Energy dissipation in sloshing waves in a rolling rectangular tank—II. Solution method and analysis of numerical technique

Abstract

In Part I of these series of papers, the complete problem formulation in a linearized form was presented. In order to provide the engineer with an in-depth knowledge about the exact solution of the problem, it is natural and essential to start with a linear solution. This will be the objective of Part II, together with an exposition to the analysis of numerical technique utilized. A truncated infinite Fourier series-type solution is adopted for the linearized boundary value problem. It is shown that such a solution is mathematically consistent and represents the phenomenon properly by satisfying all of the field equations and the imposed boundary conditions. The dependence of the Fourier coefficients on the truncation limit has been investigated. The best lower and upper “cutoff limits” for the truncation of an infinite series are determined. An error analysis of the solution technique is performed.