Title: **Motion of a rigid body in a
viscous fluid**

Author(s): Conca C, **San Martin J**,
Tucsnak M

Source: COMPTES RENDUS DE L ACADEMIE
DES SCIENCES SERIE I-MATHEMATIQUE 328 (6): 473-478 MAR 15 1999

Document Type: Article

Language: English

Abstract: We
introduce a concept of weak solution for a boundary value problem
modelling the motion of a rigid body immersed in a viscous fluid. The
time variation of the fluid's domain (due to the motion of the rigid
body) is not known a priori, so we deal with a free boundary value
problem. Our main theorem asserts the existence of at least one weak
solution for this problem. The result is global in time provided that
the rigid body does not touch the boundary. (C) Academie des
Sciences/Elsevier, Paris.

Addresses: Conca C (reprint author),
Univ Chile, Dept Ingn Matemat, Santiago, Chile

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Fac Sci, Inst Elie Cartan, Vandoeuvre Nancy, F-54506 France

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Fac Sci, Inst Elie Cartan, Vandoeuvre Nancy, F-54506 France

Publisher: EDITIONS SCIENTIFIQUES
MEDICALES ELSEVIER, 23 RUE LINOIS, 75724 PARIS CEDEX 15, FRANCE

Subject Category: MATHEMATICS

IDS Number: 182ED

ISSN: 0764-4442

2) 2000:

Title: **Existence of solutions for
the equations modelling the motion of a rigid body in a viscous fluid**

Author(s): Conca C, **San Martin J**,
Tucsnak M

Source: COMMUNICATIONS IN PARTIAL
DIFFERENTIAL EQUATIONS 25 (5-6): 1019-1042 2000

Document Type: Article

Language: English

Abstract: We
introduce a concept of weak solution for a boundary value problem
modelling the interactive motion of a coupled system consisting in a
rigid body immersed in a viscous fluid. The fluid, and the solid are
contained in a fixed open bounded set of R-3. The motion of the fluid
is governed by the incompressible Navier-Stokes equations and the
standard conservation's laws of linear, and angular momentum rules the
dynamics of the rigid body. The time variation of the fluid's domain
(due to the motion of the rigid body) is not known apriori, so we deal
with a free boundary value problem. Our main theorem asserts the
existence of at least one weak solution for this problem. The result is
global in time provided that the rigid body does not touch the
boundary.

Addresses: Conca C (reprint author),
Univ Chile, Dept Ingn Matemat, Casilla 170-3,Correo 3, Santiago, Chile

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Fac Sci, Inst Elie Cartan, Vandoeuvre Nancy, F-54506 France

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Fac Sci, Inst Elie Cartan, Vandoeuvre Nancy, F-54506 France

Publisher: MARCEL DEKKER INC, 270
MADISON AVE, NEW YORK, NY 10016 USA

Subject Category: MATHEMATICS, APPLIED;
MATHEMATICS

IDS Number: 310ZQ

ISSN: 0360-5302

3) 2001:

Title: **Numerical study of the
unsteady flow and heat transfer in channels with periodically mounted
square bars**

Author(s): Valencia A, Martin JS, Gormaz R

Source: HEAT AND MASS TRANSFER 37
(2-3): 265-270 APR 2001

Document Type: Article

Language: English

Abstract: Numerical
investigations of unsteady laminar flow and heat transfer in a channel
of height H with periodically mounted square bars of height d = 0.2H
arranged side by side to the approaching flow have been conducted for
different transverse separation distances of the bars. Five cases with
transverse separation distance of 0, 0.5, 1, 1.5 and 2d for a Reynolds
number of 300 in a channel with a periodicity length of 2H were
studied. The unsteady Navier-Stokes equations and the energy equation
have been solved by a finite volume code with staggered grids combined
with the SIMPLEC algorithm and a fine grid resolution. Due to the
arrangement of bars detached from the channel walls the flow is
unsteady with vortex shedding from the bars. The amplitude and mean
values of the drag coefficients, skin friction coefficients, friction
factor and Nusselt numbers have a strong dependence of the transverse
separation distance of the bars.

