124 research outputs found
Scale interactions in compressible rotating fluids
We study a triple singular limit for the scaled barotropic Navier-Stokes
system modeling the motion of a rotating, compressible, and viscous fluid,
where the Mach and Rossby numbers are proportional to a small parameter, while
the Reynolds number becomes infinite. If the fluid is confined to an infinite
slab bounded above and below by two parallel planes, the limit behavior is
identified as a purely horizontal motion of an incompressible inviscid fluid,
the evolution of which is described by an analogue of the Euler system
Weak solutions for some compressible multicomponent fluid models
The principle purpose of this work is to investigate a "viscous" version of a
"simple" but still realistic bi-fluid model described in [Bresch, Desjardin,
Ghidaglia, Grenier, Hillairet] whose "non-viscous" version is derived from
physical considerations in \cite[Ishii, Hibiki]{ISHI} as a particular sample of
a multifluid model with algebraic closure. The goal is to show existence of
weak solutions for large initial data on an arbitrarily large time interval. We
achieve this goal by transforming the model to an academic system which
resembles to the compressible Navier-Stokes equations, with however two
continuity equations and a momentum equation endowed with pressure of
complicated structure dependent on two variable densities. The new "academic
system" is then solved by an adaptation of the Lions--Feireisl approach for
solving compressible Navier--Stokes equation, completed with several
observations related to the DiPerna--Lions transport theory inspired by
[Maltese, Michalek, Mucha, Novotny, Pokorny, Zatorska] and [Vasseur, Wen, Yu].
We also explain how these techniques can be generalized to a model of mixtures
with more then two species.
This is the first result on the existence of weak solutions for any realistic
multifluid system
A singular limit for compressible rotating fluids
We consider a singular limit problem for the Navier-Stokes system of a
rotating compressible fluid, where the Rossby and Mach numbers tend
simultaneously to zero. The limit problem is identified as the 2-D
Navier-Stokes system in the ``horizontal'' variables containing an extra term
that accounts for compressibility in the original system
Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations
We present here a general method based on the investigation of the relative
energy of the system, that provides an unconditional error estimate for the
approximate solution of the barotropic Navier Stokes equations obtained by time
and space discretization. We use this methodology to derive an error estimate
for a specific DG/finite element scheme for which the convergence was proved in
[27]. This is an extended version of the paper submitted to IMAJNA
On singular limits arising in the scale analysis of stratified fluid flows
We study the low Mach low Freude numbers limit in the compressible
Navier-Stokes equations and the transport equation for evolution of an entropy
variable -- the potential temperature . We consider the case of
well-prepared initial data on "flat" tours and Reynolds number tending to
infinity, and the case of ill-prepared data on an infinite slab. In both cases,
we show that the weak solutions to the primitive system converge to the
solution to the anelastic Navier-Stokes system and the transport equation for
the second order variation of Comment: 25 page
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