# The Numerical Modeling of Coupled Motions of a Moored Floating Body in Waves

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Methods

#### 2.1. Fluid Flow Governing Equations

#### 2.2. Equations for Mooring Line Dynamics

#### 2.3. Equations for Floating Body Dynamics

#### 2.4. Numerical Stability Criterion

## 3. Numerical Validation and Discussion

#### 3.1. Motions of a Free-Floating Box in Waves

#### 3.2. Motions of a Moored Floating Box in Still Water

#### 3.3. Motions of a Moored Floating Box in Waves

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The illustration of a moored floating body and force analysis of a mooring line in four different states.

**Figure 3.**The time sequences of the motions of the floating box under regular waves (H = 0.04 m); (

**a**): heave; (

**b**): sway; (

**c**): roll.

**Figure 4.**The time sequences of the motions of the floating box under regular waves (H = 0.1 m); (

**a**): heave; (

**b**): sway; (

**c**): roll.

**Figure 9.**The schematic computational domain for a moored floating box in waves ((

**a**): top view; (

**b**): side view).

**Table 1.**The comparison of measured and present numerical response amplitude operators (RAO) of the motion responses.

RAO | Experimental Data [26] | Present Result |
---|---|---|

RAO (sway) | 1.17 | 1.23 |

RAO (heave) | 1.14 | 1.19 |

RAO (roll): °/cm | 1.42 | 2.09 |

**Table 2.**The comparison of measured and present numerical response amplitude operators (RAO) of the mooring forces.

RAO | Experimental Data [26] | Present Result |
---|---|---|

RAO (F_{m1}): $\mathrm{N}/\mathrm{cm}$ | 0.392 | 0.390 |

RAO (F_{m2}): $\mathrm{N}/\mathrm{cm}$ | 0.392 | 0.245 |

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**MDPI and ACS Style**

Cheng, L.; Lin, P.
The Numerical Modeling of Coupled Motions of a Moored Floating Body in Waves. *Water* **2018**, *10*, 1748.
https://doi.org/10.3390/w10121748

**AMA Style**

Cheng L, Lin P.
The Numerical Modeling of Coupled Motions of a Moored Floating Body in Waves. *Water*. 2018; 10(12):1748.
https://doi.org/10.3390/w10121748

**Chicago/Turabian Style**

Cheng, Lin, and Pengzhi Lin.
2018. "The Numerical Modeling of Coupled Motions of a Moored Floating Body in Waves" *Water* 10, no. 12: 1748.
https://doi.org/10.3390/w10121748