The Effect of Numerical Integration Stiffness in Ship Motio Simulation

Abstract

In ship motion stability, generally, capsizing occurs due to the following effects: loss in directional control such as in broaching-to; loss in stability (pure loss of stability) and transient effect like parametric excitation. It is generally accepted that hydrodynamic forces due to waves are dominant that cause vessels' capsizing. It is generally accepted that numerical simulation using computers are reliable to study the ship motions. As a result, the 6 degrees-of-freedom time domain simulation will be used to study the ship motions especially the large amplitude motions. In this paper, we adopt three classes of numerical approach namely explicit Runge-Kutta, implicit Runge-Kutta and Rosenbrock-type Runge-Kutta methods in order to verify the effect of stiffness in ship motion simulation. Keywords: Time Domain Ship Simulation; Explicit Runge-Kutta method; Implicit Runge-Kutta method; Rosenbrock-type Runge-Kutta method. Stiff Ordinary Differential Equations. Dalam aspek kestabilan pergerakan kapal, secara amnya, kapal tersebut terbalik disebabkan oleh keadaan berikut: kehilangan kawalan arah seperti ``broaching-to"; kehilangan keseimbangan (kehilangan keseimbangan tulen) dan keadaan ketidaktetapan seperti rangsangan parametrik. Daya hidrodinamik merupakan daya dominan yang menyebabkan kapal terbalik. Pada masa kini, penggunaan simulasi berpandukan komputer telah menjadi terkenal dan boleh dipercayai untuk mengkaji pergerakan kapal. Seterusnya, simulasi enam darjah kebebasan domain masa akan digunakan untuk mengkaji pergerakan kapal khususnya pergerakan beramplitud besar. Dalam penyelidikan ini, kita menggunakan tiga kelas pendekatan berangka iaitu kaedah Runge-Kutta jenis tak tersirat, kaedah Runge-Kutta jenis tersirat dan kaedah Runge-Kutta jenis Rosenbrock untuk mengkaji kesan kaku dalam simulasi pergerakan kapal. Katakunci: Simulasi kapal berlandas domain masa, kaedah Runge-Kutta jenis tak tersirat; kaedah Runge-Kutta jenis tersirat; kaedah Runge-Kutta jenis Rosenbrock. Sistem Persamaan Terbitan Biasa kaku.