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Free Boundary (free + boundary)

Distribution by Scientific Domains
Mathematics and Statistics71%
Engineering14%

Terms modified by Free Boundary

  • free boundary problem
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    Selected Abstracts

    A finite-volume particle method for conservation laws on moving domains

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2008
    D. Teleaga
    Abstract The paper deals with the finite-volume particle method (FVPM), a relatively new method for solving hyperbolic systems of conservation laws. A general formulation of the method for bounded and moving domains is presented. Furthermore, an approximation property of the reconstruction formula is proved. Then, based on a two-dimensional test problem posed on a moving domain, a special Ansatz for the movement of the particles is proposed. The obtained numerical results indicate that this method is well suited for such problems, and thus a first step to apply the FVPM to real industrial problems involving free boundaries or fluid,structure interaction is taken. Finally, we perform a numerical convergence study for a shock tube problem and a simple linear advection equation. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    A system of variational inequalities arising from finite expiry Russian option with two regimes

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2009
    Zhou Yang
    Abstract In this paper we consider a system of variational inequalities arising from the value of finite expiry Russian option with two regimes. We achieve the existence and uniqueness of the solution to the problem. Moreover, we show that the free boundaries are infinitely differentiable and monotonic with respect to time and some parameters in this system, as well as the mutual relationship between the solutions in two regimes. Moreover, we establish the bound of the free boundaries and analyze their property as time converges to infinite. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    On the Lp,Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domain

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2007
    Rieko Shimada
    Abstract We obtain the Lp,Lq maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ,n (n,2). The Robin condition consists of two conditions: v , u=0 and ,u+,(T(u, p)v , ,T(u, p)v, v,v)=h on the boundary of the domain with ,, ,,0 and ,+,=1, where u and p denote a velocity vector and a pressure, T(u, p) the stress tensor for the Stokes flow and v the unit outer normal to the boundary of the domain. It presents the slip condition when ,=1 and non-slip one when ,=1, respectively. The slip condition is appropriate for problems that involve free boundaries. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Temporal behaviour of global perturbations in compressible axisymmetric flows with free boundaries

    ASTRONOMISCHE NACHRICHTEN, Issue 1 2009
    V.V. Zhuravlev
    Abstract The dynamics of small global perturbations in the form of a linear combination of a finite number of non-axisymmetric eigenmodes is studied in the two-dimensional approximation. The background flow is assumed to be an axisymmetric perfect fluid with adiabatic index , = 5/3 rotating with a power law angular velocity distribution , , r,q, 1.5 < q < 2.0, confined by free boundaries in the radial direction. The substantial transient growth of acoustic energy of optimized perturbations is discovered. An optimal energy growth G is calculated numerically for a variety of parameters. Its value depends essentially on the perturbation azimuthal wavenumber m and increases for higher values of m. The closer the rotation profile to the Keplerian law, the larger growth factors can be obtained but over a longer time. The highest acoustic energy increase found numerically is of order ,102 over ,6 typical Keplerian periods. Slow neutral eigenmodes with corotation radius beyond the outer boundary mostly contribute to the transient growth. The revealed linear temporal behaviour of perturbations may play an important role in angular momentum transfer in toroidal flows near compact relativistic objects (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Pseudo-reflection phenomena for singularities in thin elastic shells

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2003
    P. Karamian-Surville
    We consider problems of statics of thin elastic shells with hyperbolic middle surface subjected to boundary conditions ensuring the geometric rigidity of the surface. The asymptotic behaviour of the solutions when the relative thickness tends to zero is then given by the membrane approximation. It is a hyperbolic problem propagating singularities along the characteristics. We address here the reflection phenomena when the propagated singularities arrive to a boundary. As the boundary conditions are not the classical ones for a hyperbolic system, there are various cases of reflection. Roughly speaking, singularities provoked elsewhere are not reflected at all at a free boundary, whereas at a fixed (or clamped) boundary the reflected singularity is less singular than the incident one. Reflection of singularities provoked along a non-characteristic curve C are also considered. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Unsaturated incompressible flows in adsorbing porous media

