Topic
Classification of discontinuities
About: Classification of discontinuities is a research topic. Over the lifetime, 5175 publications have been published within this topic receiving 124858 citations. The topic is also known as: classification of discontinuities & discontinuities.
Papers published on a yearly basis
Papers
More filters
TL;DR: This work recognizes the need for additional dissipation in any higher-order Godunov method of this type, and introduces it in such a way so as not to degrade the quality of the results.
3,892 citations
TL;DR: In this paper, a peridynamic formulation for the basic equations of continuum mechanics is proposed, and the propagation of linear stress waves in the new theory is discussed, and wave dispersion relations are derived.
Abstract: Some materials may naturally form discontinuities such as cracks as a result of deformation. As an aid to the modeling of such materials, a new framework for the basic equations of continuum mechanics, called the "peridynamic" formulation, is proposed. The propagation of linear stress waves in the new theory is discussed, and wave dispersion relations are derived. Material stability and its connection with wave propagation is investigated. It is demonstrated by an example that the reformulated approach permits the solution of fracture problems using the same equations either on or off the crack surface or crack tip. This is an advantage for modeling problems in which the location of a crack is not known in advance.
2,842 citations
TL;DR: In this article, a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws, and the best ones are determined, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2-3 meshpoints.
Abstract: : In this paper a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws. Among these schemes we determine the best ones, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2-3 meshpoints. These schemes are tested for stability and are found to be stable under a mild strengthening of the Courant-Friedrichs-Levy criterion. Test calculations of one dimensional flows of compressible fluids with shocks, rarefaction waves and contact discontinuities show excellent agreement with exact solutions. In particular, when Lagrange coordinates are used, there is no smearing of interfaces. The additional terms introduced into the difference scheme for the purpose of keeping the shock transition narrow are similar to, although not identical with, the artificial viscosity terms, and the like of them introduced by Richtmyer and von Neumann and elaborated by other workers in this field.
2,408 citations
TL;DR: A new approach for modelling discrete cracks in meshfree methods is described, in which the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed.
Abstract: A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data. Copyright © 2004 John Wiley & Sons, Ltd.
1,274 citations
TL;DR: The authors examine prior smoothness constraints of a different form, which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity.
Abstract: The linear image restoration problem is to recover an original brightness distribution X/sup 0/ given the blurred and noisy observations Y=KX/sup 0/+B, where K and B represent the point spread function and measurement error, respectively. This problem is typical of ill-conditioned inverse problems that frequently arise in low-level computer vision. A conventional method to stabilize the problem is to introduce a priori constraints on X/sup 0/ and design a cost functional H(X) over images X, which is a weighted average of the prior constraints (regularization term) and posterior constraints (data term); the reconstruction is then the image X, which minimizes H. A prominent weakness in this approach, especially with quadratic-type stabilizers, is the difficulty in recovering discontinuities. The authors therefore examine prior smoothness constraints of a different form, which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity. In this sense, discontinuities are addressed implicitly rather than explicitly. >
1,205 citations