Pub Date : 2025-12-28DOI: 10.1016/j.compfluid.2025.106955
Anas Jnini , Flavio Vella , Marius Zeinhofer
We propose Gauss-Newton’s method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, this yields a natural gradient method that provably mimics the function space dynamics. Our computational results demonstrate close to single-precision accuracy measured in relative L2 norm on a number of benchmark problems. To the best of our knowledge, this constitutes the first contribution in the PINN literature that solves the Navier-Stokes equations to this degree of accuracy. Finally, we show that given a suitable integral discretization, the proposed optimization algorithm agrees with Gauss-Newton’s method in parameter space. This allows a matrix-free formulation enabling efficient scalability to large network sizes.
{"title":"Gauss-Newton Natural Gradient Descent for Physics-informed Computational Fluid Dynamics","authors":"Anas Jnini , Flavio Vella , Marius Zeinhofer","doi":"10.1016/j.compfluid.2025.106955","DOIUrl":"10.1016/j.compfluid.2025.106955","url":null,"abstract":"<div><div>We propose Gauss-Newton’s method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, this yields a natural gradient method that provably mimics the function space dynamics. Our computational results demonstrate close to single-precision accuracy measured in relative <em>L</em><sup>2</sup> norm on a number of benchmark problems. To the best of our knowledge, this constitutes the first contribution in the PINN literature that solves the Navier-Stokes equations to this degree of accuracy. Finally, we show that given a suitable integral discretization, the proposed optimization algorithm agrees with Gauss-Newton’s method in parameter space. This allows a matrix-free formulation enabling efficient scalability to large network sizes.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"307 ","pages":"Article 106955"},"PeriodicalIF":3.0,"publicationDate":"2025-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-12-27DOI: 10.1016/j.compfluid.2025.106957
Ryuta Takao , Satoshi Ii
Physics-informed neural networks (PINNs) have attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for many applications. Despite the versatility of PINNs, it remains challenging to reduce their training cost. Using a DNN pre-trained with an arbitrary dataset with transfer learning or fine-tuning is a potential solution. However, a pre-trained model using a different geometry and flow condition than the target may not produce suitable results. This paper proposes a fine-tuning approach for PINNs with coordinate transformation, modelling lid-driven cavity flows with various shapes. We formulate the inverse problem, where the reference data inside the domain and wall boundary conditions are given. A pre-trained PINN model with an arbitrary Reynolds number and shape is used to initialize a target DNN. To reconcile the reference shape with different targets, governing equations as a loss of the PINNs are given with coordinate transformation using a deformation gradient tensor. Numerical examples for various cavity flows with square, rectangular, shear deformed and inflated geometries demonstrate that the proposed fine-tuning approach improves the training convergence compared with a randomly-initialized model. A pre-trained model with a similar geometry to the target further increases training efficiency. These findings are useful for real-world applications such as modelling intra-aneurysmal blood flows in clinical use.
{"title":"Fine-tuning physics-informed neural networks for cavity flows using coordinate transformation","authors":"Ryuta Takao , Satoshi Ii","doi":"10.1016/j.compfluid.2025.106957","DOIUrl":"10.1016/j.compfluid.2025.106957","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) have attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for many applications. Despite the versatility of PINNs, it remains challenging to reduce their training cost. Using a DNN pre-trained with an arbitrary dataset with transfer learning or fine-tuning is a potential solution. However, a pre-trained model using a different geometry and flow condition than the target may not produce suitable results. This paper proposes a fine-tuning approach for PINNs with coordinate transformation, modelling lid-driven cavity flows with various shapes. We formulate the inverse problem, where the reference data inside the domain and wall boundary conditions are given. A pre-trained PINN model with an arbitrary Reynolds number and shape is used to initialize a target DNN. To reconcile the reference shape with different targets, governing equations as a loss of the PINNs are given with coordinate transformation using a deformation gradient tensor. Numerical examples for various cavity flows with square, rectangular, shear deformed and inflated geometries demonstrate that the proposed fine-tuning approach improves the training convergence compared with a randomly-initialized model. A pre-trained model with a similar geometry to the target further increases training efficiency. These findings are useful for real-world applications such as modelling intra-aneurysmal blood flows in clinical use.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"306 ","pages":"Article 106957"},"PeriodicalIF":3.0,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-12-26DOI: 10.1016/j.compfluid.2025.106954
Dingyu Song , Fu Ling , Yonggang Zhang , Binghai Wen
Boundary treatment is an essential issue in the modelling of fluid flows with high accuracy. While the curved boundary conditions can improve the accuracy of simulating complex geometric boundaries in single-phase flows in the lattice Boltzmann method, they usually lead to significant mass leakage and computational errors in multiphase flow. This is primarily because the traditional curved boundary conditions fail to account for nonlinear density variations in the transition region caused by nonideal effects. This study incorporates the nonideal effect into an interpolation scheme and proposes the interpolation-based curved boundary algorithm for multiphase flow, including linear, quadratic, and cubic interpolation schemes. Static and dynamic multiphase simulations with large density ratios demonstrate that this method effectively improves the computational accuracy of multiphase flow boundary conditions. The required mass compensation is negligible, and the spurious velocity is reduced by an order of magnitude compared to conventional methods.
