33,358 research outputs found
On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions
We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds
Artificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane
We discuss artificial boundary conditions for stationary Navier-Stokes flows
past bodies in the half-plane, for a range of low Reynolds numbers. When
truncating the half-plane to a finite domain for numerical purposes, artificial
boundaries appear. We present an explicit Dirichlet condition for the velocity
at these boundaries in terms of an asymptotic expansion for the solution to the
problem. We show a substantial increase in accuracy of the computed values for
drag and lift when compared with results for traditional boundary conditions.
We also analyze the qualitative behavior of the solutions in terms of the
streamlines of the flow. The new boundary conditions are universal in the sense
that they depend on a given body only through one constant, which can be
determined in a feed-back loop as part of the solution process
Long time behavior of unsteady flow computations
This paper addresses a specific issue of time accuracy in the calculation of external aerodynamic problems. The class of problems discussed consists of inviscid compressible subsonic flows. These problems are governed by a convective equation. A key issue that is not understood is the long time behavior of the solution. This is important if one desires transient calculations of problems governed by the Euler equations or its derivatives such as the small disturbance equations or the potential formulations for the gust problem. Difficulties arise for two dimensional problems where the time rate decay solutions of the wave equation is slow. In concert with the above mentioned problem, exterior flows require proper modeling of the boundary conditions. In particular, this requires the truncation of infinite regions into finite regions with the aid of artificial boundaries. These boundary conditions must be consistent with the physics of the unbounded problem as well as consistent in time and space. Our treatment of the problem is discussed in detail and examples are given to verify the results
Adaptive absorbing boundary conditions for Schrodinger-type equations: application to nonlinear and multi-dimensional problems
We propose an adaptive approach in picking the wave-number parameter of
absorbing boundary conditions for Schr\"{o}dinger-type equations. Based on the
Gabor transform which captures local frequency information in the vicinity of
artificial boundaries, the parameter is determined by an energy-weighted method
and yields a quasi-optimal absorbing boundary conditions. It is shown that this
approach can minimize reflected waves even when the wave function is composed
of waves with different group velocities. We also extend the split local
absorbing boundary (SLAB) method [Z. Xu and H. Han, {\it Phys. Rev. E},
74(2006), pp. 037704] to problems in multidimensional nonlinear cases by
coupling the adaptive approach. Numerical examples of nonlinear Schr\"{o}dinger
equations in one- and two dimensions are presented to demonstrate the
properties of the discussed absorbing boundary conditions.Comment: 18 pages; 12 figures. A short movie for the 2D NLS equation with
absorbing boundary conditions can be downloaded at
http://home.ustc.edu.cn/~xuzl/movie.avi. To appear in Journal of
Computational Physic
A simple preconditioned domain decomposition method for electromagnetic scattering problems
We present a domain decomposition method (DDM) devoted to the iterative
solution of time-harmonic electromagnetic scattering problems, involving large
and resonant cavities. This DDM uses the electric field integral equation
(EFIE) for the solution of Maxwell problems in both interior and exterior
subdomains, and we propose a simple preconditioner for the global method, based
on the single layer operator restricted to the fictitious interface between the
two subdomains.Comment: 23 page
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