Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106084
Jinwei Ma , Qinglin Duan , Rong Tian , Siqi Shu
A consistent generalized finite element method (C-GFEM) is proposed, showing excellent accuracy and convergence in distorted quadrilateral and hexahedral meshes. Both displacement approximation and domain integration are taken into consideration regarding the declining performance of the finite element method (FEM) in distorted meshes. In the displacement approximation, extra-degrees of freedom-free and linearly independent enrichments developed in GFEM are employed, which restores the reproducibility of the approximation in distorted meshes. In the domain integration, the idea of correcting nodal derivatives in the framework of the Hu–Washizu three-field variational principle is introduced into GFEM, based on which consistent integration schemes using quadrilateral and hexahedral elements are developed in this work. Furthermore, to consistently enforce the essential boundary condition, additional terms of boundary integral are introduced into the weak form. As a result, the proposed C-GFEM can pass patch tests and keep high accuracy even though the computational mesh is distorted. Its perfect performance in distorted meshes is sufficiently demonstrated by the numerical investigation of several benchmark examples.
{"title":"Consistent generalized finite element method: An accurate and robust mesh-based method even in distorted meshes","authors":"Jinwei Ma , Qinglin Duan , Rong Tian , Siqi Shu","doi":"10.1016/j.enganabound.2024.106084","DOIUrl":"10.1016/j.enganabound.2024.106084","url":null,"abstract":"<div><div>A consistent generalized finite element method (C-GFEM) is proposed, showing excellent accuracy and convergence in distorted quadrilateral and hexahedral meshes. Both displacement approximation and domain integration are taken into consideration regarding the declining performance of the finite element method (FEM) in distorted meshes. In the displacement approximation, extra-degrees of freedom-free and linearly independent enrichments developed in GFEM are employed, which restores the reproducibility of the approximation in distorted meshes. In the domain integration, the idea of correcting nodal derivatives in the framework of the <em>Hu–Washizu</em> three-field variational principle is introduced into GFEM, based on which consistent integration schemes using quadrilateral and hexahedral elements are developed in this work. Furthermore, to consistently enforce the essential boundary condition, additional terms of boundary integral are introduced into the weak form. As a result, the proposed C-GFEM can pass patch tests and keep high accuracy even though the computational mesh is distorted. Its perfect performance in distorted meshes is sufficiently demonstrated by the numerical investigation of several benchmark examples.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106084"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142901665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106098
Sha Xiao , Zhongqi Quentin Yue
This paper examines the contact problem of a heterogeneous geo-material medium indented by a circular rigid plate. The rigid plate is subjected to an applied moment about a horizontal axis. An n-layered half-space model is employed to analyze a heterogeneous geo-material half-space. The mathematical formulation of the n-layered half-space model is derived using classical integral transforms and a Fredholm integral equation of the second kind. Numerical methods are developed to solve the proposed analytical model. Numerical verification demonstrates that the layered approach can provide accurate solutions for the contact problem of the heterogeneous half-space with arbitrarily variable elastic constants in depth. Numerical results reveal the influence of geo-material heterogeneity on the elastic field of a heterogeneous medium under antisymmetric loading on a circular rigid plate.
