Linear solvers for the flow exterior to the hull may be used to solve for the fluid dynamics also in the interior of a tank, as discussed in Newman (2005) and Ludvigsen et al. (2013). This introduces extra, erroneous terms in the radiation part of the pressure in the tank, but due to cancellation in restoring and radiation terms, the total representation of the pressure and the global response is correctly obtained.
For some kinds of analysis, specific knowledge is needed of the radiation and restoring parts separately. The cancellation of the extra terms can then not be utilized.
Examples of this are stability analysis and eigenvalue analysis. In stability analysis we need to know the actual real global restoring coefficients. In eigenvalue analysis, we should have the separately correct representations of the added mass and restoring coefficients, respectively, to be able to conveniently use them as input to standard eigenvalue solvers.
Here, we develop the expressions for the corrected, actual terms of the total added mass and restoring coefficients for tanks. This is used in our computer program for performing eigenvalue analysis. Results for peak global response and natural periods of the structure with the influence of tank dynamics are presented. Comparisons are made with results obtained by a quasi-static method for an FPSO and a ship with more largely extensive tanks.
For a completely filled tank, the boundary value problem (BVP) for the velocity potential is reduced to Laplace equation in the fluid domain, subject to a Neuman condition on the fixed boundary and it is not closed. The extra condition of having zero pressure at some point in the tank is then added.
Direct re-use of the BVP solver for the external flow, gives an undetermined set of linear equations for the velocity potential in the tank fluid. A typical solver for sets of linear equations may still return a solution, but this will contain a random undetermined constant. After imposing zero pressure in the top of the tank, this solution is still unstable, contaminated by numerical noise.
An improved method is introduced by imposing algebraically, in the equation system, the constraint of zero pressure in the top of the tank. This gives a non-singular equation system with a stable solution holding zero pressure in some selected point in the tank.
Stability analysis of cable–bar structures by inverse-power method for eigenvalue analysis with penalization
