Efficient and accurate computation of free surface Green’s functions is critical for solving ship hydrodynamic problems via the boundary element method (BEM). Mathematically formulated as high-frequency oscillatory integrals, these functions pose challenges for traditional numerical methods. This paper presents a general efficient numerical strategy based on the Levin method, transforming the original problem into a differential equation, and then into a linear system via the Chebyshev pseudo-spectral method, thus avoiding direct computation of oscillatory integrals. Numerical results show the method achieves good accuracy and remarkably higher efficiency than traditional approaches like adaptive integration, demonstrating significant application value.

Energy analysis of ship motion in waves is carried out, and a novel method to predict the corresponding wave added resistance is proposed in this paper. First, a semi-analytical three-dimensional translating and pulsating source method that accounts for steady wave effects is employed to solve the first-order radiation and diffraction hydrodynamic problems. The work expressions of various forces in the ship motion equation, i.e., the different energy components, are derived based on the principle of energy conservation. Based on the derived formulas, a numerical program is developed to validate the first-order hydrodynamic results and investigate the energy conversion relationships of ship motion in waves. It is found that the incident wave energy is dissipated by the ship in the form of radiated and diffracted waves, while the inertial and restoring forces have no impact on energy conversion. Furthermore, the wave-induced resistance of ships sailing in waves is divided into the steady wave-induced resistance in calm water and the unsteady radiated wave-induced and diffracted wave-induced resistance. The mean value of this unsteady wave-induced resistance is equal to the wave added resistance. Accordingly, a novel method for predicting wave added resistance is proposed, which comprehensively incorporates both radiation and diffraction effects. For short waves, an empirical formula is employed to compensate for the insufficient consideration of viscous and nonlinear effects, and the smooth transition of the wave added resistance response function in the full wavelength range is achieved by analyzing its generation mechanism.

Accurate simulation of fully nonlinear surface gravity waves remains challenging, as most numerical methods suffer from inadequate efficiency or reduced accuracy under strong nonlinearity. In this study, we propose a novel periodic fundamental solution (PFS) method for simulating strongly nonlinear waves, which advances the classical method of fundamental solutions by reducing the computational complexity from O(N3) to O(N log N). The PFS method transforms the free-surface Dirichlet problem into a linear system with a convolution-structured coefficient matrix by leveraging source periodicity and a tailored fitting procedure, allowing efficient solution via fast Fourier transforms combined with a preconditioned iterative solver. Numerical experiments show that the PFS approach typically converges within two to three iterations, preserves high accuracy even for wave steepness as large as " = 0.4, and reconstructs subsurface velocity fields with greater stability than the Dirichlet-Neumann operator method. Overall, the PFS method provides a scalable and robust framework for long-term, large-domain simulations of fully nonlinear ocean waves in deep and intermediate water depths.

This study presents a spectral-fundamental solution (SFS) method which enables efficient simulation of large-scale nonlinear wave-body interactions. The SFS method combines spectral basis functions and fundamental solutions to achieve both global efficiency and local accuracy. Based on the linearity of the Laplace equation, it decomposes large-scale boundary-value problems into independent subproblems, enabling efficient full-domain computation. Numerical validations show that SFS achieves higher accuracy than the high-order spectral method for short, steep waves and outperforms the method of fundamental solutions in long-wave conditions. Applications to nonlinear ship waves in large-scale domains yield results in good agreement with experimental data, successfully capturing higher-order nonlinear effects. The simulations reveal the physical origins of distinct energy bands in the wave spectrogram and demonstrate how ship acceleration influences the ship-generated wake field. Furthermore, the simulations explain why high-speed ships exhibit wake angles that are narrower than classical predictions. Beyond ship waves, this efficient SFS framework can be extended to a wide range of unsteady wave-structure interaction problems in ocean engineering.

Hydrodynamic interactions between multi-scale ships pose significant challenges due to the substantial scale disparity, which drastically elevates computational complexity and typically induces numerical instability in conventional methods. To address this, this paper develops a one-way coupling method based on frequency-domain potential flow theory, achieved by decoupling the hydrodynamic solutions of the two ships. Specifically, the background flow field (including radiation and diffraction components) induced by the larger ship is first solved, after which the hydrodynamic forces and motions of the smaller ship are evaluated within this field. The theoretical framework is formulated, a dedicated numerical code is developed, and its computational accuracy and efficiency are systematically validated. Numerical results demonstrate that for a scale ratio of 1:5, the proposed one-way coupling method achieves accuracy comparable to the two-way coupling method, while offering approximately double the computational efficiency. Notably, as the scale disparity increases to 1:10, the two-way coupling method suffers from numerical instability attributed to the significantly elevated condition number of the coefficient matrix, whereas the present one-way coupling method maintains stability and accuracy by decoupling the boundary integral equations of the two ships. Consequently, this study establishes the one-way coupling strategy as a robust and efficient alternative that overcomes the stability limitations of conventional methods, particularly for simulating interactions between multi-scale or tandem-arranged ships with forward speed.

