Pub Date : 2025-12-21DOI: 10.1016/j.cma.2025.118640
Tong Zhang, Chuanjun Chen
We consider a temporally second-order variable time-step, decoupled, linear and fully discrete finite element method for the incompressible magnetohydrodynamic (MHD) equations. The implicit scheme is adopted for the linear terms, while the semi-implicit scheme is used to the fluid convection term and the explicit treatment is adopted for the other coupling terms. In addition, the zero energy contribution (ZEC) technique is utilized to maintain the unconditional stability of the designed splitting scheme. The L2 and H1-norms convergence results of numerical solutions in both the temporal discrete and temporal-spatial fully discrete schemes are provided. Furthermore, the optimal L2 error estimates of numerical approximations are developed by the negative norm technique and the mathematical induction. Finally, some numerical experiments are provided to illustrate the established theoretical findings.
{"title":"A second-order, decoupled, linear and unconditional stable scheme with variable time steps for the MHD equations","authors":"Tong Zhang, Chuanjun Chen","doi":"10.1016/j.cma.2025.118640","DOIUrl":"10.1016/j.cma.2025.118640","url":null,"abstract":"<div><div>We consider a temporally second-order variable time-step, decoupled, linear and fully discrete finite element method for the incompressible magnetohydrodynamic (MHD) equations. The implicit scheme is adopted for the linear terms, while the semi-implicit scheme is used to the fluid convection term and the explicit treatment is adopted for the other coupling terms. In addition, the zero energy contribution (ZEC) technique is utilized to maintain the unconditional stability of the designed splitting scheme. The <em>L</em><sup>2</sup> and <em>H</em><sup>1</sup>-norms convergence results of numerical solutions in both the temporal discrete and temporal-spatial fully discrete schemes are provided. Furthermore, the optimal <em>L</em><sup>2</sup> error estimates of numerical approximations <span><math><mrow><mo>(</mo><msubsup><mi>u</mi><mi>h</mi><mi>n</mi></msubsup><mo>,</mo><msubsup><mi>B</mi><mi>h</mi><mi>n</mi></msubsup><mo>)</mo></mrow></math></span> are developed by the negative norm technique and the mathematical induction. Finally, some numerical experiments are provided to illustrate the established theoretical findings.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118640"},"PeriodicalIF":7.3,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145796193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 : 2025-12-21DOI: 10.1016/j.cma.2025.118661
Chao Wang , Yi Wu , Mu He , Wei-Zhi Luo , Liang Xia
In this paper, we investigate the multi-material topology optimization method for designing thermal buckling-resistant cellular materials. The optimization framework is based on the buckling strength evaluation method. Specifically, the local stress of the materials subjected to simultaneous mechanical and thermal loadings is calculated using the asymptotic homogenization theory. The evaluation of the buckling strength of periodic material is then achieved by combining linear buckling analysis (LBA) and Floquet-Bloch boundary conditions. Based on the recursive solid isotropic material with penalization (SIMP) model, the topology optimization formulation is defined to maximize the buckling strength under a volume constraint, for which the sensitivity analysis is derived through the adjoint method. Several numerical examples are presented, illustrating that the proposed method is effective for designing thermal buckling-resistant material. Furthermore, the results reveal that thermal stresses can be exploited to enhance the buckling strength of cellular material through a reasonable multi-material distribution. To validate the proposed method, macro-scale analyses based on finite arrays of optimized unit cells are conducted. The results demonstrate that the design principles derived from the homogenization framework remain valid, confirming the effectiveness of the proposed method for practical finite structures.