KeyWords Plus: ENHANCEMENT; VORTICES

Addresses: Valencia A (reprint author),
Univ Chile, Dept Ingn Mecan, Casilla 2777, Santiago, Chile

Univ Chile, Dept Ingn Mecan, Santiago, Chile

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Univ Chile, Dept Ingn Mecan, Santiago, Chile

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Publisher: SPRINGER-VERLAG, 175 FIFTH
AVE, NEW YORK, NY 10010 USA

Subject Category: MECHANICS;
THERMODYNAMICS

IDS Number: 431PB

ISSN: 0947-7411

4) 2001/2

Title: **A new mathematical model for
supercooling**

Author(s): Fremond M, **Gormaz R**,
Martin JAS

Source: JOURNAL OF MATHEMATICAL
ANALYSIS AND APPLICATIONS 261 (2): 578-603 SEP 15 2001

Document Type: Article

Language: English

Abstract: In
this article we study supercooling from a macroscopic point of view by
modeling the evolution of a supercooled body from its liquid state to
its solid state. A first model, which would be expected to have
discontinuous solutions, is regularized by introducing an intrinsic
viscous dissipation. By applying the classical method of
Faedo-Galerkin, this regularized model is shown to have a global smooth
solution, which describes the state transition of the supercooled body
approximately. (C) 2001 Academic Press.

Addresses: Fremond M (reprint author),
LCPC, Lab Lagrange, 58 Blvd Lefebvre, Paris, France

LCPC, Lab Lagrange, Paris, France

Univ Chile, Dept Ingn Matemat, Santiago, Chile

LCPC, Lab Lagrange, Paris, France

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Publisher: ACADEMIC PRESS INC, 525 B
ST, STE 1900, SAN DIEGO, CA 92101-4495 USA

Subject Category: MATHEMATICS, APPLIED;
MATHEMATICS

IDS Number: 472QB

ISSN: 0022-247X

5) 2002:

Title: **Global
weak solutions for the two-dimensional motion of several rigid bodies
in an incompressible viscous fluid**

Author(s): **San
Martin JA**, Starovoitov V, Tucsnak M

Source: ARCHIVE
FOR RATIONAL MECHANICS AND ANALYSIS 161 (2): 113-147 FEB 2002

Document Type: Article

Language: English

Abstract: We
consider the two-dimensional motion of several non-homogeneous rigid
bodies immersed in an incompressible non-homogeneous viscous fluid. The
fluid, and the rigid bodies are contained in a fixed open bounded set
of R-2. The motion of the fluid is governed by the Navier-Stokes
equations for incompressible fluids and the standard conservation laws
of linear and angular momentum rule the dynamics of the rigid bodies.
The time variation of the fluid domain (due to the motion of the rigid
bodies) is not known a priori, so we deal with a free boundary value
problem. The main novelty here is the demonstration of the global
existence of weak solutions for this problem. More precisely, the
global character of the solutions we obtain is due to the fact that we
do not need any assumption concerning, the lack of collisions between
several rigid bodies or between a rigid body and the boundary. We give
estimates of the velocity of the bodies when their mutual distance or
the distance to the boundary tends to zero.

