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Convection of a scalar quantity by a compressible velocity field may give rise to unbounded solutions or nonphysical overshoots at the continuous and discrete level. In this paper, we are concerned with solving continuity equations that govern the evolution of volume fractions in Eulerian models of disperse two-phase flows. An implicit Galerkin finite(More)
We introduce a discrete network approximation to the problem of the effective conductivity of the high contrast, highly packed composites in three dimensions. The inclusions are irregularly (randomly) distributed in a hosting medium, so that a significant fraction of them may not participate in the conducting spanning cluster. For this class of spacial(More)
We consider the conductivity problem in an array structure with square closely spaced absolutely conductive inclusions of the high concentration , i.e. the concentration of inclusions is assumed to be close to 1. The problem depends on two small parameters: ε, the ratio of the period of the micro-structure to the characteristic macroscopic size, and δ, the(More)
In this paper, we discuss the numerical treatment of three-dimensional mixture models for (semi-)dilute and concentrated suspensions of particles in incompressible fluids. The generalized Navier-Stokes system and the continuity equation for the volume fraction of the disperse phase are discretized using an implicit high-resolution finite element scheme, and(More)
We present an asymptotic study of the Dirichlet to Neumann map of high contrast composite media with perfectly conducting inclusions that are close to touching. The result is an explicit characterization of the map in the asymptotic limit of the distance between the particles tending to zero. 1. Introduction. The Dirichlet to Neumann (DtN) map of an(More)
The dynamic, transient propagation of a semi-infinite, mode I fracture is considered for an infinite elastic body. While the bulk constitutive response is assumed to be linearly elastic, the crack tip is modeled through inclusion of a nonlinear, viscoelastic cohesize zone. The model is motivated by dynamic fracture in brittle polymers in which crack(More)
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