{"title":"Elastic fields for a heterogeneous geo-material medium under antisymmetric indentation of a circular rigid plate","authors":"Sha Xiao , Zhongqi Quentin Yue","doi":"10.1016/j.enganabound.2024.106098","DOIUrl":"10.1016/j.enganabound.2024.106098","url":null,"abstract":"<div><div>This paper examines the contact problem of a heterogeneous geo-material medium indented by a circular rigid plate. The rigid plate is subjected to an applied moment about a horizontal axis. An <em>n</em>-layered half-space model is employed to analyze a heterogeneous geo-material half-space. The mathematical formulation of the <em>n</em>-layered half-space model is derived using classical integral transforms and a Fredholm integral equation of the second kind. Numerical methods are developed to solve the proposed analytical model. Numerical verification demonstrates that the layered approach can provide accurate solutions for the contact problem of the heterogeneous half-space with arbitrarily variable elastic constants in depth. Numerical results reveal the influence of geo-material heterogeneity on the elastic field of a heterogeneous medium under antisymmetric loading on a circular rigid plate.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106098"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106062
Like Deng , Dongdong Wang
Although kernel functions play a pivotal role in meshfree approximation, the selection of kernel functions is often experience-based and lacks a theoretical basis. As an attempt to resolve this issue, a rational matching between kernel functions and nodal supports is proposed in this work for Galerkin meshfree methods, where the quadratic through quintic B-spline kernel functions are particularly investigated. The foundation of this rational matching is the design of an efficient quantification of relative interpolation errors. The proposed relative interpolation error measures are not problem-dependent and can be easily and efficiently evaluated. More importantly, these relative interpolation error measures effectively reflect the variation of the real interpolation errors for meshfree approximation, which essentially control the solution accuracy of the Galerkin meshfree formulation with consistent numerical integration. Consequently, an optimal selection of kernel functions that match the nodal supports of meshfree approximation can be readily realized via minimizing the relative interpolation errors of meshfree approximation. The efficacy of the proposed rational matching between kernel functions and nodal supports is well demonstrated by meshfree numerical solutions.
{"title":"A rational kernel function selection for Galerkin meshfree methods through quantifying relative interpolation errors","authors":"Like Deng , Dongdong Wang","doi":"10.1016/j.enganabound.2024.106062","DOIUrl":"10.1016/j.enganabound.2024.106062","url":null,"abstract":"<div><div>Although kernel functions play a pivotal role in meshfree approximation, the selection of kernel functions is often experience-based and lacks a theoretical basis. As an attempt to resolve this issue, a rational matching between kernel functions and nodal supports is proposed in this work for Galerkin meshfree methods, where the quadratic through quintic B-spline kernel functions are particularly investigated. The foundation of this rational matching is the design of an efficient quantification of relative interpolation errors. The proposed relative interpolation error measures are not problem-dependent and can be easily and efficiently evaluated. More importantly, these relative interpolation error measures effectively reflect the variation of the real interpolation errors for meshfree approximation, which essentially control the solution accuracy of the Galerkin meshfree formulation with consistent numerical integration. Consequently, an optimal selection of kernel functions that match the nodal supports of meshfree approximation can be readily realized via minimizing the relative interpolation errors of meshfree approximation. The efficacy of the proposed rational matching between kernel functions and nodal supports is well demonstrated by meshfree numerical solutions.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106062"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142793486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106052
A. Lamei , M. Hayatdavoodi , H.R. Riggs , R.C. Ertekin
This study is concerned with rigid-body responses and elastic motion of floating offshore wind turbines (FOWTs) under combined wave, current and wind loads. A numerical approach is developed in frequency domain based on the linear diffraction theory with a Green function for small current speeds and the blade-element momentum method for hydrodynamic and aerodynamic analysis, respectively. This approach is coupled with the finite-element method to obtain the hydro- and aeroelastic motion of FOWTs. The interaction of combined wave–current–wind with three FOWTs, namely SPAR, semisubmersible and barge, is considered. Rigid-body responses of the three FOWTs to waves and wind are compared to those when current loads are present. Furthermore, the effect of current speed and misalignment of incident waves with current-wind on the motion of the FOWTs is investigated. Discussion is provided on the importance of considering wave–current interaction together with aerodynamic loads on the responses of the considered FOWTs. It is observed that the motion of the SPAR FOWT to combined waves and wind changes the most when the current loads are added. Finally, the effect of wave–current-wind interaction on the elastic motion of flexible FOWTs is investigated and compared with their rigid-body counterparts.
