated by a nonlinear coupling of the wall with lower-order harmonics of the free surface. It also accounts for bistable resonance, and produces a minimum model whose solution is similar to that of the Duffing oscillator. 相似文献
996.
The directed flow of protons is studied in the quark-gluon string model as a function of the impact parameter for S+S and Pb+Pb reactions at 160 AGeV/c. A significant reduction of the directed flow in midrapidity range, which can lead to the development of the antiflow, is found due to the absorption of early emitted particles by massive spectators (shadowing effect). This effect can mimic the formation of the quark-gluon plasma (QGP). However, in the absorption scenario the antiflow is stronger for the system of light colliding nuclei than for the heavy ones, while in the case of the plasma creation the effect should be opposite. 相似文献
997.
Summary. We derive a set of asymptotically exact coupled amplitude-streaming flow ({CASF}) equations governing the evolution of weakly nonlinear nearly inviscid multimode Faraday waves and the associated
streaming flow in finite geometries. The streaming flow is found to play a particularly important role near mode interactions.
Such interactions come about either through a suitable choice of parameters or through breaking of degeneracy among modes
related by symmetry. An example of the first case is provided by the interaction of two nonaxisymmetric modes in a circular
container with different azimuthal wavenumbers. The second case arises when the shape of the container is changed from square
to slightly rectangular, or from circular to slightly noncircular but with a plane of symmetry. The generation of streaming
flow in each of these cases is discussed in detail and the properties of the resulting CASF equations are described. A preliminary
analysis suggests that these equations can resolve discrepancies between existing theory and experimental results in the first
two of the above cases. 相似文献
998.
In the design process of hydrodynamical and aerodynamical technical applications, the numerical simulation of massively separated vortical flow is crucial for predicting, for example, lift or drag. To obtain reliable numerical results, it is mandatory to accurately predict the physical behavior of vortices. Thus, the dominant vortical flow structures have to be resolved in detail, which requires a local grid refinement and certain adaptation techniques. In this paper, a vortex flow structure adaptation algorithm is presented, which is particularly designed for local grid refinement at vortex axes positions and associated vortex core border locations. To this end, a fast and efficient vortex axis detection scheme is introduced and the algorithm for the vortex core border determination is explained. As the interaction between vortices makes the assignment of grid points to a certain vortex axis difficult, a helicity‐based vortex distinction approach in combination with a geometrical rotational sensor is developed. After describing the combined different techniques in detail, the vortex feature adaptation algorithm is applied to analytical and more realistic examples, which show that the described grid adaptation algorithm is able to enhance the grid cell resolution locally such that all significant vortical flow phenomena are resolved. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
999.
Information of flow-induced vibration (FIV) in two-phase flow with wire coil inserts at atmospheric pressure, is presented in this study. FIV was measured in an upward vertical tube for four different wire coil inserts using an air–water mixture as process fluid. Vibration increased along with mass flux and quality. The narrower wire coils produced more vibration. The FIV prediction correlation for two-phase flow with wire coil inserts was experimentally developed with coefficient correlation value of 0.956. 相似文献
1000.
Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献