{"title":"Multi-material topology optimization of thermal buckling-resistant cellular materials","authors":"Chao Wang , Yi Wu , Mu He , Wei-Zhi Luo , Liang Xia","doi":"10.1016/j.cma.2025.118661","DOIUrl":"10.1016/j.cma.2025.118661","url":null,"abstract":"<div><div>In this paper, we investigate the multi-material topology optimization method for designing thermal buckling-resistant cellular materials. The optimization framework is based on the buckling strength evaluation method. Specifically, the local stress of the materials subjected to simultaneous mechanical and thermal loadings is calculated using the asymptotic homogenization theory. The evaluation of the buckling strength of periodic material is then achieved by combining linear buckling analysis (LBA) and Floquet-Bloch boundary conditions. Based on the recursive solid isotropic material with penalization (SIMP) model, the topology optimization formulation is defined to maximize the buckling strength under a volume constraint, for which the sensitivity analysis is derived through the adjoint method. Several numerical examples are presented, illustrating that the proposed method is effective for designing thermal buckling-resistant material. Furthermore, the results reveal that thermal stresses can be exploited to enhance the buckling strength of cellular material through a reasonable multi-material distribution. To validate the proposed method, macro-scale analyses based on finite arrays of optimized unit cells are conducted. The results demonstrate that the design principles derived from the homogenization framework remain valid, confirming the effectiveness of the proposed method for practical finite structures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118661"},"PeriodicalIF":7.3,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145796191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mixed-mode behaviors are critical in both quasi-static and dynamic fracture. To investigate dynamic mixed-mode fracture in quasi-brittle materials, we developed a rate-independent Phase-Field Cohesive-Zone Model (PF-CZM). This model incorporates damage-induced anisotropy through a directional decomposition scheme. A modified G-criterion determines the fracture plane’s orientation, and a multiscale framework is introduced to stabilize crack orientation once formed. We solved the governing equations using an implicit time integration scheme implemented in Julia, and adaptive mesh refinement (AMR) accelerated computations. Numerical examples confirm the model’s length-insensitivity and its flexibility in capturing failure mode transitions. Notably, our work reveals that Y-joint crack structures in dynamic Brazilian split test form from the intersection of a central mode-I crack and corner-generated mode-II cracks. This study marks the first application of a directional decomposition scheme to dynamic fracture, offering novel insights into quasi-brittle dynamic mixed-mode fracture.
{"title":"Adaptive phase-field cohesive-zone model for mixed-mode dynamic fracture with directional decomposition scheme","authors":"Pei-Liang Bian , Fu-Ling Liao , Hai Qing , Siegfried Schmauder , Tiantang Yu","doi":"10.1016/j.cma.2025.118619","DOIUrl":"10.1016/j.cma.2025.118619","url":null,"abstract":"<div><div>Mixed-mode behaviors are critical in both quasi-static and dynamic fracture. To investigate dynamic mixed-mode fracture in quasi-brittle materials, we developed a rate-independent Phase-Field Cohesive-Zone Model (PF-CZM). This model incorporates damage-induced anisotropy through a directional decomposition scheme. A modified G-criterion determines the fracture plane’s orientation, and a multiscale framework is introduced to stabilize crack orientation once formed. We solved the governing equations using an implicit time integration scheme implemented in Julia, and adaptive mesh refinement (AMR) accelerated computations. Numerical examples confirm the model’s length-insensitivity and its flexibility in capturing failure mode transitions. Notably, our work reveals that Y-joint crack structures in dynamic Brazilian split test form from the intersection of a central mode-I crack and corner-generated mode-II cracks. This study marks the first application of a directional decomposition scheme to dynamic fracture, offering novel insights into quasi-brittle dynamic mixed-mode fracture.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118619"},"PeriodicalIF":7.3,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145796190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 : 2025-12-20DOI: 10.1016/j.cma.2025.118580
David Dalton, Hao Gao, Dirk Husmeier
We introduce finite-element Gaussian processes (FEGPs), a novel physics-informed machine learning approach for solving inverse problems involving steady-state, linear partial differential equations (PDEs). Our framework combines a Gaussian process prior for the unknown solution function with a likelihood that incorporates the PDE in its weak form, using a finite-element approximation. This approach offers significantly better scalability than physics-informed Gaussian processes (PIGPs), which rely on the strong form of the PDE. Through numerical experiments on a range of synthetic benchmark problems, we show that FEGPs offer results which outperform PIGPs, and are competitive with physics-informed neural networks (PINNs) with improved uncertainty quantification.