{"title":"Wave–current–wind interaction with elastic floating offshore wind turbines","authors":"A. Lamei , M. Hayatdavoodi , H.R. Riggs , R.C. Ertekin","doi":"10.1016/j.enganabound.2024.106052","DOIUrl":"10.1016/j.enganabound.2024.106052","url":null,"abstract":"<div><div>This study is concerned with rigid-body responses and elastic motion of floating offshore wind turbines (FOWTs) under combined wave, current and wind loads. A numerical approach is developed in frequency domain based on the linear diffraction theory with a Green function for small current speeds and the blade-element momentum method for hydrodynamic and aerodynamic analysis, respectively. This approach is coupled with the finite-element method to obtain the hydro- and aeroelastic motion of FOWTs. The interaction of combined wave–current–wind with three FOWTs, namely SPAR, semisubmersible and barge, is considered. Rigid-body responses of the three FOWTs to waves and wind are compared to those when current loads are present. Furthermore, the effect of current speed and misalignment of incident waves with current-wind on the motion of the FOWTs is investigated. Discussion is provided on the importance of considering wave–current interaction together with aerodynamic loads on the responses of the considered FOWTs. It is observed that the motion of the SPAR FOWT to combined waves and wind changes the most when the current loads are added. Finally, the effect of wave–current-wind interaction on the elastic motion of flexible FOWTs is investigated and compared with their rigid-body counterparts.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106052"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142793488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106094
Yukai Jin, Yidan Zhang
This paper focuses on applying non-linear transformations for near singularity regularization combined distance transformations. In the previous methods, near singularities are usually considered in only the polar direction, ignoring those in the circular direction, which leads to low accuracy when calculating nearly singular integrals of narrow element or when the projection point is located near the element end. In this paper, the near singularities are traced firstly based on the distance function, by which the distance function can be constructed in two ways. The general form of nearly singular integrals in the two directions is extracted. Then, several non-linear transformations are introduced about removal of the near singularities in one direction. In our method, the only one directional methods are combined to solve the nearly singular integrals. Finally, comparisons of the results by the combined distance transformations show that by employing the non-linear transformations in both directions, more stable and accurate results can be obtained especially for nearly singular integrals of the narrow elements.
{"title":"Various near singularity regularization methods derived from distance transformations in 3D boundary element method","authors":"Yukai Jin, Yidan Zhang","doi":"10.1016/j.enganabound.2024.106094","DOIUrl":"10.1016/j.enganabound.2024.106094","url":null,"abstract":"<div><div>This paper focuses on applying non-linear transformations for near singularity regularization combined distance transformations. In the previous methods, near singularities are usually considered in only the polar direction, ignoring those in the circular direction, which leads to low accuracy when calculating nearly singular integrals of narrow element or when the projection point is located near the element end. In this paper, the near singularities are traced firstly based on the distance function, by which the distance function can be constructed in two ways. The general form of nearly singular integrals in the two directions is extracted. Then, several non-linear transformations are introduced about removal of the near singularities in one direction. In our method, the only one directional methods are combined to solve the nearly singular integrals. Finally, comparisons of the results by the combined distance transformations show that by employing the non-linear transformations in both directions, more stable and accurate results can be obtained especially for nearly singular integrals of the narrow elements.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106094"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142901667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106089
Tinesh Pathania
In the present study, a meshless BIOEFGM II model is proposed to simulate the natural attenuation of BTEX contaminant (benzene, toluene, ethylbenzene, and xylenes) through multiple aerobic and anaerobic electron acceptors in the two-dimensional groundwater system. This model is the extension of the BIOEFGM I model for aerobic BTEX degradation. In BIOEFGM II, the meshless element-free Galerkin method (EFGM) is applied to governing groundwater flow and reactive transport equations. The weak-integral form of EFGM is also applied to the Darcy law equation to compute the groundwater velocity directly at scattered field nodes representing the aquifer domain. This step allows the easy coupling of flow and transport models with both regular and irregular nodes in BIOEFGM II, unlike grid/mesh-based models. The proposed model is the first multispecies model that can simulate natural BTEX degradation using regular/irregular field nodes. In this study, proposed BIOEFGM II-RG and BIOEFGM II-IRG for regular and irregular nodes respectively are applied to a hypothetical aquifer and field-type large heterogeneous aquifer, and results are verified with the benchmark RT3D model. The results of this study reveal that aerobic and anaerobic processes contribute to 30%–40% and 60%–70% of the total BTEX degradation respectively.