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2003
    A. Fasano
    We study a free boundary problem modelling the penetration of a liquid through a porous material in the presence of absorbing granules. The geometry is one dimensional. The early stage of penetration is considered, when the flow is unsaturated. Since the hydraulic conductivity depends both on saturation and on porosity and the latter change due to the absorption, the main coefficient in the flow equation depends on the free boundary and on the history of the process. Some results have been obtained in Fasano (Math. Meth. Appl. Sci. 1999; 22:605) for a simplified version of the model. Here existence and uniqueness are proved in a class of weighted Hölder spaces in a more general situation. A basic tool are the estimates on a non-standard linear boundary value problem for the heat equation in an initially degenerate domain (Rend. Mat. Acc. Lincei 2002; 13:23). Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Global behaviour of 1-D viscous compressible barotropic flows with free boundary and self-gravitation

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2003
    Alexander Zlotnik
    We consider an initial,boundary value problem for a system of quasilinear equations for one-dimensional flows of a viscous compressible barotropic fluid with large data. An outer pressure (possibly zero) is prescribed on one of the boundaries; also a self-gravitation is taken into account. The case of the stationary pressure with possible degeneration is studied. For a general non-monotone state function, either global estimates for the solution and its stabilization are proved or the growth of the fluid volume is bounded from below as t , ,. For the power state function, in addition, stabilization rate estimates (of the power type) are given. The study is accomplished in the Lagrangian mass co-ordinates. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    The elastic echo problem

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2003
    Mongi Mabrouk
    Abstract We consider a homogeneous isotropic unbounded linear elastic medium ,,,3, having a free boundary ,. A forcing f(t,x) creates an incident displacement field u0(t,x). This primary field is scattered by , giving rise to a secondary field or echo, for which we determine the asymptotic behaviour in time. These results are obtained via the use of an tension of the time-dependent scattering theory of C. Wilcox. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    An optimal shape design formulation for inhomogeneous dam problems

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2002
    Abdelkrim Chakib
    In this paper, the flow problem of incompressible liquid through an inhomogeneous porous medium (say dam), with permeability allowing parametrization of the free boundary by a graph of continuous unidimensional function, is considered. We propose a new formulation on an optimal shape design problem. We show the existence of a solution of the optimal shape design problem. The finite element method is used to obtain numerical results which show the efficiency of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Compressible Navier,Stokes system in 1-D

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2001
    Piotr Bogus, aw Mucha
    Abstract The compressible barotropic Navier,Stokes system in monodimensional case with a Neumann boundary condition given on a free boundary is considered. The global existence with uniformly boundedness for large initial data and a positive force is proved. The result concerning an asymptotic behavior shows that the solutions tends to the stationary solution. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Numerical simulation of non-viscous liquid pinch off using a coupled level set boundary integral method

    PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
    Maria Garzon
    The pinch off of an inviscid fluid column is described using a potential flow model with capillary forces. The interface velocity is obtained via a Galerkin boundary integral method for the 3D axisymmetric Laplace equation, whereas the interface location and the velocity potential on the free boundary are both approximated using level set techniques on a fixed domain. The algorithm is validated computing the Raleigh-Taylor instability for liquid columns which provides an analytical solution for short times. The simulations show the time evolution of the fluid tube and the algorithm is capable of handling pinch-off and after pinch-off events. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Regularity of the free boundary of an American option on several assets,

    COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2009
    Peter Laurence
    We establish the C, regularity of the free boundary for an American option on several assets in the case where the payoff is convex and the assets follow correlated geometric Brownian motions. Our work builds on results concerning the qualitative properties and initial regularity of the free boundary by Broadie and Detemple; Jaillet, Lamberton, and Lapeyre; and Villeneuve. © 2008 Wiley Periodicals, Inc. [source]