{"title":"Finite-element Gaussian processes for the machine learning of steady-state linear partial differential equations","authors":"David Dalton, Hao Gao, Dirk Husmeier","doi":"10.1016/j.cma.2025.118580","DOIUrl":"10.1016/j.cma.2025.118580","url":null,"abstract":"<div><div>We introduce finite-element Gaussian processes (FEGPs), a novel physics-informed machine learning approach for solving inverse problems involving steady-state, linear partial differential equations (PDEs). Our framework combines a Gaussian process prior for the unknown solution function with a likelihood that incorporates the PDE in its weak form, using a finite-element approximation. This approach offers significantly better scalability than physics-informed Gaussian processes (PIGPs), which rely on the strong form of the PDE. Through numerical experiments on a range of synthetic benchmark problems, we show that FEGPs offer results which outperform PIGPs, and are competitive with physics-informed neural networks (PINNs) with improved uncertainty quantification.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118580"},"PeriodicalIF":7.3,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 : 2025-12-20DOI: 10.1016/j.cma.2025.118672
Yu Cao, Zhan Kang
Topology optimization considering linear buckling strength is of great importance for conceptual design of engineering structures. Conventional methods generally rely on a nested double-loop iteration approach, in which the inner-loop iteration solves the linear buckling problem characterized by an eigenvalue problem, while the outer loop optimizes the design variables to improve the objective function under specified constraints. However, for large-scale problems, the computational cost required by the repeated eigenvalue analyses and sensitivity computations during the iterative design process often imposes a significant barrier to practical applications. To address this issue, the strategy of successive iteration of analysis and design (SIAD) is applied to large-scale buckling-related structural topology optimization. With the aim of achieving simultaneous convergence of the buckling modes and design variables, the method integrates approximate eigenvalue analysis and design variable updating into a single iteration loop, thereby avoiding the need to solve the computationally expensive eigenvalue problem at each design iteration and significantly improving computational efficiency. In addition, a criterion is proposed to identify spurious buckling modes induced by stress concentration, thus preventing the inclusion of spurious buckling modes in the sensitivity analysis. Several numerical examples are presented to demonstrate the computational efficiency of the proposed SIAD method. It is shown that the method effectively solves topology optimization problems for buckling strength with over 30 million degrees of freedom on a desktop computer at an affordable computational cost.
{"title":"An efficient linear buckling topology optimization framework based on successive iteration of analysis and design","authors":"Yu Cao, Zhan Kang","doi":"10.1016/j.cma.2025.118672","DOIUrl":"10.1016/j.cma.2025.118672","url":null,"abstract":"<div><div>Topology optimization considering linear buckling strength is of great importance for conceptual design of engineering structures. Conventional methods generally rely on a nested double-loop iteration approach, in which the inner-loop iteration solves the linear buckling problem characterized by an eigenvalue problem, while the outer loop optimizes the design variables to improve the objective function under specified constraints. However, for large-scale problems, the computational cost required by the repeated eigenvalue analyses and sensitivity computations during the iterative design process often imposes a significant barrier to practical applications. To address this issue, the strategy of successive iteration of analysis and design (SIAD) is applied to large-scale buckling-related structural topology optimization. With the aim of achieving simultaneous convergence of the buckling modes and design variables, the method integrates approximate eigenvalue analysis and design variable updating into a single iteration loop, thereby avoiding the need to solve the computationally expensive eigenvalue problem at each design iteration and significantly improving computational efficiency. In addition, a criterion is proposed to identify spurious buckling modes induced by stress concentration, thus preventing the inclusion of spurious buckling modes in the sensitivity analysis. Several numerical examples are presented to demonstrate the computational efficiency of the proposed SIAD method. It is shown that the method effectively solves topology optimization problems for buckling strength with over 30 million degrees of freedom on a desktop computer at an affordable computational cost.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118672"},"PeriodicalIF":7.3,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 : 2025-12-19DOI: 10.1016/j.cma.2025.118648
Inocencio Castañar , Laura Moreno , Ramon Codina
This work applies and compares mixed formulations for both fluid and solid domains in Fluid-Structure Interaction (FSI) problems to the standard irreducible formulations. The study focuses on a nonlinear setting involving laminar incompressible Newtonian fluids and hyperelastic solids, with the fluid described using an arbitrary Lagrangian-Eulerian framework and the solid modeled within a total Lagrangian framework. Stabilization is achieved through the use of the variational multiscale method, which allows for arbitrary interpolations of the unknowns. The results demonstrate that mixed formulations not only enhance stability and accuracy but also address key numerical challenges in FSI problems. These formulations effectively mitigate volumetric locking in nearly or fully incompressible materials and shear locking in bending-dominated scenarios, ensuring robust performance across a wide range of conditions. Additionally, they provide significantly improved precision in stress computations, which is particularly valuable in FSI problems where traction conditions at the interface must be accurately satisfied. While mixed formulations introduce additional degrees of freedom per node, they achieve comparable accuracy to standard irreducible formulations even with coarser meshes, making them a highly competitive and efficient alternative for complex coupled simulations. The mixed formulations are tested through FSI numerical results for semi-stationary and fully transient cases, highlighting their potential for robust and efficient FSI simulations.
