We are currently studying microstructural responses to diffusion-limited coarsening in twophase materials. A mathematical solution to late-stage multiparticle diffusion in finite systems is formulated with account taken of particle-particle interactions and their microstructural correlations, or “locales”. The transition from finite system behavior to that for an infinite microstructure is esta...

Development of a new meshless technique is described, called the meshless volume scheme. The method is completely meshless, yet retains the low storage and simple flux distribution technique characteristic of finite volume methods. The new method is based on the well-known Taylor series expansion method with least squares. A least squares weighting scheme is introduced that significantly reduce...

Staggered grid finite volume methods (also called central schemes) were introduced in one dimension by Nessyahu and Tadmor in 1990 in order to avoid the necessity of having information on solutions of Riemann problems for the evaluation of numerical fluxes. We consider the general case in multidimensions and on general staggered grids which have to satisfy only an overlap assumption. We interpr...

SUMMARY The MultiScale Finite-Volume (MSFV) method is known to produce non-monotone solutions. The causes of the non-monotone solutions are identified and connected to the local flux across the boundaries of primal coarse cells induced by the basis functions. We propose a monotone MSFV (m-MSFV) method based on a local stencil-fix that guarantees monotonicity of the coarse-scale operator, and th...

Inflow of high-saline water of oceanic origin and diapycnal mixing force the vertical circulation of the Baltic Sea. The inflows of saline water are also enriched with oxygen and therefore the oxygen concentrations of the deep layers of the Baltic are strongly dependent on long-term inflow variations. This paper presents flux calculations for water, salt, nutrients and oxygen from the Arkona Ba...

We consider conservation laws with discontinuous flux where the initial datum, function, and spatial dependency coefficient are subject to randomness. establish a notion of random adapted entropy solutions these equations prove well-posedness provided that is piecewise constant finitely many discontinuities. In particular, setting under consideration allows change across points in space whose p...