By Heinz W. Engl, Ewald Lindner (auth.), a. Univ. Prof. Dipl.-Ing., Dr. Heinz W. Engl, o. Univ. Prof. Dr. Hansjörg Wacker, Dipl.-Ing. Dr. Walter Zulehner (eds.)

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Additional resources for Case Studies in Industrial Mathematics

Example text

6 The hydrodynamic coefficients for this problem are explicitly known. By means of ellipsoidal harmonics one obtains a r -2B-a(a 2 -1) a(a 2 -1) 1 i3 with 1 couh- b- coth- 1 a+ B-a(a 2 -1) a (a 2 -1) with a 2-2 a(a 2 -1) 46 B 2B-a(a 2 -1) 2 2 2 a(a-1)(2a-1) B with B = y where a = 0 /r~ Jr~ + 1' b + 1 ' r2 and r1 being the semiminor axes of CJG2 and Cl G1 ' resp. Tab. 42 % o. 04 % Tab. 1 As Tab. 1 shows, the numerical approximations are in good agreement with the exact solutions. Moreover, the numerical solutions are lower bounds (as expected, although G and Gh slightly differ) .

This is the well-known buoyancy effect. b. e. the body seems to have more inertia. , for a simple one-dimensional translational motion, the mass of a body seems to have increased by some amount, usually called added mass or hydrodynamic mass. For a general motion, the effect of the surrounding water is expressed in terms of a virtually increased kinetic energy of the body, represented by a number of so-called hydrodynamic coefficients (including the hydrodynamic mass) . This paper deals with the second phenomenon.

M. To each vertex Pi there is an associated basis function pi ~ PL(Sh) with 0 .. lJ These basis functions form a basis for the space PL(Sh). 3 suggests the following choice for E~, A,B,C. rdrdz sh 0} 41 Remark: E~ C H~ (Sh x The condition p(O,z) 0 guarantees that [0,2n[) fork= A,B. The basis functions of PL(Sh) naturally generate a basis k for Eh. The additional requirement p(0 1 z) for k = A,B excludes basis functions whose associated vertex lies on the z-axis. Instead of the scaling condition J p r drdz for k = C one of sh the basis functions is excluded from the basis.