{"title":"Study of stabilized mixed formulations for fluid-structure interaction problems within a variational multiscale framework","authors":"Inocencio Castañar , Laura Moreno , Ramon Codina","doi":"10.1016/j.cma.2025.118648","DOIUrl":"10.1016/j.cma.2025.118648","url":null,"abstract":"<div><div>This work applies and compares mixed formulations for both fluid and solid domains in Fluid-Structure Interaction (FSI) problems to the standard irreducible formulations. The study focuses on a nonlinear setting involving laminar incompressible Newtonian fluids and hyperelastic solids, with the fluid described using an arbitrary Lagrangian-Eulerian framework and the solid modeled within a total Lagrangian framework. Stabilization is achieved through the use of the variational multiscale method, which allows for arbitrary interpolations of the unknowns. The results demonstrate that mixed formulations not only enhance stability and accuracy but also address key numerical challenges in FSI problems. These formulations effectively mitigate volumetric locking in nearly or fully incompressible materials and shear locking in bending-dominated scenarios, ensuring robust performance across a wide range of conditions. Additionally, they provide significantly improved precision in stress computations, which is particularly valuable in FSI problems where traction conditions at the interface must be accurately satisfied. While mixed formulations introduce additional degrees of freedom per node, they achieve comparable accuracy to standard irreducible formulations even with coarser meshes, making them a highly competitive and efficient alternative for complex coupled simulations. The mixed formulations are tested through FSI numerical results for semi-stationary and fully transient cases, highlighting their potential for robust and efficient FSI simulations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118648"},"PeriodicalIF":7.3,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 : 2025-12-19DOI: 10.1016/j.cma.2025.118652
Åsmund Aa Resell , Anders Aa Resell
Modelling of rods that are inserted and rotated around its own axis within curved conduits is a relevant industrial problem typically encountered in well construction operations, but is also relevant for various medical applications. In these problems, the rod can undergo large rotations of its cross-section relative to a global Cartesian frame due to the constraints imposed by the curved conduit walls. As a result, modelling these problems typically requires solving large-rotation operators, and small-angle simplifications are not valid globally. Nevertheless, the lateral rotations of the rod cross-section relative to a local frame that follows the curved conduit are generally small, owing to the geometric constraints of the problem. In this article, we propose a mathematical framework derived from the geometrically exact beam theory (GEBT) that describes rod kinematics relative to the curved centerline of the conduit, referred to as the hole. We then develop a finite element (FEM) model from the framework that utilizes small-angle assumptions for the lateral angles relative to the hole centerline. Importantly, the formulation imposes no restrictions on large axial rotation, allowing the rod to rotate freely inside the hole. The proposed approach is verified against a corotational beam model that employs a large rotation formulation, which shows excellent agreement. Finally, a case study from drilling is presented to validate and demonstrate the capabilities of the model.
{"title":"Dynamics of rods in curved holes","authors":"Åsmund Aa Resell , Anders Aa Resell","doi":"10.1016/j.cma.2025.118652","DOIUrl":"10.1016/j.cma.2025.118652","url":null,"abstract":"<div><div>Modelling of rods that are inserted and rotated around its own axis within curved conduits is a relevant industrial problem typically encountered in well construction operations, but is also relevant for various medical applications. In these problems, the rod can undergo large rotations of its cross-section relative to a global Cartesian frame due to the constraints imposed by the curved conduit walls. As a result, modelling these problems typically requires solving large-rotation operators, and small-angle simplifications are not valid globally. Nevertheless, the lateral rotations of the rod cross-section relative to a local frame that follows the curved conduit are generally small, owing to the geometric constraints of the problem. In this article, we propose a mathematical framework derived from the geometrically exact beam theory (GEBT) that describes rod kinematics relative to the curved centerline of the conduit, referred to as the hole. We then develop a finite element (FEM) model from the framework that utilizes small-angle assumptions for the lateral angles relative to the hole centerline. Importantly, the formulation imposes no restrictions on large axial rotation, allowing the rod to rotate freely inside the hole. The proposed approach is verified against a corotational beam model that employs a large rotation formulation, which shows excellent agreement. Finally, a case study from drilling is presented to validate and demonstrate the capabilities of the model.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118652"},"PeriodicalIF":7.3,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 : 2025-12-19DOI: 10.1016/j.cma.2025.118669
Jian Li , Chunhao Chen , Xiaoyong Chen , Rui Li , Xiaoming He
To study natural convection problems in two-phase flows, a non-isothermal two-phase flow model incorporating differential viscosities and thermal diffusivities is considered and analyzed via the phase-field method. This modeling framework involves the multiphysics coupling of the Cahn-Hilliard phase field equations, heat transfer equation, and Navier-Stokes equations, resulting in a strongly nonlinear system. To efficiently solve the sophisticated system, we develop, analyze, and demonstrate a decoupled linear fully discrete scheme, which leverages the invariant energy quadratization strategy for the Cahn-Hilliard phase field system, the artificial compressibility method without artificial pressure boundary condition, an explicit-implicit treatment of nonlinear terms, and the addition of several key stabilization terms. This scheme is proven uniquely solvable per time step and unconditionally stable. A range of 2D and 3D numerical simulations, including accuracy tests, stability tests, interface pinchoff, one or two non-isothermal air bubbles rising, Rayleigh-Taylor instability, and thermal plumes, are carried out to illustrate the model and algorithm’s features and broad applicability.
