24 research outputs found
Investigations of a Two-Phase Fluid Model
We study an interface-capturing two-phase fluid model in which the
interfacial tension is modelled as a volumetric stress. Since these stresses
are obtainable from a Van der Waals-Cahn-Hilliard free energy, the model is, to
a certain degree, thermodynamically realistic. Thermal fluctuations are not
considered presently for reasons of simplicity. The utility of the model lies
in its momentum-conservative representation of surface tension and the
simplicity of its numerical implementation resulting from the volumetric
modelling of the interfacial dynamics. After validation of the model in two
spatial dimensions, two prototypical applications---instability of an initially
high-Reynolds-number liquid jet in the gaseous phase and spinodal decomposition
in a liquid-gas system--- are presented.Comment: Self unpacking uuencoded and compressed postscript file (423928
bytes). Includes 6 figure
An Euler Solver Based on Locally Adaptive Discrete Velocities
A new discrete-velocity model is presented to solve the three-dimensional
Euler equations. The velocities in the model are of an adaptive nature---both
the origin of the discrete-velocity space and the magnitudes of the
discrete-velocities are dependent on the local flow--- and are used in a finite
volume context. The numerical implementation of the model follows the
near-equilibrium flow method of Nadiga and Pullin [1] and results in a scheme
which is second order in space (in the smooth regions and between first and
second order at discontinuities) and second order in time. (The
three-dimensional code is included.) For one choice of the scaling between the
magnitude of the discrete-velocities and the local internal energy of the flow,
the method reduces to a flux-splitting scheme based on characteristics. As a
preliminary exercise, the result of the Sod shock-tube simulation is compared
to the exact solution.Comment: 17 pages including 2 figures and CMFortran code listing. All in one
postscript file (adv.ps) compressed and uuencoded (adv.uu). Name mail file
`adv.uu'. Edit so that `#!/bin/csh -f' is the first line of adv.uu On a unix
machine say `csh adv.uu'. On a non-unix machine: uudecode adv.uu; uncompress
adv.tar.Z; tar -xvf adv.ta
Enhanced inverse-cascade of energy in the averaged Euler equations
For a particular choice of the smoothing kernel, it is shown that the system of partial differential equations governing the vortex-blob method corresponds to the averaged Euler equations. These latter equations have recently been derived by averaging the Euler equations over Lagrangian fluctuations of length scale α, and the same system is also encountered in the description of inviscid and incompressible flow of second-grade polymeric (non-Newtonian) fluids. While previous studies of this system have noted the suppression of nonlinear interaction between modes smaller than α, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energy in two-dimensional turbulence and thereby affects scales of motion larger than α as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added. 1 The two-dimensional incompressible, Euler equations are ∂tω + ∇ · (uω) = 0, ∇ · u = 0, ω(t = 0) = ω0, (1
Bistability and hysteresis of maximum-entropy states in decaying two-dimensional turbulence
We propose a theory that qualitatively predicts the stability and equilibrium structure of long-lived, quasi-steady flow states in decaying two-dimensional turbulence. This theory combines a maximum entropy principal with a nonlinear parameterization of the vorticity-stream-function dependency of such long-lived states. In particular, this theory predicts unidirectional-flow states that are bistable, exhibit hysteresis, and undergo large abrupt changes in flow topology; and a vortex-pair state that undergoes continuous changes in flow topology. These qualitative predictions are confirmed in numerical simulations of the two-dimensional Navier-Stokes equation. We discuss limitations of the theory, and why a reduced quantitative theory of long-lived flow states is difficult to obtain. We also provide a partial theoretical justification for why certain sets of initial conditions go to certain long-lived flow states