{"title":"Curve boundary algorithms based on interpolation for multiphase lattice Boltzmann method","authors":"Dingyu Song , Fu Ling , Yonggang Zhang , Binghai Wen","doi":"10.1016/j.compfluid.2025.106954","DOIUrl":"10.1016/j.compfluid.2025.106954","url":null,"abstract":"<div><div>Boundary treatment is an essential issue in the modelling of fluid flows with high accuracy. While the curved boundary conditions can improve the accuracy of simulating complex geometric boundaries in single-phase flows in the lattice Boltzmann method, they usually lead to significant mass leakage and computational errors in multiphase flow. This is primarily because the traditional curved boundary conditions fail to account for nonlinear density variations in the transition region caused by nonideal effects. This study incorporates the nonideal effect into an interpolation scheme and proposes the interpolation-based curved boundary algorithm for multiphase flow, including linear, quadratic, and cubic interpolation schemes. Static and dynamic multiphase simulations with large density ratios demonstrate that this method effectively improves the computational accuracy of multiphase flow boundary conditions. The required mass compensation is negligible, and the spurious velocity is reduced by an order of magnitude compared to conventional methods.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"306 ","pages":"Article 106954"},"PeriodicalIF":3.0,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the context of the numerical approximation of Euler equations, great efforts have been devoted to developing schemes that can accurately reproduce solutions in low Mach number flows. Solutions of classic Finite Volume (FV) schemes are usually plagued by an excessive diffusion as the numerical scheme is not consistent with the limit equations for the Mach number that tends to zero. Instead, a numerical scheme that satisfies such a property is called Asymptotic-Preserving (AP). In this paper, we propose an AP FV scheme for the multi-dimensional Euler equations. In classic FV methods, the numerical approximation of the face flux is obtained by means of a two-state 1D approximate Riemann Solver (RS) in the normal direction to the face. Here, we rely on a node-based flux approximation that exploits a particular RS involving a nodal quantity which depends on all the cells around a given node. Such an idea has been exploited by Barsukow et al. (2023) for the linear acoustic equations. Their method is vorticity-preserving, but its extension to the Euler equations proved to be far from trivial. For such a reason, a change of perspective is needed in the definition of the RS.
{"title":"An all-Mach cell-centered multi-dimensional finite volume numerical scheme for the Euler equations","authors":"Alessia Del Grosso , Wasilij Barsukow , Raphaël Loubère , Pierre-Henri Maire","doi":"10.1016/j.compfluid.2025.106951","DOIUrl":"10.1016/j.compfluid.2025.106951","url":null,"abstract":"<div><div>In the context of the numerical approximation of Euler equations, great efforts have been devoted to developing schemes that can accurately reproduce solutions in low Mach number flows. Solutions of classic Finite Volume (FV) schemes are usually plagued by an excessive diffusion as the numerical scheme is not consistent with the limit equations for the Mach number that tends to zero. Instead, a numerical scheme that satisfies such a property is called Asymptotic-Preserving (AP). In this paper, we propose an AP FV scheme for the multi-dimensional Euler equations. In classic FV methods, the numerical approximation of the face flux is obtained by means of a two-state 1D approximate Riemann Solver (RS) in the normal direction to the face. Here, we rely on a node-based flux approximation that exploits a particular RS involving a nodal quantity which depends on all the cells around a given node. Such an idea has been exploited by Barsukow et al. (2023) for the linear acoustic equations. Their method is vorticity-preserving, but its extension to the Euler equations proved to be far from trivial. For such a reason, a change of perspective is needed in the definition of the RS.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"306 ","pages":"Article 106951"},"PeriodicalIF":3.0,"publicationDate":"2025-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-12-24DOI: 10.1016/j.compfluid.2025.106953
Zihao Zhu, Pau Fradera-Soler, Yalu Zhu, Feng Liu
The flow induced by a pair of Dielectric-Barrier-Discharge (DBD) plasma actuators symmetrically-mounted on a circular cylinder in quiescent air is simulated by solving the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. A new body-force model for the plasma actuator is developed, which yields significantly improved agreement with experiments. In addition to velocity and vorticity fields, the computations provide time-instantaneous and time-averaged pressure field and pressure and skin friction distributions over the cylinder, which have not been available from existing experiments for this problem. The computational results are analyzed to reveal the relations between the plasma body force, pressure field, velocity, vorticity, forces on the cylinder, and momentum imparted to the flow as they impact the flow control effectiveness for different duty-cycle ratio and frequency of the plasma actuation input. A pair of cumulative vortices is discovered outside the experimental measurement window for the first time by the computations. Regardless of the level of duty-cycle frequency and the detailed near field vortex patterns, the vortices appear to eventually accumulate some distance downstream of the cylinder and move very slowly downstream. The present study is of direct relevance to problems involving vortex shedding and noise production from many circular-shaped aeronautical and civil structures. It helps to provide the necessary fundamental understanding of the flow physics and guidance for future design and optimization of DBD plasma actuators for flow control.
