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81.
Summary. A finite element formulation is developed for the two dimensional nonlinear time dependent compressible Navier–Stokes equations
on a bounded domain. The existence and uniqueness of the solution to the numerical formulation is proved. An error estimate
for the numerical solution is obtained.
Received September 9, 1997 / Revised version received August 12, 1999 / Published online July 12, 2000 相似文献
82.
Lutz Angermann 《Numerische Mathematik》2000,85(2):175-195
Summary. The proposed method is based on an additive decomposition of the differential operator and the subsequent fitted discretization
of the resulting components. For standard situations, the derived stability and error estimates in the energy norm qualitatively
coincide with well-known estimates. In the case of small diffusion, a uniform error estimate with reduced order is obtained.
Received August 7, 1997 / Revised version received July 15, 1998 / Published online December 6, 1999 相似文献
83.
84.
Summary The convergence of semi-discrete and discrete linear approximation schemes is analysed for nonlinear degenerate parabolic systems of porous medium type. The enthalpy formulation and variational technique are used. The semi-discretization used reduces the original parabolic P.D.E. to linear elliptic P.D.E. The algebraic correction arising from nonlinearities is treated by Newton-like iterations in finite steps. Some numerical experiments are discussed and compared with the analytical solutions.Supported by the Alexander von Humboldt-Foundation in 1989, and by SFB 123, University Heidelberg 相似文献
85.
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
86.
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
87.
88.
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
89.
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
90.
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