A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.

Recherches sur léphébie attique et en particulier sur la date de l'institution,

"Bibliographie": p. [xxi]-xxiii.

Essai sur l'éphébie attique.

t. I. Origines de l'éphébie. Tableau des institutions éphébiques. Devoirs politiques, religieux et militaires des éphèbes. Exercices gymnastiques. Études littéraires. Les finances du collège.--t. II. Textes éphébiques classés par ordre de dates. Chronologie des éponymes athéniens. Succession des fonctionnairs de l'éphébie attique. Tableaux donnant la suite de ces fonctionnaires par archontats.

Jingshi da xue shi fan sheng bi ye ji bie tu.

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Wu chao shi bie cai ji.

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Sheng li fen li zhi bie /

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Die gusseisernen Brücken der Badischen Eisenbahn, insbesondere die Kinzigbrücke bie Offenburg und Elzbrücke bei Sexau. Mit Versuchen über die Senkungen dieser Brücken und Berechnung ihres Tragvermögens.

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Xianfeng yi lai gong chen bie zhuan.

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Song ming chen yan xing lu : [qian ji 10 juan, hou ji 14 juan, xu ji 8 juan, bie ji 26 juan, wai ji 17 juan] /

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Qian ming zhong yi bie zhuan : [32 juan] /

Mo hua zhai ju zhen ban ben.

Ru bu ji zhai bie hao lu : 48 juan /

Double leaves, oriental style, in case.

Lehrbuch der theoretischen Philosophie und philosophischen Propädeutik zum Gebrauche bie akademischen Vorlesungen.

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Le fils de la Grande Catherine, Paul 1er, empereur de Russie, sa bie, son règn et sa mort, 1754-1801, d̕après des documents nouveaux et en grande partie inédits.

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Ting yu zhai shi ji : 20 juan, bu bian 1 juan, bie ji 1 juan /

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Chun qiu bie dian : 15 juan /

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