Free Surface Waves in a Wave Tank
We consider the motion of an inviscid and incompressible fluid in an closed or semi-infinite basin with free surface waves. An intrinsic feature of the problem is the formation of waves by a periodic motion of one part of the boundary of the basin. Sharp corners of the rectangular domain and between the free surface and the side walls of the basin are critical regions of the solution. The correct formulation and solution of the problem in these regions is necessary for the simulation of the free surface waves in a bounded domain. We formulate compatibility relations for the dynamic contact lines as necessary conditions for the existence of a solution to the free boundary problem for a potential flow. We derive a formulation and numerical solution in a compact way so that natural compatibility conditions can be satisfied at the interface between the walls of the basin and the free surface.
KeywordsFree Surface Surface Wave Contact Line Free Boundary Problem Absorb Boundary Condition
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- Cohen, G. (editor): Mathematical and numerical Aspects of wave propagation, Philadelphia, 1995. SIAM.Google Scholar
- Lions, P.-L.: Mathematical Topics in Fluid Mechanics, I incompressibe Models. Oxford Lecture Series in Mathematics and its Applications. Clarendon Press, Oxford, 1996.Google Scholar
- Miloh, T. (editor): Mathematical Approaches in Hydrodynamics, Philadelphia, 1991. SIAM.Google Scholar
- Pawell, A.: The motion of an inviscid and incompressible fluid in a non-smooth domain. In Proceedings of the ICIAM 95, Applied Sciences — Especially Mechanics, ZAMM, 76(5):375–376. Akademie Verlag, Berlin, 1996.Google Scholar
- Pawell, A.; Guenther, R. B.: A numerical solution to a free surface wave problem. Top. Methods in Nonlin. Anal., 6(2), 1996.Google Scholar
- Tanaka, N.: Two-phase free boundary problem for viscous incompressible thermocapillary convection. Japan. J. Math., 21(l):l–42, 1995.Google Scholar
- Wagata, L.: Absorbierende Randbedingungen für hyperbolische partielle Differentialgleichungen. PhD thesis, Ludwig-Maximilians-Universität München, März 1982.Google Scholar