{"title":"BIOEFGM II: Two-dimensional meshless model to simulate the aerobic and anaerobic biodegradation of BTEX contaminant through multiple electron acceptors in groundwater","authors":"Tinesh Pathania","doi":"10.1016/j.enganabound.2024.106089","DOIUrl":"10.1016/j.enganabound.2024.106089","url":null,"abstract":"<div><div>In the present study, a meshless BIOEFGM II model is proposed to simulate the natural attenuation of BTEX contaminant (benzene, toluene, ethylbenzene, and xylenes) through multiple aerobic and anaerobic electron acceptors in the two-dimensional groundwater system. This model is the extension of the BIOEFGM I model for aerobic BTEX degradation. In BIOEFGM II, the meshless element-free Galerkin method (EFGM) is applied to governing groundwater flow and reactive transport equations. The weak-integral form of EFGM is also applied to the Darcy law equation to compute the groundwater velocity directly at scattered field nodes representing the aquifer domain. This step allows the easy coupling of flow and transport models with both regular and irregular nodes in BIOEFGM II, unlike grid/mesh-based models. The proposed model is the first multispecies model that can simulate natural BTEX degradation using regular/irregular field nodes. In this study, proposed BIOEFGM II-RG and BIOEFGM II-IRG for regular and irregular nodes respectively are applied to a hypothetical aquifer and field-type large heterogeneous aquifer, and results are verified with the benchmark RT3D model. The results of this study reveal that aerobic and anaerobic processes contribute to 30%–40% and 60%–70% of the total BTEX degradation respectively.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106089"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106107
YaoDi Li , Mei Huang , Boxue Wang , Xiangyuan Meng , YanTing Cheng
This article presents an extension of the Half Boundary Method (HBM) for solving two-dimensional mass transfer problems in a lead-bismuth eutectic (LBE) loop. We propose a procedure that integrates the Finite Volume Method (FVM) with the HBM coupling algorithm to address flow and mass transfer issues. The FVM is used to solve the velocity field, while a small number of nodes are selected within the solution domain to apply HBM for solving the concentration field. By reducing the number of grids required by HBM, the maximum order of the matrix is also reduced, leading to savings in computational storage and improved efficiency. The proposed procedure is applied to solve the transport problem of corrosion products (Fe) in the hot pipe section of the UPBEAT circuit. By comparing different flow and oxygen control conditions, we find that the corrosion rate increases with velocity. Under oxygen control, the concentration of corrosion products is only 0.5 % of that under anaerobic conditions, and the corrosion rate is reduced to only 0.19 %. These findings significantly reduce the corrosion rate, making long-term pipeline use feasible.
