Full Record -- Web of Science 7.2

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

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

Subject Category: MATHEMATICS

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

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

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

Subject Category: MATHEMATICS, APPLIED; MATHEMATICS

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

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

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

Subject Category: MECHANICS; THERMODYNAMICS

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

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

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

Subject Category: MATHEMATICS, APPLIED; MATHEMATICS

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

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

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

Subject Category: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS; MECHANICS

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

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

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

Subject Category: PHYSICS, FLUIDS & PLASMAS; MECHANICS

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

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