Topological fluid dynamics of interfacial flows

Topological Fluid Dynamics

T opological fluid dynamics is a young mathematical discipline that studies topological features of flows with complicated trajectories and their applications to fluid motions, and develops group-theoretic and geometric points of view on various problems of hydrodynamical origin. It is situated at a crossroads of several disciplines, including Lie groups, knot theory, partial differential equat...

Topological fluid dynamics for fluid dynamicists

These notes are preliminary and informal. My aim is to provide an introduction to some of the basic ideas that have emerged in recent decades in the fluids literature that have a fundamentally topological character. That is, rather than focusing on details such as velocity profile or pressure field, this material deals with persistent invariant properties of a flow field, features which often h...

Comments on Modeling Interfacial Flows with Volume-of-Fluid Methods

Interfacial gauge methods for incompressible fluid dynamics

Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the correspondi...

MULTI PHASE COMPUTATIONAL FLUID DYNAMICS MODELING OF CAVITATING FLOWS OVER AXISYMMETRIC HEAD-FORMS

 In the present paper, partial cavitation over various head-forms was studied numerically to predict the shape of the cavity. Navier-Stokes equations in addition to an advection equation for vapor volume fraction were solved. Mass transfer between the phases was modeled by a sink term in vapor equation in the numerical analysis for different geometries in wide range of cavitation numbers. The r...