{"title":"A new procedure for solving the transport of corrosion products in liquid lead bismuth eutectic loop","authors":"YaoDi Li , Mei Huang , Boxue Wang , Xiangyuan Meng , YanTing Cheng","doi":"10.1016/j.enganabound.2024.106107","DOIUrl":"10.1016/j.enganabound.2024.106107","url":null,"abstract":"<div><div>This article presents an extension of the Half Boundary Method (HBM) for solving two-dimensional mass transfer problems in a lead-bismuth eutectic (LBE) loop. We propose a procedure that integrates the Finite Volume Method (FVM) with the HBM coupling algorithm to address flow and mass transfer issues. The FVM is used to solve the velocity field, while a small number of nodes are selected within the solution domain to apply HBM for solving the concentration field. By reducing the number of grids required by HBM, the maximum order of the matrix is also reduced, leading to savings in computational storage and improved efficiency. The proposed procedure is applied to solve the transport problem of corrosion products (Fe) in the hot pipe section of the UPBEAT circuit. By comparing different flow and oxygen control conditions, we find that the corrosion rate increases with velocity. Under oxygen control, the concentration of corrosion products is only 0.5 % of that under anaerobic conditions, and the corrosion rate is reduced to only 0.19 %. These findings significantly reduce the corrosion rate, making long-term pipeline use feasible.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106107"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106101
Ziling Song , Tiantang Yu , Lin Wang , Tinh Quoc Bui
The analysis of complex multipatch structures has been solved with numerical tools, however, isogeometric shape optimization has not yet been applicable for designing free-form surface. Benefiting from the key concept of isogeometric analysis (IGA) for integration of design and analysis, a morphogenesis method is presented for shape optimization of complex free-form surfaces, especially built with multipatches. The optimization is based on control points’ information to adjust the nodal positions to achieve a structure with the minimum strain energy by particle swarm optimization. In this setting, the constraints of control point on both sides are used to connect interfaces between patches during shape modifications. For the analysis, we introduce the Kirchhoff–Love shell element and Nitsche’s method to couple non-conforming patches. The NURBS composition defines the geometry of the shell while the displacement field is approximated using the same spline functions as the free-form surface. The effectiveness and performance of the proposed method are verified by some numerical examples, and the mechanical properties of the optimized structure are greatly improved.
{"title":"Multi-patch IGA associated with Nitsche’s method for morphogenesis of complex free-form surface","authors":"Ziling Song , Tiantang Yu , Lin Wang , Tinh Quoc Bui","doi":"10.1016/j.enganabound.2024.106101","DOIUrl":"10.1016/j.enganabound.2024.106101","url":null,"abstract":"<div><div>The analysis of complex multipatch structures has been solved with numerical tools, however, isogeometric shape optimization has not yet been applicable for designing free-form surface. Benefiting from the key concept of isogeometric analysis (IGA) for integration of design and analysis, a morphogenesis method is presented for shape optimization of complex free-form surfaces, especially built with multipatches. The optimization is based on control points’ information to adjust the nodal positions to achieve a structure with the minimum strain energy by particle swarm optimization. In this setting, the constraints of control point on both sides are used to connect interfaces between patches during shape modifications. For the analysis, we introduce the Kirchhoff–Love shell element and Nitsche’s method to couple non-conforming patches. The NURBS composition defines the geometry of the shell while the displacement field is approximated using the same spline functions as the free-form surface. The effectiveness and performance of the proposed method are verified by some numerical examples, and the mechanical properties of the optimized structure are greatly improved.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106101"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142974915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2025.106128
Xiao Zhang , Yong Cheng , Saishuai Dai , Mingxin Li , Zhiming Yuan , Atilla Incecik
Multi-ship encountering results in complex interactions that significantly modify the surrounding flow field, particularly in the presence of incident waves. Due to the disturbing effect of the complex wave system, the behavior of each ship during the encounter is influenced by the wave characteristics and the relative motions between the ships. This paper establishes a model for ship-to-ship encountering in incident waves using the time-domain Rankine Boundary Element Method (BEM). The transient responses and wave field of ships are investigated. The approach is based on the global fixed system dealing with complex external wavefields and dynamics, moment-to-moment iterative updating of the computational grid simulates the two-ship encountering, using the fourth-order Runge-Kutta method for time integration. The classical Wigley III is chosen to calculate and better validate the numerical results for a two-ship encountering in calm water and a single-ship advancing in an incident wave based on the time-domain method. On this basis, a study is carried out to investigate the transient motion and instantaneous wave field of two ships encountering toward an opposite direction in incident waves. Sensitivity analyses of parameters such as wave characteristics, transverse distance between ships, ship-to-ship speed ratio, and water depths reveal that the transient motions of ships are closely related to the incident wave characteristics. Notably, the encounter frequency differs when two ships advance in opposing directions, with variations in transverse distance, speed ratio and water depths significantly affecting the amplitude and frequency of their motions during the encounter.