{"title":"A fully discrete decoupled scheme and applications for non-isothermal two-phase flow model with different viscosities and thermal diffusivities","authors":"Jian Li , Chunhao Chen , Xiaoyong Chen , Rui Li , Xiaoming He","doi":"10.1016/j.cma.2025.118669","DOIUrl":"10.1016/j.cma.2025.118669","url":null,"abstract":"<div><div>To study natural convection problems in two-phase flows, a non-isothermal two-phase flow model incorporating differential viscosities and thermal diffusivities is considered and analyzed via the phase-field method. This modeling framework involves the multiphysics coupling of the Cahn-Hilliard phase field equations, heat transfer equation, and Navier-Stokes equations, resulting in a strongly nonlinear system. To efficiently solve the sophisticated system, we develop, analyze, and demonstrate a decoupled linear fully discrete scheme, which leverages the invariant energy quadratization strategy for the Cahn-Hilliard phase field system, the artificial compressibility method without artificial pressure boundary condition, an explicit-implicit treatment of nonlinear terms, and the addition of several key stabilization terms. This scheme is proven uniquely solvable per time step and unconditionally stable. A range of 2D and 3D numerical simulations, including accuracy tests, stability tests, interface pinchoff, one or two non-isothermal air bubbles rising, Rayleigh-Taylor instability, and thermal plumes, are carried out to illustrate the model and algorithm’s features and broad applicability.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118669"},"PeriodicalIF":7.3,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145771993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 : 2025-12-19DOI: 10.1016/j.cma.2025.118665
Juan M. Gimenez , Francisco M. Sívori , Axel E. Larreteguy , Eugenio Oñate , Sergio R. Idelsohn
Turbulence modeling remains one of the most challenging problems in computational fluid dynamics due to the wide range of scales involved. The Pseudo-Direct Numerical Simulation (P-DNS) methodology offers a multiscale approach capable of resolving all turbulence scales while reducing the computational cost associated with fully resolved simulations. In this work, the P-DNS methodology is extended to weakly compressible flows, under the key assumption that the fine-scale dynamics can still be considered effectively incompressible. This assumption allows reusing the available fine-scale incompressible databases, which ensure a physically consistent and robust multiscale representation through two distinct representative volume elements for the flow behaviour near and far from walls, while leaving compressibility effects to be considered only at the coarse-scale level. Additionally, the memory model is reformulated into a single transport equation, facilitating its integration into compressible solvers and enabling a continuous representation of the inertial stress tensor time evolution. The extended P-DNS framework is validated against canonical test cases including flat plate boundary layers, axisymmetric subsonic jets (hot and cold), and the Common Research Model (CRM) aircraft configuration. Results demonstrate that P-DNS accurately predicts skin-friction, drag, velocity profiles, turbulent kinetic energy and shear stresses across these diverse flow configurations.
