2025-05-14 2026, Volume 25 Issue 2

  • Select all
  • research-article
    Chol Jun Pak, Min Hyok Jon, Yong Gwang Ri, Ryong Il Ju

    The water entry problem is an important issue in the field of marine engineering, and predicting the behavior of a body entering water is extremely difficult because of water’s strong nonlinearity. In this study, we investigate hydrodynamic load acting on a two-dimensional (2D) wedge during water entry. The adopted approach is the moving particle semi-implicit (MPS) method, which is widely utilized in the simulation of nonlinear free surface flow. Moreover, two techniques to enhance the performance of MPS are suggested and a symmetry domain technique for reducing the computational cost is also proposed. Additionally, a fluid–solid coupling algorithm using the MPS method is suggested. Several cases are numerically investigated to verify the proposed method, and its performance is verified through the simulation of hydrostatic pressure and dam break. Furthermore, 2D wedge water entry problems with symmetric or asymmetric characteristics are studied using the proposed MPS method and compared with some experimental and previous numerical studies. The results show that the MPS with the proposed schemes can provide a reliable numerical prediction for water entry problems.

  • research-article
    Jacopo Bardiani, Luca Lomazzi, Claudio Sbarufatti, Andrea Manes

    In naval engineering, understanding underwater explosions is crucial for structural integrity and safety, particularly for combat ships. Coupled numerical analyses, which account for fluid-structure interaction (FSI), are accurate but computationally expensive and impractical for real-time applications. In contrast, uncoupled methods are efficient but overlook FSI effects. This study introduces a data-driven approach using a feedforward Deep Neural Network (DNN) to estimate FSI-induced displacements from uncoupled simulations. Trained on numerical datasets of blast-loaded plates with varying characteristics, the DNN predicts the coupled displacement field based on structural parameters of uncoupled simulations. Results demonstrate that this framework provides a fast and reliable alternative to coupled simulations, offering a practical engineering tool for underwater blast scenarios. This work serves as proof of concept that deep-learning-enhanced uncoupled simulations can replace coupled ones, with validity beyond the specific structure in the case study.

  • research-article
    Long Zhu, Yanzhuo Xue, Ruinan Guo, Yingfei Zan, Yang Lu, Yicheng Zhang

    The form of an icebreaker bow is numerically optimized using a platform that relies on three methods ship geometry morphing under a fully parameterized modeling approach, a cyclic process of contact compression bending failure to calculate the icebreaking loads, and a differential evolution algorithm for optimization. The main objectives of this study are to optimize the total resistance and the average pressure in the ice zone. Surface sensitivity analysis based on an adjoint solver is used to identify the most significant regions of the hull. The hull in these regions is then formed using a cubic nonuniform rational B-spline technique. The differential evolution algorithm is employed to optimize the objectives associated with the hull form and determine the corresponding optimized variables. The optimal values are obtained by comparing the Pareto optimal designs. The optimization results show that the acquired hull form reduces the total resistance by 4.2% and decreases the average pressure in the ice zone by 0.6%. The main modifications introduced by the optimization process are to increase the buttock angle and the waterline angle.

  • research-article
    Alireza Nadery, Hossein Shafigh, Amin Najafi, Hassan Ghassemi, S. Yasin Ziabari

    This study parametrically explores the hydrodynamic characteristics of a toroidal propeller. Seven geometrical parameters (skew angle, pitch angle, chord length, rake, roll angle, blade alpha vertical angle, and blade section) are introduced, and their effects on thrust, torque, and efficiency are analyzed. The performance of the propellers is simulated using computational fluid dynamics based on the finite volume method. First, an open-water simulation is conducted for a common B-series propeller. The numerical results are compared with available experimental data, and an acceptable agreement is achieved. Then, the investigations were extended to the toroidal propeller by changing the seven geometrical parameters (±5%, ±10%, and ±20%). The analysis demonstrates hydrodynamic performance improvements relative to the B-series propeller. Numerical results indicate that changes in pitch angles exert the greatest influence on hydrodynamic efficiency, whereas variations in skew angle have the least impact. Furthermore, a comparative study examines the flow field around and downstream of the propellers under different operating conditions.