通过求解非定常reynolds - average Navier-Stokes （URANS）方程，模拟了对称安装在圆柱上的一对介质阻挡放电（DBD）等离子体致动器在静止空气中的流动。建立了一种新的等离子体作动器的体力模型，该模型与实验结果吻合较好。除了速度和涡量场之外，计算还提供了时间瞬时和时间平均的压力场以及气缸上的压力和表面摩擦分布，这些都是现有实验无法得到的。通过对计算结果的分析，揭示了在不同占空比和频率下，等离子体体力、压力场、速度、涡量、施加在气缸上的力和传递给流动的动量对流动控制效果的影响关系。通过计算，首次在实验测量窗口外发现了一对累积涡。不管占空比频率的高低和详细的近场涡旋模式如何，涡旋似乎最终会在圆柱体下游积累一定距离，并向下游缓慢移动。本研究直接涉及许多圆形航空和民用结构的涡脱落和噪声产生问题。它有助于为流动物理提供必要的基本理解，并为未来设计和优化用于流动控制的DBD等离子体致动器提供指导。
{"title":"Numerical investigation of flow induced by plasma actuators around a circular cylinder in quiescent air under duty-cycle actuation","authors":"Zihao Zhu, Pau Fradera-Soler, Yalu Zhu, Feng Liu","doi":"10.1016/j.compfluid.2025.106953","DOIUrl":"10.1016/j.compfluid.2025.106953","url":null,"abstract":"<div><div>The flow induced by a pair of Dielectric-Barrier-Discharge (DBD) plasma actuators symmetrically-mounted on a circular cylinder in quiescent air is simulated by solving the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. A new body-force model for the plasma actuator is developed, which yields significantly improved agreement with experiments. In addition to velocity and vorticity fields, the computations provide time-instantaneous and time-averaged pressure field and pressure and skin friction distributions over the cylinder, which have not been available from existing experiments for this problem. The computational results are analyzed to reveal the relations between the plasma body force, pressure field, velocity, vorticity, forces on the cylinder, and momentum imparted to the flow as they impact the flow control effectiveness for different duty-cycle ratio and frequency of the plasma actuation input. A pair of cumulative vortices is discovered outside the experimental measurement window for the first time by the computations. Regardless of the level of duty-cycle frequency and the detailed near field vortex patterns, the vortices appear to eventually accumulate some distance downstream of the cylinder and move very slowly downstream. The present study is of direct relevance to problems involving vortex shedding and noise production from many circular-shaped aeronautical and civil structures. It helps to provide the necessary fundamental understanding of the flow physics and guidance for future design and optimization of DBD plasma actuators for flow control.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"306 ","pages":"Article 106953"},"PeriodicalIF":3.0,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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.compfluid.2025.106950
Qiushuo Qin , Jie Wu , Lan Jiang
In this paper, an efficient high-order gas-kinetic scheme for compressible flow simulation is presented. It combines the fifth-order targeted essentially non-oscillatory (TENO) reconstruction with a circular-function-based gas kinetic flux solver (C-GKFS), which enhances the resolution of flow field details while maintaining stability and high accuracy. To further improve the efficiency of time advancement, this work introduces two-derivative, multi-step or multi-stage time discretization schemes with strong stability preserving time coefficients. These schemes are combined with the Lax-Wendroff spatio-temporal coupling strategy, which effectively reduce the number of function evaluations, lowers the computational complexity, and improves the overall robustness. The numerical results of several typical examples verify the advantages of the proposed method in terms of resolution, stability and efficiency, especially in the simulations of the shock-bubble interaction and the inviscid 3D Taylor-Green vortex, which show good potential for applications in complex flows.
