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Applications of knot theory in fluid mechanics

Renzo Ricca (1998)

Banach Center Publications

In this paper we present an overview of some recent results on applications of knot theory in fluid mechanics, as part of a new discipline called `topological fluid mechanics' (TFM). The choice of the topics covered here is deliberately restricted to those areas that involve mainly a combination of ideal fluid mechanics techniques and knot theory concepts, complemented with a brief description of some other concepts that have important applications in fluid systems. We begin with the concept of...

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

P. E. Vincent, A. Jameson (2011)

Mathematical Modelling of Natural Phenomena

Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order...

Geometrical methods in hydrodynamics

Adrian Constantin (2001)

Journées équations aux dérivées partielles

We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.

Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system

Helmut Abels (2009)

Banach Center Publications

We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids of the same density in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Moreover, diffusion of both components is taken into account. This leads to a coupled Navier-Stokes/Cahn-Hilliard system, which can describe the evolution of droplet formation and collision during the flow. We review some results on...

Recent results on the Boltzmann equation

Carlo Cercignani (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the last few years the theory of the nonlinear Boltzmann equation has witnessed a veritable turrent of contributions, spurred by the basic result of DiPerna and Lions. Here we wish to survey these results with particular attention to some recent developments.

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