  • research-article
    Ming He, Yexian Wang, Enfan Lin, Wenzhi Cui, Jiale Yan

    Structural water entry remains a significant issue in fluid mechanics. Technological advancements and the diversification of application scenarios have introduced complex environmental boundaries, including irregular fluid and limited-domain boundaries, which are encountered during water entry. This study employs the Eulerian finite element method to simulate fluid dynamics and applies an improved immersed boundary method to address problems involving fluid–structure interaction interfaces. A coupled numerical model for structural water entry in limited-domain water is developed. Initially, a theory of water entry cavitation is derived, and the approximate range of boundary effects is determined. Results of pressure regulation experiments show that the numerical model fully demonstrates the numerical algorithm’s effectiveness. Therefore, numerical methods are used in comprehensively analyzing the effects of structural size, water domain size, and water entry speed. Modifications to these factors can alter cavitation evolution characteristics, influencing a structure’s motion state by qualitatively revealing the physical mechanisms of the process through the evolution of free surfaces, speed attenuation, and acceleration evolution at varying parameters. The findings provide valuable technical support for future navigation design.

  • research-article
    Sreejith Kunnamkulangara, Anil Kumar Dash, Vishwanath Nagarajan

    This study examined the impact of the leading-edge sweep angle on the vibration characteristics of a marine cycloidal propeller (MCP) blade during different ship maneuvering motions using a coupled three-dimensional boundary element method (BEM) and finite element method (FEM) approach. Through this approach, the study captured the interaction between hydrodynamics and structural dynamics, providing a comprehensive understanding of the response of the swept MCP blade. The following ship maneuvers were analyzed: bollard pull, crabbing, crash stop, cruising, and turning circle. During MCP operation, each blade undergoes one oscillation about its own longitudinal axis for each rotation of the horizontal propeller disc. The face and back of the propeller blade interchange during each oscillation. Consequently, the propeller blades are subjected to higher fluctuations in loading because of changes in the angle of attack and inflow velocity at each time instant. This results in complex and unstable fluid dynamics at the blade location. Variations in the sweep angle can profoundly influence the performance of the blade by altering the hydrodynamic loads and structural responses. The impact of the sweep angle is depicted through changes in the displacement, velocity, twisting angle, twisting moment, and von Mises stress of the blade. Furthermore, because of the load fluctuations on the blade, fatigue and load variations in each disc revolution must be considered during the design of cycloidal propellers. Therefore, a preliminary fatigue assessment for each maneuver was conducted. The research provides valuable information into the behavior of swept MCP blades under various loading conditions.

  • research-article
    Kumar Gaurav, Nagothu Venkatesh, Aman Raj, Ashish Karn

    Underwater warfare in the modern world demands the development of fast, supercavitating torpedoes. Torpedoes typically achieve supercavitation via a single cavitator mounted at the nose; the cavitator’s dimensions dictate the supercavity size. This study introduces a novel approach of incorporating a secondary cavitator to enhance the supercavity and improve the performance of supercavitating torpedoes. Numerical simulations are performed using Reynolds-averaged Navier – Stokes equations solved with a pressure-based algorithm. The volume of fluid (VOF) multiphase model, in conjunction with the Schnerr–Sauer cavitation model, is employed to model the supercavitation phenomenon. The effects of cavitator size, positioning, and operating conditions on supercavity behavior are also examined. Results indicate that positioning the secondary cavitator at 70%–90% of the primary supercavity length significantly enlarges the supercavity, achieving a 30%–35% increase in supercavity length. The optimal size for the secondary cavitator is also identified, beyond which reverse flow and cavity shrinkage occur. The dependence of the secondary cavitator’s critical size on the primary cavitator’s diameter and Froude number is further investigated. This research provides new insights into the design of supercavitating vehicles and establishes a framework for optimizing cavitator configurations in heavyweight torpedoes.

  • review-article
    Yu Han, Qiang Fu, Shuangyin Chen, Chengwang Xiong

    Water infiltration and freeze-thaw processes in soils involve pore-scale flow, phase change, and heat transfer. These processes are difficult to describe using conventional continuum methods. Such methods rely on averaged properties and cannot resolve pore-scale interfaces, connectivity changes, or moving phase boundaries. The lattice Boltzmann method (LBM) provides a mesoscopic approach for this type of problem. It represents pore geometry and multiphase interfaces directly on discrete lattices. This feature makes it suitable for simulating saturated and unsaturated seepage, heat transfer under freezing conditions, and freeze-thaw cycles. This paper reviews recent studies on LBM applications in these areas. Different model frameworks and numerical strategies are compared. The results show that LBM can capture pore-scale mechanisms that are not accessible to continuum models. However, several limitations remain. These include high computational cost, unclear physical meaning of some model parameters, and limited experimental validation.

