56 research outputs found
A kinetic scheme for unsteady pressurised flows in closed water pipes
The aim of this paper is to present a kinetic numerical scheme for the
computations of transient pressurised flows in closed water pipes. Firstly, we
detail the mathematical model written as a conservative hyperbolic partial
differentiel system of equations, and the we recall how to obtain the
corresponding kinetic formulation. Then we build the kinetic scheme ensuring an
upwinding of the source term due to the topography performed in a close manner
described by Perthame et al. using an energetic balance at microscopic level
for the Shallow Water equations. The validation is lastly performed in the case
of a water hammer in a uniform pipe: we compare the numerical results provided
by an industrial code used at EDF-CIH (France), which solves the Allievi
equation (the commonly used equation for pressurised flows in pipes) by the
method of characteristics, with those of the kinetic scheme. It appears that
they are in a very good agreement
Interior feedback stabilization of wave equations with dynamic boundary delay
In this paper we consider an interior stabilization problem for the wave
equation with dynamic boundary delay.We prove some stability results under the
choice of damping operator. The proof of the main result is based on a
frequency domain method and combines a contradiction argument with the
multiplier technique to carry out a special analysis for the resolvent
Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions
The goal of this work is to study a model of the wave equation with dynamic
boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin
method combined with the fixed point theorem, we show the existence and
uniqueness of a local in time solution. Second, we show that under some
restrictions on the initial data, the solution continues to exist globally in
time. On the other hand, if the interior source dominates the boundary damping,
then the solution is unbounded and grows as an exponential function. In
addition, in the absence of the strong damping, then the solution ceases to
exist and blows up in finite time.Comment: arXiv admin note: text overlap with arXiv:0810.101
A pseudo active kinematic constraint for a biological living soft tissue: an effect of the collagen network
Recent studies in mammalian hearts show that left ventricular wall thickening
is an important mechanism for systolic ejection and that during contraction the
cardiac muscle develops significant stresses in the muscular cross-fiber
direction. We suggested that the collagen network surrounding the muscular
fibers could account for these mechanical behaviors. To test this hypothesis we
develop a model for large deformation response of active, incompressible,
nonlinear elastic and transversely isotropic living soft tissue (such as
cardiac or arteries tissues) in which we include a coupling effect between the
connective tissue and the muscular fibers. Then, a three-dimensional finite
element formulation including this internal pseudo-active kinematic constraint
is derived. Analytical and finite element solutions are in a very good
agreement. The numerical results show this wall thickening effect with an order
of magnitude compatible with the experimental observations
A model for unsteady mixed flows in non uniform closed water pipes and a well-balanced finite volume scheme
We present the derivation of a new unidirectional model for We present the
derivation of a new unidirectional model for unsteady mixed flows in non
uniform closed water pipes. We introduce a local reference frame to take into
account the local perturbation caused by the changes of section and slope. Then
an asymptotic analysis is performed to obtain a model for free surface flows
and another one for pressurized flows. By coupling these models through the
transition points by the use of a common set of variables and a suitable
pressure law, we obtain a simple formulation called PFS-model close to the
shallow water equations with source terms. It takes into account the changes of
section and the slope variation in a continuous way through transition points.
Transition point between the two types of flows is treated as a free boundary
associated to a discontinuity of the gradient of pressure. The numerical
simulation is performed by making use of a Roe-like finite volume scheme that
we adapted to take into account geometrical source terms in the convection
matrix. Finally some numerical tests are presented
Air entrainment in transient flows in closed water pipes: a two-layer approach
In this paper, we first construct a model for free surface flows that takes
into account the air entrainment by a system of four partial differential
equations. We derive it by taking averaged values of gas and fluid velocities
on the cross surface flow in the Euler equations (incompressible for the fluid
and compressible for the gas). The obtained system is conditionally hyperbolic.
Then, we propose a mathematical kinetic interpretation of this system to
finally construct a two-layer kinetic scheme in which a special treatment for
the "missing" boundary condition is performed. Several numerical tests on
closed water pipes are performed and the impact of the loss of hyperbolicity is
discussed and illustrated. Finally, we make a numerical study of the order of
the kinetic method in the case where the system is mainly non hyperbolic. This
provides a useful stability result when the spatial mesh size goes to zero
A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms
We present a numerical kinetic scheme for an unsteady mixed pressurised and
free surface model. This model has a source term depending on both the space
variable and the unknown, U, of the system. The source term is composed by a
topography, a section variation, a curvature (also called corrective) and a
friction term. Using the Finite Volume and Kinetic (FVK) framework, we propose
an approximation of the source terms following the principle of interfacial
upwind with a kinetic interpretation: the source term is not treated as a
volumic term, but included in the numerical fluxes. Then, several numerical
tests are presented
Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions
In this paper we consider a multi-dimensional damped semiliear wave equation
with dynamic boundary conditions, related to the Kelvin-Voigt damping. We
firstly prove the local existence by using the Faedo-Galerkin approximations
combined with a contraction mapping theorem. Secondly, the exponential growth
of the energy and the norm of the solution is presented
Unsteady mixed flows in non uniform closed water pipes: a Full Kinetic Appraoch
We recall the PFS model constructed for the modeling of unsteady mixed flows
in closed water pipes where transition points between the free surface and
pressurized flow are treated as a free boundary associated to a discontinuity
of the gradient of pressure. Then we present a numerical kinetic scheme for the
computations of unsteady mixed flows in closed water pipes. This kinetic method
that we call FKA for "Full Kinetic Approach" is an easy and mathematically
elegant way to deal with multiple transition points when the changes of state
between free surface and pressurized flow occur. We use two approaches namely
the "ghost waves approach" and the "Full Kinetic Approach" to treat these
transition points. We show that this kinetic numerical scheme has the following
properties: it is wet area conservative, under a CFL condition it preserves the
wet area positive, it treats "naturally" the drying and flooding area and most
of all it preserves every stationary flow. Finally numerical experiment versus
laboratory experiment is presented and the scheme produces results that are in
a very good agreement. We also present a numerical experiment when flooding and
drying flows may occur and finally make a numerical study of the order of the
kinetic method
A kinetic scheme for pressurized flows in non uniform pipes
The aim of this paper is to present a kinetic numerical scheme for the
computations of transient pressurised flows in closed water pipes with variable
sections. Firstly, we detail the derivation of the mathematical model in
curvilinear coordinates under some hypothesis and we performe a formal
asymptotic analysis. Then the obtained system is written as a conservative
hyperbolic partial differential system of equations, and we recall how to
obtain the corresponding kinetic formulation based on an upwinding of the
source term due to the "pseudo topography" performed in a close manner
described by Perthame and al
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