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61.
The Rayleigh-Stokes-Problem for an edge is solved within
the context of a Maxwell model and the similar solution for a
Navier-Stokes fluid appears as a limiting case of our solution. 相似文献
62.
Harray Yserentant 《Numerische Mathematik》1997,76(1):87-109
Summary. Particle methods are numerical methods designed to solve problems in fluid mechanics and related problems in continuum mechanics.
A general approach to the construction of such particle methods is presented in this article. The particles are no mass points
but possess a finite extension. They can rotate in space and have a spin. The conservation of mass is automatically guaranteed
by the ansatz. The forces of interaction between the particles are derived in a canonical way from the force laws of continuum
mechanics and are directly based on a regularized stress tensor. In the absence of external forces and of heat sources and
sinks, momentum, angular momentum, and energy are conserved as in the continuum case.
Received February 17, 1995 / Revised version received December 28, 1995 相似文献
63.
64.
This paper develops an efficient particle tracking algorithm to be used in fluid simulations approximated by a high-order multidomain discretization of the Navier–Stokes equations. We discuss how to locate a particle's host subdomain, how to interpolate the flow field to its location, and how to integrate its motion in time. A search algorithm for the nearest subdomain and quadrature point, tuned to a typical quadrilateral isoparametric spectral subdomain, takes advantage of the inverse of the linear blending equation. We show that to compute particle-laden flows, a sixth-order Lagrangian polynomial that uses points solely within a subdomain is sufficiently accurate to interpolate the carrier phase variables to the particle position. Time integration of particles with a lower-order Adams–Bashforth scheme, rather than the fourth-order Runge–Kutta scheme often used for the integration of the carrier phase, increases computational efficiency while maintaining engineering accuracy. We verify the tracking algorithm with numerical tests on a steady channel flow and an unsteady backward-facing step flow. 相似文献
65.
In this paper we consider a singularly perturbed elliptic problem with two small parameters posed on the unit square. Its solution may have exponential, parabolic and corner layers. We give a decomposition of the solution into regular and layer components and derive pointwise bounds on the components and their derivatives. The estimates are obtained by the analysis of appropriate problems on unbounded domains. 相似文献
66.
In this article we study the limit, as the Rossby number ε goes to zero, of the primitive equations of the atmosphere and the ocean. From the mathematical viewpoint we study the averaging of a penalization problem displaying oscillations generated by an antisymmetric operator and by the presence of two time scales. 相似文献
67.
A. D. Fitt D. P. Mason E. A. Moss 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(6):1049-1067
The propagation of a two-dimensional fluid-driven fracture in impermeable rock is considered. The fluid flow in the fracture
is laminar. By applying lubrication theory a partial differential equation relating the half-width of the fracture to the
fluid pressure is derived. To close the model the PKN formulation is adopted in which the fluid pressure is proportional to
the half-width of the fracture. By considering a linear combination of the Lie point symmetries of the resulting non-linear
diffusion equation the boundary value problem is expressed in a form appropriate for a similarity solution. The boundary value
problem is reformulated as two initial value problems which are readily solved numerically. The similarity solution describes
a preexisting fracture since both the total volume and length of the fracture are initially finite and non-zero. Applications
in which the rate of fluid injection into the fracture and the pressure at the fracture entry are independent of time are
considered. 相似文献
68.
Alexis F. Vasseur 《NoDEA : Nonlinear Differential Equations and Applications》2007,14(5-6):753-785
In this paper we give a new proof of the partial regularity of solutions to the incompressible Navier-Stokes equation in dimension
3 first proved by Caffarelli, Kohn and Nirenberg. The proof relies on a method introduced by De Giorgi for elliptic equations.
This work was supported in part by NSF Grant DMS-0607953. 相似文献
69.
Piotr Bogus?aw Mucha Wojciech M. Zaj?czkowski 《Journal of Differential Equations》2002,186(2):377-393
In this paper a special Lp-estimate for the linearized compressible Navier-Stokes in the Lagrangian coordinates for the Dirichlet boundary conditions is obtained. The constant in the estimate does not depend on the length of time interval [0,T]. The result is essential to obtain an existence for regular solutions for the nonlinear problem with the lowest class of regularity in Lp-spaces. 相似文献
70.
Summary We prove the existence of martingale solutions and of stationary solutions of stochastic Navier-Stokes equations under very general hypotheses on the diffusion term. The stationary martingale solutions yield the existence of invariant measures, when the transition semigroup is well defined. The results are obtained by a new method of compactness. 相似文献