{"title":"A P-DNS approach for weakly compressible turbulent flows","authors":"Juan M. Gimenez , Francisco M. Sívori , Axel E. Larreteguy , Eugenio Oñate , Sergio R. Idelsohn","doi":"10.1016/j.cma.2025.118665","DOIUrl":"10.1016/j.cma.2025.118665","url":null,"abstract":"<div><div>Turbulence modeling remains one of the most challenging problems in computational fluid dynamics due to the wide range of scales involved. The Pseudo-Direct Numerical Simulation (P-DNS) methodology offers a multiscale approach capable of resolving all turbulence scales while reducing the computational cost associated with fully resolved simulations. In this work, the P-DNS methodology is extended to weakly compressible flows, under the key assumption that the fine-scale dynamics can still be considered effectively incompressible. This assumption allows reusing the available fine-scale incompressible databases, which ensure a physically consistent and robust multiscale representation through two distinct representative volume elements for the flow behaviour near and far from walls, while leaving compressibility effects to be considered only at the coarse-scale level. Additionally, the memory model is reformulated into a single transport equation, facilitating its integration into compressible solvers and enabling a continuous representation of the inertial stress tensor time evolution. The extended P-DNS framework is validated against canonical test cases including flat plate boundary layers, axisymmetric subsonic jets (hot and cold), and the Common Research Model (CRM) aircraft configuration. Results demonstrate that P-DNS accurately predicts skin-friction, drag, velocity profiles, turbulent kinetic energy and shear stresses across these diverse flow configurations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118665"},"PeriodicalIF":7.3,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 : 2025-12-18DOI: 10.1016/j.cma.2025.118656
Christoph Hollweck , Lukas Leidinger , Stefan Hartmann , Marcus Wagner , Roland Wüchner
Isogeometric analysis (IGA) combined with explicit dynamics is increasingly used in academia and has already been successfully applied in industrial simulations, including crash and sheet-metal forming. Since explicit schemes are only conditionally stable, accurate estimation of the critical time step is essential for both stability and efficiency. Adaptive mesh refinement is widely used to balance accuracy and computational cost. In IGA, THB- and LR-splines break the tensor-product structure of standard B-splines and enable local refinement, but their effect on the critical time step under trimming has not been systematically studied - a key requirement for reliable time step estimation.
We investigate the critical time step in explicit dynamic simulations using trimmed B-splines, LR-splines, and THB-splines, based on a lumped mass matrix obtained by simple row summation. One-dimensional bar, two-dimensional membrane, and trimmed shell models are analyzed to determine how trimming and local refinement influence element and system eigenfrequencies, which directly control the stable time step. Refined boundary elements in open knot vectors are identified as the main bottleneck. Trimming these elements can increase the stable time step, though certain trimming configurations introduce new restrictions.
Results show that LR- and THB-splines impose time step constraints similar to B-splines, making them equally suitable for explicit simulations. We also present a general method for computing element-wise Bézier extraction operators for LR- and THB-splines, enabling straightforward integration into standard finite element solvers. The findings are validated through nonlinear sheet-metal forming simulations in LS-DYNA using shells discretized with trimmed B-, LR-, and THB-splines. This represents the first such application and demonstrates their practical feasibility for industrial use.
{"title":"An analysis of the critical time step size for explicit dynamics using trimmed B-splines, LR-splines, and THB-splines","authors":"Christoph Hollweck , Lukas Leidinger , Stefan Hartmann , Marcus Wagner , Roland Wüchner","doi":"10.1016/j.cma.2025.118656","DOIUrl":"10.1016/j.cma.2025.118656","url":null,"abstract":"<div><div>Isogeometric analysis (IGA) combined with explicit dynamics is increasingly used in academia and has already been successfully applied in industrial simulations, including crash and sheet-metal forming. Since explicit schemes are only conditionally stable, accurate estimation of the critical time step is essential for both stability and efficiency. Adaptive mesh refinement is widely used to balance accuracy and computational cost. In IGA, THB- and LR-splines break the tensor-product structure of standard B-splines and enable local refinement, but their effect on the critical time step under trimming has not been systematically studied - a key requirement for reliable time step estimation.</div><div>We investigate the critical time step in explicit dynamic simulations using trimmed B-splines, LR-splines, and THB-splines, based on a lumped mass matrix obtained by simple row summation. One-dimensional bar, two-dimensional membrane, and trimmed shell models are analyzed to determine how trimming and local refinement influence element and system eigenfrequencies, which directly control the stable time step. Refined boundary elements in open knot vectors are identified as the main bottleneck. Trimming these elements can increase the stable time step, though certain trimming configurations introduce new restrictions.</div><div>Results show that LR- and THB-splines impose time step constraints similar to B-splines, making them equally suitable for explicit simulations. We also present a general method for computing element-wise Bézier extraction operators for LR- and THB-splines, enabling straightforward integration into standard finite element solvers. The findings are validated through nonlinear sheet-metal forming simulations in LS-DYNA using shells discretized with trimmed B-, LR-, and THB-splines. This represents the first such application and demonstrates their practical feasibility for industrial use.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118656"},"PeriodicalIF":7.3,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号