  • research-article
    Minh Thao Nguyen, Francesco Balduzzi, Alessandro Bianchini, Anders Goude

    The hydrodynamic behavior of vertical-axis marine current turbines is analyzed through a multivariate study considering various combinations of blade numbers, chord lengths, and rotor radii across 16 geometrical configurations operating over a wide range of tip speed ratios (TSRs) using two-dimensional computational fluid dynamics (CFD) simulations. The results reveal that reducing the number of blades from 6 to 3 at a given solidity can increase the power coefficient by up to 7.9%. However, this performance gain comes at the cost of a considerable increase in torque fluctuation amplitude, which in water applications could affect structural loading and operational stability. While these results align well with the literature in aggregate, the present study provides additional insights by reconstructing lift and drag polars using an advanced methodology to extract the instantaneous angle of attack of the flow approaching the blades. This approach provides not only a more in-depth analysis of blade hydrodynamics under unsteady conditions but also contextualizes the impact of the Reynolds number and chord-to-radius (c/R) ratio on turbine performance through the virtual cambering effect. The results demonstrate that higher Reynolds numbers enhance resistance to flow separation, while larger chord lengths amplify the virtual curvature effect. These findings improve the understanding of the interplay between key geometric and operational parameters, offering valuable guidance for optimizing vertical-axis turbine design in marine energy applications.A simple local watertight plate adjustment in the high-risk area can improve the safety of the ship.

  • research-article
    Jiang Xu, Jun Guo, Zhen Bao, Xiaojun Zhao

    The vibration and noise reduction characteristics of submersibles have been extensively investigated. Composite materials have various applications in automotive, aerospace, and other fields because of their excellent damping, corrosion resistance, specific strength, and other properties. However, compared with steel, composites are still deficient in terms of stability, stiffness, and economy. Composites also present structural dynamic parameter properties that differ from those of steel structures, which limit their application on submarines. This study aims to improve the vibration and noise reduction performance of submarines and further enhance the application of composite materials in submarine vehicles. For this purpose, the structural design of a laminated reinforced cylindrical shell made of steel and composite materials is conducted, and a traditional form of steel comparative structure with equal mass and shape is designed to contrast with the laminated model. The modal characteristics reflect the inherent frequency features of a structure. By altering the natural frequency, the model can be shifted away from the excitation frequency, which avoids intense resonance and effectively suppresses sound radiation caused by resonance. Therefore, the characteristics of the two structures in terms of modal and damping are compared and explored through experiments and simulations. The results show that the relative error of the modal between experiment and computation does not exceed 6%. After replacing 40% of the mass of steel with carbon fiber, the first three orders of the intrinsic frequency of the structure are increased by more than 13%, the amplitude of the transfer function is reduced by 9.6%, and the damping is improved by more than 75%. Therefore, the vibration and noise reduction characteristics of submersibles have been improved.

  • review-article
    Jixiang Zhang, Shan Wang, Milad Shadman, Mojtaba Maali Amiri, Baiqiao Chen, Chen An, Segen Farid Estefen

    The long-term responses of offshore wind turbines (OWTs) are critical in the design phase, where precise assessments ensure structural reliability and operational efficiency. The environmental contour method (ECM) enables efficient analysis of design responses by focusing on a selected set of critical environmental conditions that predominantly drive long-term extreme responses. Despite its extensive use in offshore engineering, ECM’s application in the structural design and strength assessment of OWTs remains underexplored. This study offers a comprehensive overview of the utilization of ECM in the context of OWT design, incorporating a bibliometric analysis of publications from the Web of Science to identify research trends and key topics. The analysis highlights diverse approaches for estimating long-term extreme responses and constructing environmental contours using statistical distributions. Additionally, the study explores the application of ECM and its modified versions in the design and strength assessment of OWTs. Challenges and opportunities associated with ECM implementation in OWTs are critically analyzed, providing insights into ECM’s potential for enhancing the efficiency and reliability of OWT structural design.

