Mixed boundary value problem in Potential Theory: Application to the hydrodynamic impact (Wagner) problem

Yves-Marie Scolan; Alexander A. Korobkin

doi:10.1016/j.crme.2012.09.006

Mixed boundary value problem in Potential Theory: Application to the hydrodynamic impact (Wagner) problem

Yves-Marie Scolan ¹ ; Alexander A. Korobkin ²

¹ ENSTA-Bretagne, LBMS/DFMS, 2, rue François-Verny, 29806 Brest cedex 9, France
² University of East Anglia, School of Mathematics, Norwich, United Kingdom

Comptes Rendus. Mécanique, Volume 340 (2012) no. 10, pp. 702-705.

Résumé

A three-dimensional solution of the mixed boundary value problem posed in Potential Theory is proposed. The support of the Neumann condition is conformally mapped onto a unit disk. On that disk, the solution is broken down as Fourier series of azimuthal angle and linear combinations of known functions of the radial coordinate. It is shown that the whole problem reduces highly nonlinear equations for the coefficients of the mapping function. The present method of solution is to be applied to hydrodynamic impact problem.

Reçu le : 2012-06-06
Accepté le : 2012-09-26
Publié le : 2012-10-01

DOI : 10.1016/j.crme.2012.09.006

Mots clés : Dynamical systems, Potential Theory, Mixed Neumann–Dirichlet problem

Affiliations des auteurs :

Yves-Marie Scolan ¹ ; Alexander A. Korobkin ²

¹ ENSTA-Bretagne, LBMS/DFMS, 2, rue François-Verny, 29806 Brest cedex 9, France
² University of East Anglia, School of Mathematics, Norwich, United Kingdom

@article{CRMECA_2012__340_10_702_0,
     author = {Yves-Marie Scolan and Alexander A. Korobkin},
     title = {Mixed boundary value problem in {Potential} {Theory:} {Application} to the hydrodynamic impact {(Wagner)} problem},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {702--705},
     publisher = {Elsevier},
     volume = {340},
     number = {10},
     year = {2012},
     doi = {10.1016/j.crme.2012.09.006},
     language = {en},
}

TY  - JOUR
AU  - Yves-Marie Scolan
AU  - Alexander A. Korobkin
TI  - Mixed boundary value problem in Potential Theory: Application to the hydrodynamic impact (Wagner) problem
JO  - Comptes Rendus. Mécanique
PY  - 2012
SP  - 702
EP  - 705
VL  - 340
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crme.2012.09.006
LA  - en
ID  - CRMECA_2012__340_10_702_0
ER  -

%0 Journal Article
%A Yves-Marie Scolan
%A Alexander A. Korobkin
%T Mixed boundary value problem in Potential Theory: Application to the hydrodynamic impact (Wagner) problem
%J Comptes Rendus. Mécanique
%D 2012
%P 702-705
%V 340
%N 10
%I Elsevier
%R 10.1016/j.crme.2012.09.006
%G en
%F CRMECA_2012__340_10_702_0

Yves-Marie Scolan; Alexander A. Korobkin. Mixed boundary value problem in Potential Theory: Application to the hydrodynamic impact (Wagner) problem. Comptes Rendus. Mécanique, Volume 340 (2012) no. 10, pp. 702-705. doi : 10.1016/j.crme.2012.09.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.09.006/

Bibliographie
Cité par

[1] H. Wagner Über Stoss- und Gleitvorgänge an der Oberfläche von Flüssigkeiten, ZAMM, Volume 12 (1932), pp. 193-215

[2] A.A. Korobkin Formulation of penetration problem as a variational inequality, Dinamika Sploshn. Sredy, Volume 58 (1982), pp. 73-79

[3] S.D. Howison; J.R. Ockendon; S.K. Wilson Incompressible water-entry problems at small deadrise angles, J. Fluid Mech., Volume 222 (1991), pp. 215-230

[4] S. Zaremba Sur un problème mixte relatif à lʼéquation de Laplace, Bull. Acad. Sci. Cracovie, Classe Sci. Math. Nat., Sér. A (1910), pp. 313-344

[5] Z. Nehari Conformal Mapping, Dover Publications, New York, 1975

[6] A.A. Korobkin; Y.-M. Scolan Three-dimensional theory of water impact. Part 2. Linearized Wagner problem, J. Fluid Mech., Volume 549 (2006), pp. 343-373

[7] E.P. Stephan Boundary integral equations for mixed boundary value problems in $R^{3}$ , Math. Nachr., Volume 134 (1987), pp. 21-53

[8] Y.-M. Scolan, A.A. Korobkin, Towards a solution of the three-dimensional Wagner problem, in: 23rd International Workshop on Water Waves and Floating Bodies, Korea, April 2008.

[9] I.N. Sneddon Mixed Boundary Value Problems in Potential Theory, J. Wiley & Sons, Inc., 1966

Cité par Sources :

Commentaires - Politique