Yuliya Gorb

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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)
Consider two perfectly conducting spheres in a homogeneous medium where the current-electric field relation is the power law. Electric field E blows up in the L∞-norm as δ, the distance between the conductors, tends to zero. We give here a concise rigorous justification of the rate of this blow-up in terms of δ. If the current-electric field relation is(More)
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 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 consider a three-dimensional mathematical model of a viscous incompressible fluid in a bounded domainwith two rigid particles modeled by spheres. One of the particles moves with prescribed translational and angular velocities, while the second one stays still. The near-contact regime of particles is considered. The hydrodynamic forces exerted on the(More)
We consider a mathematical model of a high contrast two phase composite material with inclusions (£bers) close to touching in two space dimensions. The inclusions form a periodic array and have the shape of curvilinear squares with rounded-off angles (“nearly square”) described by the ¤attening parameter m. We present an asymptotic formula for the effective(More)
This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients. A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a description of the problem whose discretization results in a linear(More)