  • research-article
    Srinivasan Chandrasekaran, Puliparambil Unnikrishnan Ashish

    The offshore triceratops platform has emerged as a promising candidate for maritime launches due to its innovative and unique responsive characteristics. Their form-dominant design facilitates dynamic equilibrium and effectively controls the impact of the deck’s rotational motion during sea-borne launch. A parametric study examines how the shape of buoyant legs influences the dynamic response during rocket launches, utilizing ANSYS AQWA for analysis. The study finds that elliptical legs with an eccentricity of 2 reduce deck responses. While the deck rotation is driven by the quasi-static rocket thrust and the differential heave of the legs, the pitch response arises from the waves and is reduced by using elliptical legs. Numerical studies conducted during rocket launches show an amplified deck response. The vertical force on the deck is maximized during vertical launches and minimized during 30° launches. The pitch moment on the deck increases with launch eccentricity, which is attributed to the cantilever effect of the launch platform.

  • research-article
    Bin Liu, Lei Zhang, Yiwen Wang, Qingyang Fan, C. Guedes Soares

    This paper evaluates the responses of equivalent stiffened panels made of steel, an aluminum alloy, and the glass fiber – reinforced plastic (GFRP) composite under extreme slamming loads. These panels are designed for bow flare structures in high-speed crafts. Their equivalence is established with respect to their designs using the same classification society rules. The analysis methods used in this work are illustrated, and slamming loads and inelastic structural responses are analyzed separately. Slamming loads are evaluated using a two-dimensional rigid bow flared section, with dynamic structural deformation and stress responses assessed through nonlinear finite-element analysis. The structures constructed of various materials are verified to meet design requirements. The primary objective of this work is to investigate the safety margin of bow flare structures constructed of steel, an aluminum alloy, and the GFRP composite under extreme sea conditions. The results show that the equivalent composite structures with larger scantlings, particularly the GFRP flat-bar stiffened structure, still exhibit considerably weaker impact strength under extreme slamming loads. The investigation of the structural responses and damage characteristics of equivalent stiffened plates under extreme slamming loads provides a reference for the potential limit state design of the bow flare structures of high-speed crafts.

  • research-article
    Seher Suendam Arici, Sukru Ilke Sezer, Emre Akyuz

    Depending on the nature of the cargo, specific temperatures must be maintained throughout the safe carrying and loading/unloading of chemical tankers. In this regard, tank heating systems are essential for maintaining the proper temperature range for chemical cargoes, particularly those transported at viscous or near-freezing temperatures. The operational process presents safety challenges because of the nature of the task that the ship crew must perform. Since human error is increasingly a major contributor to marine mishaps, this paper conducts a systematic human error prediction to ensure safe tank heating operations under various conditions. However, improper use of these systems can cause problems such as fire and explosion risk due to overheating, toxic gas formation, cargo deterioration, and equipment damage. This study examines operational practices and risks related to using tank heating systems in chemical tankers; evaluations are made in terms of energy efficiency, cargo safety, and environmental impacts. The paper discusses the fuzzy approach’s Success Likelihood Index Method (SLIM) to achieve this. The fuzzy approach in the suggested method can assist experts’ judgment in decision-making, and the SLIM offers a thorough human error prediction tool. “Perform the temperature increase gradually and prevent sudden temperature increases” is identified as a critical task with the highest human error probability (HEP: 5.28E-02) during chemical tanker tank heating operations.

  • research-article
    Ao Zhou, Yadong Zhang, Wentie Yang, Zuoshuai Wang, Jianxun Wang, Zhiwei Chen

    Accurate modeling of ship magnetic fields is important for predicting their spatial distribution to improve the magnetic stealth effect of ships. This study proposes an extrapolation model for ship magnetic fields based on genetic algorithms and convolutional neural networks (CNNs). The magnetic probe position matrix of the traditional equivalent source is utilized as input, and the three-directional components of the magnetic field measured by the probes are employed as output. The extrapolation model for ship magnetic fields is obtained through iterative training and fitting with CNNs. Variables such as the number of magnetic dipoles, the distance between magnetic dipoles, the size and quantity of convolutional kernels, batch size, learning rate, and L2 regularization coefficient are optimized to boost the accuracy of the extrapolation model for magnetic fields. The fitting accuracy of the extrapolation model for ship magnetic fields is used as the optimization objective. Based on a finite element simulation model of ship magnetic fields, the accuracy and robustness of the CNN algorithm under different magnetic field conditions are validated using the known standard depth plane, the unknown depth at 1.125 times the standard depth plane, and the unknown depth at 1.25 times the standard depth plane. Results show that, after optimization, the fitting error for the magnetic field extrapolation model based on CNN is 1.50% for the standard depth plane, 1.63% for the unknown depth at 1.125 times the standard depth plane, and 2.36% for the unknown depth at 1.25 times the standard depth plane. The error remains below 5% under varying magnetic field conditions. When a random measurement error of 0%–5% is introduced for the magnetic probes, the prediction error at 1.25 times the standard depth plane is 2.30%; with a random error of 0%–10%, the prediction error is 4.95%. This approach significantly improves the accuracy and robustness of magnetic field extrapolation, which makes it an effective and feasible method for ship magnetic field modeling.