This paper presents a novel two-way coupling strategy between viscous and potential flows, termed the Spectral Coupling Layer (SCL) method. This approach integrates a locally resolved viscous region, simulated via OpenFOAM (OF), within a global potential-flow domain solved by the High-Order Spectral (HOS) method. Coupling the pseudo-spectral HOS formulation with time-domain viscous solvers is non-trivial. To address this, the SCL method employs a free-surface velocity-potential correction to transfer flow information from the viscous region to the potential field. A virtual disturbance layer is constructed by sampling velocities from the viscous solution and integrating them directly into the HOS field without iterative matching. Furthermore, a dedicated sampling strategy is introduced to eliminate spurious free-surface velocities inherent to the viscous solver. The proposed approach is validated against pure HOS simulations of wave propagation in two- and three-dimensional domains and demonstrated using a KRISO container ship advancing in calm water. Results indicate that the method achieves high computational accuracy while offering superior flexibility and applicability for complex coastal and marine engineering problems.

The challenge of simulating the broad open sea with limited computational resources has long been of interest in ocean engineering research. In view of this issue, this paper proposes a fully nonlinear potential flow method named the spectral coupled boundary element method (SCBEM). By leveraging the approach of domain decomposition, SCBEM achieves significantly reduced computational cost and an order of magnitude increase in computational domain compared to the conventional boundary element method (BEM). The SCBEM encompasses the marine structure with only a tiny BEM domain and employs a high-order spectral layer to simulate the broad water outside the BEM domain. The performance of the SCBEM is evaluated through comparison with the wave damping approach and literature results for regular waves, modulated wave trains, focused waves, and diffraction of a vertical cylinder. The numerical results demonstrate the effectiveness and accuracy of the SCBEM in simulating a wide range of wavelengths and nonlinear wave interactions. (c) 2023 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

The frequency-domain free-surface Green’s function method is widely used in solving ship hydrodynamic problems, with its core challenge lying in the computation of the Green’s function and its partial derivatives. This study analyzes the relationship between the free-surface Green’s function and its derivatives, proposing a machine learning-based recursive prediction method termed the pulsating source recursive prediction method. The accuracy and efficiency of this method under various parameter settings are investigated, and its application to the hydrodynamic calculations of container ship S175 and a bulk carrier is demonstrated. Results show that the predicted Green’s function achieves an accuracy of 3–6 decimals, with computational efficiency surpassing numerical methods and matching analytical approaches. The hydrodynamic results are reliable, confirming the method’s practical value.

In potential flow theory, the accurate and efficient calculation of free-surface Green's functions is essential for solving hydrodynamic issues. Given the impressive performance of machine learning methods in nonlinear function fitting, the present study utilizes an effective machine learning model called StripeGF for numerical approximation. In this model, equidistant horizontal datum lines are arranged in the computational domain away from the singularity, and Green's function and its derivatives on each line are fitted by a multi-layer perceptron (MLP) with a single input. Based on the first-order ordinary differential equation (ODE) that they satisfy, the fourth-order Runge-Kutta method is used to solve the Green's function and its derivatives between adjacent lines. In the domain nearing the singularity, a double-input MLP is applied. Use the Romberg quadrature to create a double-precision data set for training and validation, the numerical results demonstrate that StripeGF outperforms all 4 comparison methods in terms of efficiency and has accuracy of at least 4 digits in more than 99.9% of all zones. The boundary element program improved by StripeGF is verified in the hydrodynamic calculation of S175, showing good accuracy and reliability.

Inspired by ITTC 2021 (International Towing Tank Conference), this paper implements the Longitudinal Cut Method (LCM), a methodology to predict wave pattern resistance (Rwp), within Computational Fluid Dynamics (CFD) simulation to explore its mechanism and feasibility in predicting wave resistance (Rw). To accurately predict the free surface, a validation study, including the grid convergence index (GCI), wave profile, and wave pattern, is conducted for a Series 60 ship model. Next, Rwp is appropriately evaluated and compared with the experiment. The influence of the transverse wave component on the LCM analysis is also discussed. Furthermore, a comparison between the EFD (Experimental Fluid Dynamics) and CFD-based LCM is made through the analysis of the Wigley Catamaran, highlighting the advantages of the present approach. Finally, the limitations of the LCM theory are systematically discussed with the nonlinear bow wave analysis of a wall-sided ship model by introducing the local adaptive mesh refinement (LAMR) approach. For the fine hull form, LCM has been validated as a suitable methodology for directly predicting Rw and consequently the other primary resistance components (frictional resistance Rf and viscous pressure resistance Rpv) by one simulation. In contrast, due to energy dissipation of the non-negligible nonlinear local field wave component in the downstream wake region, Rw could be underestimated for the full hull form. (c) 2023 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