{"title":"High-order gas-kinetic scheme with two-derivative-based time discretization for compressible flows","authors":"Qiushuo Qin , Jie Wu , Lan Jiang","doi":"10.1016/j.compfluid.2025.106950","DOIUrl":"10.1016/j.compfluid.2025.106950","url":null,"abstract":"<div><div>In this paper, an efficient high-order gas-kinetic scheme for compressible flow simulation is presented. It combines the fifth-order targeted essentially non-oscillatory (TENO) reconstruction with a circular-function-based gas kinetic flux solver (C-GKFS), which enhances the resolution of flow field details while maintaining stability and high accuracy. To further improve the efficiency of time advancement, this work introduces two-derivative, multi-step or multi-stage time discretization schemes with strong stability preserving time coefficients. These schemes are combined with the Lax-Wendroff spatio-temporal coupling strategy, which effectively reduce the number of function evaluations, lowers the computational complexity, and improves the overall robustness. The numerical results of several typical examples verify the advantages of the proposed method in terms of resolution, stability and efficiency, especially in the simulations of the shock-bubble interaction and the inviscid 3D Taylor-Green vortex, which show good potential for applications in complex flows.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"306 ","pages":"Article 106950"},"PeriodicalIF":3.0,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-12-17DOI: 10.1016/j.compfluid.2025.106947
Koen J. Groot , Jordi Casacuberta , Stefan Hickel
A detailed derivation, analysis, and verification is given for the non-orthogonal, plane-marching Parabolized Stability Equations (PSE) approach. In applying the approach to a flow distorted by a medium-amplitude crossflow vortex, we determine its linear secondary instability mechanisms. We show that converged solutions can be achieved for a broad frequency range with an existing stabilization method for the line-marching PSE approach. We verify that 1) solutions converge versus grid size in all dimensions, 2) primary disturbance solutions agree with line-marching PSE results, and 3) secondary disturbance solutions match amplitude and growth-rate evolution of reference Direct Numerical Simulation (DNS) results. We show how and why the type-II instability displays a delayed neutral point when modeled with the plane-marching approach versus the considered local stability approaches, whether the streamwise evolution of the distorted base flow is accounted for or not. This may explain why the type-II disturbance is scarcely captured by DNS in the literature.
{"title":"Non-orthogonal plane-marching parabolized stability equations for the secondary instability of crossflow vortices","authors":"Koen J. Groot , Jordi Casacuberta , Stefan Hickel","doi":"10.1016/j.compfluid.2025.106947","DOIUrl":"10.1016/j.compfluid.2025.106947","url":null,"abstract":"<div><div>A detailed derivation, analysis, and verification is given for the non-orthogonal, plane-marching Parabolized Stability Equations (PSE) approach. In applying the approach to a flow distorted by a medium-amplitude crossflow vortex, we determine its linear secondary instability mechanisms. We show that converged solutions can be achieved for a broad frequency range with an existing stabilization method for the line-marching PSE approach. We verify that 1) solutions converge versus grid size in all dimensions, 2) primary disturbance solutions agree with line-marching PSE results, and 3) secondary disturbance solutions match amplitude and growth-rate evolution of reference Direct Numerical Simulation (DNS) results. We show how and why the <em>type</em>-II instability displays a delayed neutral point when modeled with the plane-marching approach versus the considered local stability approaches, whether the streamwise evolution of the distorted base flow is accounted for or not. This may explain why the <em>type</em>-II disturbance is scarcely captured by DNS in the literature.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"306 ","pages":"Article 106947"},"PeriodicalIF":3.0,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-12-16DOI: 10.1016/j.compfluid.2025.106949
Kush Pandya, Aravind Balan
The shape of an aerospace vehicle significantly influences its performance, and Aerodynamic Shape Optimization (ASO) refines the shape to achieve objectives such as drag reduction and lift improvement. ASO typically combines Computational Fluid Dynamics (CFD) simulations with gradient-based optimization. Adjoint methods can compute gradients independently of the number of shape parameters, making it computationally efficient when optimizing for a large number of shape parameters. For high reliability on the results of ASO, we need accurate evaluation of the objective functions and their gradients. High-order numerical methods, such as the Discontinuous Galerkin (DG) method, provide superior accuracy for compressible flow simulations at a computational cost comparable to traditional methods, making them ideal for ASO. The present study highlights the impact of discretization errors on optimal geometry, emphasizing the need for controlling them in an efficient way during optimization. A novel strategy is proposed that efficiently integrates adjoint-based mesh optimization within the ASO framework that uses a high-order DG method for the flow simulations. The approach ensures that discretization errors in the objective function remain bounded throughout the ASO process by dynamically adapting the meshes based on adjoint-based error estimates. The mesh adaptation is formulated in such a way that one gets optimum meshes with minimal number of elements for a prescribed error tolerance. The strategy results in a multi-fidelity approach where there is an effective utilization of computation cost by progressively refining the mesh as ASO progresses. The effectiveness of the proposed methodology is demonstrated through a comparative analysis with conventional ASO performed on a fixed fine mesh, using a benchmark test case from the AIAA Aerodynamic Design Optimization Discussion Group (ADODG). The results highlight significant improvements in the optimization process’s reliability and computational efficiency.
