3,458 research outputs found
First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow
This paper develops a first-order system least-squares (FOSLS) formulation
for equations of two-phase flow. The main goal is to show that this
discretization, along with numerical techniques such as nested iteration,
algebraic multigrid, and adaptive local refinement, can be used to solve these
types of complex fluid flow problems. In addition, from an energetic
variational approach, it can be shown that an important quantity to preserve in
a given simulation is the energy law. We discuss the energy law and inherent
structure for two-phase flow using the Allen-Cahn interface model and indicate
how it is related to other complex fluid models, such as magnetohydrodynamics.
Finally, we show that, using the FOSLS framework, one can still satisfy the
appropriate energy law globally while using well-known numerical techniques.Comment: 22 pages, 8 figures submitted to Journal of Computational Physic
Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality
We consider the evolution of interfaces in binary mixtures permeating
strongly heterogeneous systems such as porous media. To this end, we first
review available thermodynamic formulations for binary mixtures based on
\emph{general reversible-irreversible couplings} and the associated
mathematical attempts to formulate a \emph{non-equilibrium variational
principle} in which these non-equilibrium couplings can be identified as
minimizers.
Based on this, we investigate two microscopic binary mixture formulations
fully resolving heterogeneous/perforated domains: (a) a flux-driven immiscible
fluid formulation without fluid flow; (b) a momentum-driven formulation for
quasi-static and incompressible velocity fields. In both cases we state two
novel, reliably upscaled equations for binary mixtures/multiphase fluids in
strongly heterogeneous systems by systematically taking thermodynamic features
such as free energies into account as well as the system's heterogeneity
defined on the microscale such as geometry and materials (e.g. wetting
properties). In the context of (a), we unravel a \emph{universality} with
respect to the coarsening rate due to its independence of the system's
heterogeneity, i.e. the well-known -behaviour for
homogeneous systems holds also for perforated domains.
Finally, the versatility of phase field equations and their
\emph{thermodynamic foundation} relying on free energies, make the collected
recent developments here highly promising for scientific, engineering and
industrial applications for which we provide an example for lithium batteries
Dynamics of rapidly rotating Bose-Einstein condensates in a harmonic plus quartic trap
A two-dimensional rapidly rotating Bose-Einstein condensate in a harmonic
plus quartic trap is expected to have unusual vortex states that do not occur
in a pure harmonic trap. At a critical rotation speed , a central
hole appears in the condensate, and at some faster rotation speed ,
the system undergoes a transition to a giant vortex state with pure
irrotational flow. Using a time-dependent variational analysis, we study the
behavior of an annular condensate with a single concentric ring of vortices.
The transition to a giant vortex state is investigated by comparing the energy
of the two equilibrium states (the ring of vortices and the giant vortex) and
also by studying the dynamical stability of small excitation modes of the ring
of vortices.Comment: 12pages, 4figure
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