Abstract
In this article, a new numerical scheme for the solution of the multidimensional fragmentation problem is presented. It is the first that uses the conservative form of the multidimensional problem. The idea to apply the finite volume scheme for solving one-dimensional linear fragmentation problems is extended over a generalized multidimensional setup. The derivation is given in detail for two-dimensional and three-dimensional problems; an outline for the extension to higher dimensions is also presented. Additionally, the existing one-dimensional finite volume scheme for solving conservative one-dimensional multi-fragmentation equation is extended to solve multidimensional problems. The accuracy and efficiency of both proposed schemes is analyzed for several test problems.
Highlights
Fragmentation, breakage or attrition, describe processes in which a single object is separated into at least two new objects
Since the new models are defined with the help of a weight factor, we call it weighted finite volume scheme (WFVS)
We need to mention that the two-dimensional extension of EFVS is not available in the literature to date, and this article proposes an improved model, and extends the existing finite volume schemes for multidimensional fragmentation events
Summary
Fragmentation, breakage or attrition, describe processes in which a single object is separated into at least two new objects. The reasons for breakage can be manifold but are often linked to some kind of stress exerted on the object, for instance thermal stress from heating and rapid cooling (or vice versa and cyclically)—a natural process observed in deserts, leading to disintegration of rocks; or mechanical stress, applied for millenia in the process of grain milling. In an attempt to describe these complex processes and make them accessible for model- and knowledge-based process design, optimization and control, multidimensional fragmentation equations have been proposed and used in different fields of application, see, for instance, the works [13,14,15,16,17]
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