This paper presents a hybrid method that combines the Harmonic Polynomial Cell (HPC) method and STF strip theory to solve marine hydrodynamics and ship motion problems. The efficient and precise HPC method is extended to three-dimensional ship hydrodynamics using STF strip theory. A new single-node hybridisation condition is introduced to enhance the stability of hydrodynamic predictions. To improve computational accuracy for complex hull shapes, automatic structured grid generation and mesh refinement techniques are applied. The hybrid HPC-STF method is then used to solve 3D ship radiation and diffraction problems in regular waves with forward speed. The method's performance is validated through comparisons of hydrodynamic coefficients, wave forces, and motion response amplitude operators (RAOs) against experimental data and results from other numerical methods. The findings demonstrate that this hybrid approach provides accurate and effective solutions for ship hydrodynamics, making it a valuable tool for analysing marine structures and motions.

As free-flooding ships are a type of vessel with openings on their hull surfaces, accurately calculating and analyzing their roll hydrodynamic coefficients is of great significance for ship motion prediction. Based on the STAR CCM+ platform that employs the computational fluid dynamics (CFD) method, this paper first conducts numerical simulations of the forced roll motion of a damaged DTMB-5415 ship model. The applicability of this method to side-opening ship types is verified by comparing with experimental results. Subsequently, this numerical method is applied to simulate the forced roll of a free-flooding aquaculture ship under different working conditions, and the roll hydrodynamic coefficients of its hull and internal compartments are calculated and analyzed. The roll hydrodynamic coefficients of the intact ship and the free-flooding ship are compared. The results indicate the characteristics of roll hydrodynamic coefficients of free-flooding ships, and this research will facilitate the prediction of roll motion for this ship type.

Added resistance in short waves is significant for large ships, as the waves encountered in their typical operating conditions are primarily short waves. This study numerically investigates the nonlinearity of added resistance in short waves due to bow shapes and breaking waves. The numerical wave generation is first validated to ensure the quality of the incident waves. The original and two modified KVLCC2 hulls in short-wave conditions with various wave heights are simulated to illustrate the nonlinearity of added resistance. The present research demonstrates the effect of bow wave diffraction on added resistance through the analysis of high-order resistance components, the corresponding wave surface and the longitudinal pressure contours. Furthermore, the influence of bow breaking waves on the nonlinearity of high-order resistance components is intuitively demonstrated and discussed through the analyses of pressure and bow wave height, incorporating the evolution of wave elevation. It is discovered that the pressure deficit occurring during breaking waves is a critical factor in this process. The present research deepens the understanding of the underlying mechanisms of added resistance in short waves and contributes to improving the empirical prediction formula.

The frequency-domain free-surface Green's function method, an efficient approach for solving the hydrodynamic problem of ship motion in waves with forward speed, has existed for decades. However, its widespread application in engineering practice remains constrained due to the challenges associated with calculating the Green's function, dealing with the waterline integral term, and handling flared ship hull forms. Additionally, factors such as hull mesh resolution, navigation speed, steady ship wave potential effects, and the speed-related restoring force introduce further uncertainties in hydrodynamic calculations. These factors are systematically investigated through a series of numerical calculations across several representative type ships, with the goal of enhancing computational accuracy, efficiency, and stability. Numerical results revealing that consistency in the treatment of forward speed effects must be maintained between the free surface boundary condition and the hull surface boundary condition. Moreover, the waterline integral term is numerically sensitive and may lead to unstable results. In the present method, sinking the waterline segment source to the centroid of the adjacent panel yields accurate and relatively stable numerical results. For flared ship, a source sinking method is proposed, which improves numerical stability without compromising the satisfaction of boundary conditions.

Wave height forecast (WHF) is of great significance to exploit the marine renewables and improve the safety of ship navigation at sea. With the development of machine learning technology, WHF can be realized in an easy-to-operate and reliable way, which improves its engineering practicability. This paper utilizes a data-driven method, Gaussian process regression (GPR), to model and predict the wave height on the basis of the input and output data. With the help of Bayes inference, the prediction results contain the uncertainty quantification naturally. The comparative studies are carried out to evaluate the performance of GPR based on the simulation data generated by high-order spectral method and the experimental data collected in the deep-water towing tank at the Shanghai Ship and Shipping Research Institute. The results demonstrate that GPR is able to model and predict the wave height with acceptable accuracy, making it a potential choice for engineering application.