{"title":"A time-domain BEM for instantaneous interaction by two ships head-on encountering in incident waves","authors":"Xiao Zhang , Yong Cheng , Saishuai Dai , Mingxin Li , Zhiming Yuan , Atilla Incecik","doi":"10.1016/j.enganabound.2025.106128","DOIUrl":"10.1016/j.enganabound.2025.106128","url":null,"abstract":"<div><div>Multi-ship encountering results in complex interactions that significantly modify the surrounding flow field, particularly in the presence of incident waves. Due to the disturbing effect of the complex wave system, the behavior of each ship during the encounter is influenced by the wave characteristics and the relative motions between the ships. This paper establishes a model for ship-to-ship encountering in incident waves using the time-domain Rankine Boundary Element Method (BEM). The transient responses and wave field of ships are investigated. The approach is based on the global fixed system dealing with complex external wavefields and dynamics, moment-to-moment iterative updating of the computational grid simulates the two-ship encountering, using the fourth-order Runge-Kutta method for time integration. The classical Wigley III is chosen to calculate and better validate the numerical results for a two-ship encountering in calm water and a single-ship advancing in an incident wave based on the time-domain method. On this basis, a study is carried out to investigate the transient motion and instantaneous wave field of two ships encountering toward an opposite direction in incident waves. Sensitivity analyses of parameters such as wave characteristics, transverse distance between ships, ship-to-ship speed ratio, and water depths reveal that the transient motions of ships are closely related to the incident wave characteristics. Notably, the encounter frequency differs when two ships advance in opposing directions, with variations in transverse distance, speed ratio and water depths significantly affecting the amplitude and frequency of their motions during the encounter.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106128"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106090
Soobin Kwak , Yongho Choi , Jian Wang , Yunjae Nam , Junseok Kim
We propose a novel phase-field model for simulating curvature-dependent and surface-limited tissue growth on curved surfaces. The proposed mathematical model consists of a modified Allen–Cahn (AC) equation with a non-standard variable mobility and a growth term that depends on curvature and surface limitations. To solve the equations numerically, we use an operator splitting technique. We split the governing equation into a modified AC equation, and curvature-dependent and surface limited growth equation. To validate the high performance of the proposed mathematical model in realistic simulations, we conduct several numerical simulations such as those with synthetic conditions and comparisons with real experimental data. The computational results demonstrate the robustness and efficiency of the new phase-field model in accurately capturing realistic tissue growth phenomena on curved surfaces.
{"title":"Phase-field modeling for curvature-dependent tissue growth on surfaces","authors":"Soobin Kwak , Yongho Choi , Jian Wang , Yunjae Nam , Junseok Kim","doi":"10.1016/j.enganabound.2024.106090","DOIUrl":"10.1016/j.enganabound.2024.106090","url":null,"abstract":"<div><div>We propose a novel phase-field model for simulating curvature-dependent and surface-limited tissue growth on curved surfaces. The proposed mathematical model consists of a modified Allen–Cahn (AC) equation with a non-standard variable mobility and a growth term that depends on curvature and surface limitations. To solve the equations numerically, we use an operator splitting technique. We split the governing equation into a modified AC equation, and curvature-dependent and surface limited growth equation. To validate the high performance of the proposed mathematical model in realistic simulations, we conduct several numerical simulations such as those with synthetic conditions and comparisons with real experimental data. The computational results demonstrate the robustness and efficiency of the new phase-field model in accurately capturing realistic tissue growth phenomena on curved surfaces.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106090"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142901664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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