  • research-article
    Conghuan Le, Xinting Zheng, Siteng Ma, Puyang Zhang, Hongyan Ding

    This paper introduces a novel three-anchor combined suction anchor (TACSA) structure and evaluates the ultimate bearing characteristics of two mooring types under mooring line failure scenarios: single-primary-anchor mooring (SPAM) and dual-primary-anchor mooring (DPAM). Utilizing the finite element software ABAQUS, the ultimate bearing capacity and failure mode of the anchor were analyzed under the mooring line failure conditions. The findings indicate that with an increase in the deflection angle, the bearing capacity of the anchor experiences a gradual decline. A comparison of the two types of mooring revealed that DPAM resulted in a reduced descending speed of the bearing capacity and a smaller deflection angle of the anchor compared to the SPAM. In the SPAM system, the occurrence of linear plastic damage is contingent upon the attainment of a deflection angle of 45°. In the DPAM system, such damage manifests when the deflection angle exceeds 60°. These findings suggest that the synergistic effect between the anchors and the soil is enhanced in the DPAM system. Consequently, DPAM system demonstrates superior ultimate bearing characteristics and a reduced rotation degree, rendering it more effective in resisting the torque load induced by the deflection angle compared to SPAM system.

  • research-article
    Haiyang Gao, Guangen Luo, Pengfei Xu, Ying Chai, Liangbi Li

    The crack propagation life of welded ship structures is considerably influenced by welding residual stresses, which are redistributed as cracks propagate. Therefore, studying the mutual interaction between welding residual stress redistribution and surface crack propagation is crucial for accurately predicting the crack propagation life of welded structures. This research uses TC4 titanium alloy specimens, applying the extended finite element method to investigate the welding residual stress redistribution during surface crack propagation. The cyclic iteration analysis method is proposed to simultaneously consider the redistribution of welding residual stresses and crack propagation. The results show that 1) the welding residual stresses at the surface crack tip and crack depth initially increase, then decrease with crack propagation, and 2) the predicted fatigue crack propagation life, when welding residual stress is not considered, is 2.01 times longer than the corresponding fatigue crack propagation life using the proposed method, which accounts for welding residual stress. In addition, when the welding residual stress is set to a constant value of 0.3 σy, the fatigue crack propagation life prediction becomes overly conservative, yielding only 0.39 times the fatigue crack propagation life predicted based on the mutual influence of welding residual stress redistribution. The fatigue crack propagation life prediction method proposed in this study, which considers the interaction between welding residual stress redistribution and crack propagation, offers a more reasonable approach. It lays the foundation for accurate prediction of fatigue crack propagation life in welded structures.

  • research-article
    Shanqiang Li, Chaoxi Li

    For unmanned surface vehicles (USVs), how to find an effective, feasible path that substantially improves mission success rates and time efficiency in dynamic marine environments is a critical issue. To address the path planning problem for USVs using deep reinforcement learning (DRL) in dynamic ocean environments, an improved algorithm based on Deep Q-Networks (DQN) is proposed, which is called Fast Guided Deep Q-Network Algorithm (FG-DQN). This algorithm combines DQN with the artificial potential field (APF) method and uses the A* algorithm to initialize a guiding path in a global static environment and to provide prior knowledge for the USVs. Additionally, the configuration of the reward function using APF and the guiding path effectively reduces the frequency of random movements during the early exploration phase of the DQN algorithm, which accelerates convergence, improves the computational efficiency of path planning, and increases path safety. Finally, the performance of the presented algorithm is validated through experiments in a 2D environment. Compared with traditional reinforcement learning methods such as Q-learning and Sarsa, as well as the original DQN algorithm, FG-DQN is more effective for USV path planning.