This paper presents an efficient time-domain method for simulating nonlinear ship waves. The proposed method, implemented in an earth-fixed coordinate system, integrates a compact boundary element domain within a high-order spectral layer, enabling accurate modeling of both near-field and far-field ship waves. An overset mesh method and an attention mechanism are employed to track the moving ship. The effectiveness of the method is validated through simulations of Wigley and Series 60 ships sailing at various speeds. The numerical results, including the nonlinear wave run-up at the ship bow, surface pressure distribution on the hull, and the ship resistance, agree well with experimental data and published numerical results, confirming that the method is capable of accurately simulating the nonlinear ship waves.

Objectives To simulate the complex nonlinear interactions between the free surface and instantaneous wetted hull surface during ship navigation, an automatic mesh generation method is proposed.MethodsThe method takes a whole-hull triangular mesh file as the input and automatically generates meshes for the instantaneously transforming free surface and wetted hull surface. It is able to handle arbitrary hullforms with complex bow and stern geometries while exhibiting strong robustness. Simulations of waves generated by a KCS hull at various speeds are then conducted using the proposed method. ResultsThe predicted ship-side wave profiles, wave patterns around the hull, and wave-making resistance show good agreement with the experimental results. Moreover, at higher speeds, the simulated wave surface at the KCS stern consistently stays below the transom, exhibiting a dry transom characteristic. ConclusionsThe results demonstrate that the proposed method can accurately model nonlinear ship waves and has the potential to simulate the flow fields around transom-stern ships.

A nonlinear numerical wave tank is established using the Harmonic Polynomial Cell (HPC) method, which is incorporated with a mass source. The numerical wave tank consists of the mass source wave generation region and the working region, with sponge layers at both ends for wave absorption. In the mass source region, a generalized HPC method is applied to solve the inhomogeneous elliptic boundary value problems. The Poisson equation's special solution is represented by a bi-quadratic function. In the remaining domains, the HPC method is employed with harmonic polynomials to solve the problems governed by the Laplace equation in each grid cell. The free surface is tackled by the immersed boundary method (IB-HPC), and the kinematic and dynamic conditions of the free surface are described using a semi-Lagrangian approach. A variety of waves propagation are simulated, including Second-order Stokes wave, fifth-order Stokes wave, solitary wave, fifth-order Fenton stream function wave, random wave and the interaction with a straight vertical wall. The numerical solutions are compared with theoretical solutions. The numerical simulation results demonstrate that the present method can generate arbitrary two-dimensional wave fields by specifying an appropriate source function. Additionally, the reflected waves can propagate through the wave generation region, ensuring that the process of wave generation is not affected by the reflections.

ObjectivesThis study seeks to address the low-frequency limitations in the computation of hydrodynamics for slender ships using strip theory, and develops an efficient method for calculating hydrodynamics over a wider frequency range for slender ships using a simplified approach. MethodsBased on the unified theory of strip theory and ordinary slender body theory, the added mass and damping coefficients of a prolate spheroid, slender, modified Wigley model and S60 ship are calculated programmatically. A comparison is made between the calculated results using the unified theory and experimental data, as well as results obtained from strip theory, 3D translating and pulsating source Green's function method and other methods. The computational characteristics and advantages of the unified theory are then analyzed. ResultsThe results indicate that the unified theory based on 2D sections produces results under zero-speed conditions that are consistent with those obtained by the 3D panel method. For conditions involving ship speed, the calculated results exhibit consistent variations with those obtained from the 3D translating and pulsating source Green's function method. ConclusionsThe proposed unified theory is capable of reflecting 3D effects in the low-frequency region, which gives it greater efficiency and simplicity compared to 3D methods, and thus significant practical value.

This study develops a novel fully nonlinear potential flow approach for predicting the seakeeping performance of the KRISO Container Ship (KCS). We utilize a spectral coupled boundary element method for enhanced numerical efficiency and an acceleration potential-based technique for six degrees of freedom (6-DoF) motion calculation, together facilitating accurate simulations of ship-wave interactions. An overset mesh technique and an automated mesh-cutting process are introduced to accurately model instantaneous boundaries. Convergence analyses are conducted to validate the proposed method. Simulations of heave and pitch responses in head waves show good agreement with experimental and computational fluid dynamics results in literature, also demonstrating the nonlinear effects of large incident waves on ship motion. Moreover, the method accurately simulates parametric rolling and reveals the coupling effect between roll and other DoFs.