It is known that the viscous damping at the free surface is an important part of the whole damping in partly filled liquid container. In order to compute the damping in partly filled rigid circular cylinder more reliably, a VOF (Volume of Fluid) method basing on FVM (Finite Volume Method) with adhesion wall boundary condition is used. Damping of viscous liquid sloshing is very difficult to compute precisely through numerical computation basing on Stokes equations with such two kinds of wall boundary conditions: One is to keep no-slip condition at tank bottom and slip condition at side walls. The other is to keep no-slip condition at side walls and slip at tank bottom. The damping computation discrepancy of these two conditions depends on the liquid height ratio h/R, where h is the liquid height and R is the radius of the cylindrical container. The method used in the present paper maintains all the wall boundary conditions, both side walls and bottom, with no slip conditions and can give an exact damping value instead of computing an estimation range. The simulation damping results show a better agreement with the published experimental measurements especially for liquid height ratio h/R < 1.

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