  • research-article
    B. Sairam Prasad, G. Ravi Kiran Sastry

    This study conducts a detailed numerical investigation into the oblique water entry dynamics of an autonomous underwater vehicle (AUV) impacting the water surface based on the fundamentals of water entry dynamics. It integrates recent advancements in numerical simulations to address the challenges of transient motion and fluid-structure interactions. This study uses advanced computational fluid dynamics (CFD) simulations to explore the complex interaction between the vehicle and the surrounding fluid during the critical transition from air to water. The primary objectives of this investigation include the assessment of resultant forces and the identification of optimal launch parameters such as entry velocity and entry angle to enhance entry effectively. The numerical methodology and results offer valuable insight into the hydrodynamic behavior of AUVs, thereby contributing to more advanced and capable air-launched AUV systems.

  • research-article
    Ruolan Zhang, Xingchen Ji, Jinichi Koue, Katsutoshi Hirayama

    The establishment of a reliable benchmark for evaluating model performance is critical for advancing deep learning (DL), including its application in the recognition of the ship navigation environment. Despite the steady progress being made in object detection models across various tasks, maritime navigation presents unique challenges, such as long distances, miscellaneous objects, wide perception scales, and local conditions and features of water areas. Therefore, the improvement of DL approaches for this domain remains a significant challenge. Using a widely applicable offshore image dataset from the ship bridge, we evaluated the performance of the state-of-the-art object detection model from three perspectives: average precision, multiscale feature calculation, and intersection-over-union design, and explored the factors that may affect the model performance evaluation benchmark from the perspective of data quality, scale calculation, feature quantification, and object association. Our experiments have demonstrated that, in the context of object detection tasks within complex water surface traffic scenes, comprehensive model performance evaluation benchmarks are essential. Such benchmarks must incorporate multiple dimensions of the model.

  • research-article
    Njideka Chima-Amaeshi, Chris O’Malley, Mark Willis

    Marine transportation is a significant source of air pollution especially around coastal areas with maritime vessels creating 12% of global sulphur oxides emission in 2014 alone. In compliance with International Maritime Organisation (IMO) regulations, the determination of sulphur content of marine fuels is typically carried out using lengthy laboratory-based analyses. The regulations prohibit the use of High-Sulphur Fuel Oil (HSFO) (>0.5% by weight of Sulphur) in Emission Control Areas (ECA). There is a need for a more efficient means of predicting Sulphur content and differentiating between HSFO and Very Low Sulphur Fuel Oil (VLSFO) samples. This study compares the application of a Support Vector Machine (SVM) and Agglomerative Hierarchical Clustering (AHC) algorithm enhanced with Principal Component Analysis for dimensionality reduction purposes to predict HSFO and VLSFO marine fuel samples based on near-infrared (NIR) industrial data from North Sea operations correlated with laboratory-measured sulphur values instead of relying on lengthy laboratory-based measurements. The study also compares the effect of normalising the data by setting the area under the curve to one and standardising it by subtracting the mean of predictor variables and scaling by standard deviation. The results show that although >70% of HSFO samples were accurately predicted with the SVM, a better result was achieved using the unsupervised learning approach of AHC/PCA with >80% of HSFO samples correctly predicted despite the imbalance in the industrial data providing an effective model for the rapid and well-informed decision-making tool for vessel operators. Normalising the area under the curve to one produced similar results to using standardised data.

  • research-article
    Jiaheng Zhang, Wei Ge, Wentao Tong, Lin Cheng

    Turbo equalization is commonly employed to compensate for multipath propagation in underwater acoustic (UWA) communication. However, the performance of turbo equalization degrades due to the imperfect channel state information (CSI) and time-varying channels. Herein, we first introduce a new derivation for turbo equalization based on the joint Gaussian criterion. On the basis of this derivation, a novel turbo equalization algorithm for time-varying UWA channels with imperfect CSI is proposed. The algorithm combines the imperfect CSI with the temporal coherence characteristics of UWA channels, which are modeled as a first-order autoregressive (AR(1)) process, to achieve a more accurate channel a posteriori distribution. Afterward, the refined distribution is incorporated into the design of the turbo equalizer, which can effectively reduce intersymbol interference and the Doppler effect. Simulation results show that the proposed algorithm has a better bit error rate performance than other turbo equalization algorithms with channel estimation error compensation or the AR(1) process for any iteration in fast time-varying scenarios.