KeyWords Plus: EXISTENCE;
BODY; EQUATIONS

Addresses: San
Martin JA (reprint author), Univ Chile, Ctr Modelamiento Matemat, Dept
Ingn Matemat, Casilla 170-3,Correo 3, Santiago, Chile

Univ Chile, Ctr Modelamiento Matemat, Dept Ingn Matemat, Santiago, Chile

MA Lavrentyev Hydrodynam Inst, Novosibirsk, 630090 Russia

Inst Elie Cartan, Fac Sci, Vandoeuvre Les Nancy, F-54506 France

Univ Chile, Ctr Modelamiento Matemat, Dept Ingn Matemat, Santiago, Chile

MA Lavrentyev Hydrodynam Inst, Novosibirsk, 630090 Russia

Inst Elie Cartan, Fac Sci, Vandoeuvre Les Nancy, F-54506 France

Publisher: SPRINGER-VERLAG,
175 FIFTH AVE, NEW YORK, NY 10010 USA

Subject Category: MATHEMATICS,
INTERDISCIPLINARY APPLICATIONS; MECHANICS

IDS Number: 547HK

ISSN: 0003-9527

6) 2003:

Title: **Collision of a solid with an
incompressible fluid**

Author(s): Fremond M, **Gormaz R**,
Martin JAS

Source: THEORETICAL AND COMPUTATIONAL
FLUID DYNAMICS 16 (6): 405-420 AUG 2003

Document Type: Article

Language: English

Abstract: We
give a predictive theory of the collisions of a viscous incompressible
fluid with solids. The theory is based on interior percussions which
account for the very large stresses and contact forces resulting from
the kinematic incompatibilities responsible for the collision. New
equation of motion and constitutive laws result from the theory.
Examples dealing with a fluid colliding with its container and with a
diver impacting the water of a swimming pool are studied.

Addresses: Fremond
M (reprint author), Lab Cent Ponts & Chaussees Cellule Mecan &
Struct, Lab Lagrange, 58 Blvd Lefebvre, Paris, F-75732 France

Lab Cent Ponts & Chaussees Cellule Mecan & Struct, Lab Lagrange, Paris, F-75732 France

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Lab Cent Ponts & Chaussees Cellule Mecan & Struct, Lab Lagrange, Paris, F-75732 France

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Publisher: SPRINGER-VERLAG, 175 FIFTH
AVE, NEW YORK, NY 10010 USA

Subject Category: PHYSICS, FLUIDS &
PLASMAS; MECHANICS

IDS Number: 724LE

ISSN: 0935-4964

7) 2004

Title: **Convergence of the
Lagrange-Galerkin method for a fluid-rigid system**

Author(s): Martin JS, Scheid JF,
Takahashi T, Tucsnak M

Source: COMPTES RENDUS MATHEMATIQUE 339
(1): 59-64 JUL 1 2004

Document Type: Article

Language: English

Abstract: In
this Note, we consider a Lagrange-Galerkin scheme to approximate a two
dimensional fluid-rigid body problem. The system is modelled by the
incompressible Navier-Stokes equations in the fluid part, coupled with
ordinary differential equations for the dynamics of the rigid body. In
this problem, the equations of the fluid are written in a domain whose
variation is one of the unknowns. We introduce a numerical method based
on the use of characteristics and on finite elements with a fixed mesh.
Our main result asserts the convergence of this scheme.

KeyWords Plus: NAVIER-STOKES EQUATIONS;
WEAK SOLUTIONS; PARTICULATE FLOW; VISCOUS-FLUID; BODIES; SIMULATION;
EXISTENCE; MOTION

Addresses: Martin JS (reprint author),
Univ Chile, Dept Ingn Matemat, Casilla 170-3,Correo 3, Santiago, Chile

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Fac Sci, Inst Elie Cartan, Vandoeuvre Les Nancy, F-54506 France

Univ Chile, Dept Ingn Matemat, Santiago, Chile

Fac Sci, Inst Elie Cartan, Vandoeuvre Les Nancy, F-54506 France

E-mail Addresses: jorge@dim.uchile.cl, scheid@ieen.u-nancy.fr, takahash@iecn.u-nancy.fr, tucsnak@iecn.u-nancy.fr

Publisher: EDITIONS SCIENTIFIQUES
MEDICALES ELSEVIER, 23 RUE LINOIS, 75724 PARIS, FRANCE

Subject Category: MATHEMATICS

IDS Number: 843DI

ISSN: 1631-073X