In this chapter, the author examines the properties of some general classes of time integration methods, derived from the well establishedtheory of integration for ODEs.

Industrial applications require both the development of techniques to generate appropriate computational meshes and the development of discretization schemes compatible with whatever type of mesh is chosen. The principal alternatives are Cartesian meshes, body-fitted curvilinear meshes, and unstructured tetrahedral meshes. Each of these approaches has some advantages that have led to their use. This chapter addresses the development of methods suitable for topologically complex domains.

This chapter addresses issues arising in the time accurate simulation of unsteady flows. In order to enable accurate simulations of time dependent flows with moving shocks and contact discontinuities, there is a need for higher order accurate time discretization schemes that can preserve the TVD property. Additionally, time dependent calculations are needed for a number of important applications, such as flutter analysis or the analysis of the flow past a helicopter rotor, in which the stability limit of an explicit scheme forces the use of much smaller time steps than would be needed for an accurate simulation. This motivates the “dual time stepping” scheme, in which a multigrid explicit scheme can be used in an inner iteration to solve the equations of a fully implicit time stepping scheme. Such schemes are developed in this chapter.

Ship-shaped offshore installations that are operated in shallow water (e.g., at depths of 10 m deep or less) are used for various purposes, such as oil terminals, floating storage and regasification units (FSRUs), power plants and bunkering. These usually remain afloat in operation, with a gap between the seabed and the bottom of the hull. In other situations, such as those for ship-shaped offshore power plant facilities containing nuclear reactors, hull bottoms are touched down onto the seabed by using heavy ballasting materials, such as concrete or sand. However, offshore installations are not fixed to the seabed and move under the effects of environmental actions, but may be moored.

Accidental limit states (ALS) are one of four types of limit states (described in Section 5.1), and they represent a condition in which a particular structural member or an entire structure fails to perform its designated function as a result of excessive structural damage, resulting from accidents such as unintended flooding, collisions, fires or explosions (Paik 2018, 2020). A range of adverse events may ensue if ALS are reached on a ship-shaped offshore installation, including severe injuries or loss of life among the crew and severe damage to and/or loss of property, with consequent substantial financial losses and environmental pollution.

Classification society rules or recommended practices dictate the types of steel to be used in the assembly of the hull structures of ship-shaped offshore installations. The steel must exhibit high levels of buckling and fatigue performance and be amenable to corrosion management. It is recommended that the proportion of reduced thickness, high strength steel be minimised and the proportion of ordinary steel (e.g., grade A) be maximised in a hull structure. However, structural members that require an ordinary steel plate with a thickness greater than 30 mm may instead be made from high strength steel to avoid the need for heavy welding and to simplify the construction. The greater resistance of high strength steel to corrosion reduces the need for repairs in dry dock, which is critical for the long on site life required in a ship-shaped offshore installation. Three grades of steel are used in the assembly of hulls for installations that will be in service at sub-zero temperatures: grade D steel for use at −20°C, grade E steel for use at −40°C and grade F steel for use at −60°C. Steel may be exposed to colder temperatures than it has been designed to withstand or even to cryogenic conditions as a result of the accidental release of liquefied gas (e.g., liquefied natural gas or hydrogen). This can cause a brittle fracture in structural steel and a subsequent catastrophic failure.

Criteria that are relevant to the safety engineering of ship-shaped offshore installations are influenced by ocean environmental conditions that affect the transit, operation, survival and decommissioning of these installations. The actions of ocean environmental conditions on ship-shaped offshore installations are different from their actions on trading ships. Particularly, the nature and operation of the former mean that the structures are substantially affected by the action of waves, winds and currents, whereas the latter are primarily affected by waves only. Thus, accurate and efficient modelling of ocean environmental conditions at the proposed sites of ship-shaped offshore installations is essential for safety engineering and long operational uptimes.

The performance of a structure and its components is described using limit state functions that separate desired from undesired states. The physical effects of exceeding a limit state may be reversible or irreversible. If the effects are reversible, the removal of the cause of the exceedance allows a structure to return to the desired state. If the effects are irreversible, a return to the desired state is not possible, and certain consequences, such as damage, may ensue depending on the nature of the limit state. These consequences may themselves be reversible or irreversible. For example, if consequential damage is limited, such as an undesired and localised permanent set, it may be repairable (e.g., by replacing the affected parts). Limit states are examined against different target safety levels, where the target to be attained for any particular type of limit state is a function of the consequences of and ease of recovery from that state.

Ultimate limit states (ULS) are one of four types of limit states (described in Section 5.1), and represent a condition in which a particular structural member or an entire structure fails to perform its designated function as a result of progressive collapse due to a loss of structural stiffness and strength caused by buckling, plasticity and fracture (Paik 2018, 2020). If ULS are reached on a ship-shaped offshore installation, catastrophic failures may occur, leading to human casualties, structural collapse and environmental damage.

A mooring system, thrusters, a dynamic positioning system or a combination of these elements is critical for the station-keeping of a floating structure in various environmental conditions involving wind, waves and current. Thus, position keeping and motion control are both required to enable the functional and operational requirements of ship-shaped offshore installations to be met. The analysis of the fluid dynamic behaviours of offshore installation structures above sea level, which are subjected to wind, involves a different set of complications from the analogous analysis of submerged parts, which are subjected to waves and current.

Various types of engineering structures have been developed over the course of human civilisation. One type is the ship-shaped offshore installation, which is a floating structural system located at sea. As a result of their multiple functionalities, these installations are widely used in the production, processing and storage of energy derived from marine sources and electrical power generation in a marine environment.