{"title":"Aerodynamic shape optimization with discretization error control for high-order compressible flow simulations","authors":"Kush Pandya, Aravind Balan","doi":"10.1016/j.compfluid.2025.106949","DOIUrl":"10.1016/j.compfluid.2025.106949","url":null,"abstract":"<div><div>The shape of an aerospace vehicle significantly influences its performance, and Aerodynamic Shape Optimization (ASO) refines the shape to achieve objectives such as drag reduction and lift improvement. ASO typically combines Computational Fluid Dynamics (CFD) simulations with gradient-based optimization. Adjoint methods can compute gradients independently of the number of shape parameters, making it computationally efficient when optimizing for a large number of shape parameters. For high reliability on the results of ASO, we need accurate evaluation of the objective functions and their gradients. High-order numerical methods, such as the Discontinuous Galerkin (DG) method, provide superior accuracy for compressible flow simulations at a computational cost comparable to traditional methods, making them ideal for ASO. The present study highlights the impact of discretization errors on optimal geometry, emphasizing the need for controlling them in an efficient way during optimization. A novel strategy is proposed that efficiently integrates adjoint-based mesh optimization within the ASO framework that uses a high-order DG method for the flow simulations. The approach ensures that discretization errors in the objective function remain bounded throughout the ASO process by dynamically adapting the meshes based on adjoint-based error estimates. The mesh adaptation is formulated in such a way that one gets optimum meshes with minimal number of elements for a prescribed error tolerance. The strategy results in a multi-fidelity approach where there is an effective utilization of computation cost by progressively refining the mesh as ASO progresses. The effectiveness of the proposed methodology is demonstrated through a comparative analysis with conventional ASO performed on a fixed fine mesh, using a benchmark test case from the AIAA Aerodynamic Design Optimization Discussion Group (ADODG). The results highlight significant improvements in the optimization process’s reliability and computational efficiency.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"306 ","pages":"Article 106949"},"PeriodicalIF":3.0,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-12-15DOI: 10.1016/j.compfluid.2025.106930
Shayan Heydari, Rui Gao, Rajeev K. Jaiman
We present a finite element-inspired hypergraph neural network framework for predicting flow-induced vibrations in freely oscillating cylinders. The surrogate architecture transforms unstructured computational meshes into node-element hypergraphs that encode higher-order spatial relationships through element-based connectivity, preserving the geometric and topological structure of the underlying finite-element discretization. The temporal evolution of the fluid-structure interaction is modeled via a modular partitioned architecture: a complex-valued, proper orthogonal decomposition-based sub-network predicts mesh deformation using a low-rank representation of Arbitrary Lagrangian-Eulerian (ALE) grid displacements, while a hypergraph-based message-passing network predicts the unsteady flow field using geometry-aware node, element, and hybrid edge features. High-fidelity ALE-based simulations provide training and evaluation data across a range of Reynolds numbers and reduced velocities for isolated and tandem cylinder configurations. The framework demonstrates stable rollouts and accurately captures the nonlinear variation of oscillation amplitudes with respect to reduced velocity, a key challenge in surrogate modeling of flow-induced vibrations. In the tandem configuration, the model successfully resolves complex wake-body interactions and multi-scale coupling effects, enabling prediction of pressure and velocity fields under strong wake interference conditions. Our results show high fidelity in reproducing force statistics, dominant frequencies, and flow-field dynamics, supporting the framework’s potential as a robust surrogate model for digital twin applications.
{"title":"Predicting flow-induced vibration in isolated and tandem cylinders using hypergraph neural networks","authors":"Shayan Heydari, Rui Gao, Rajeev K. Jaiman","doi":"10.1016/j.compfluid.2025.106930","DOIUrl":"10.1016/j.compfluid.2025.106930","url":null,"abstract":"<div><div>We present a finite element-inspired hypergraph neural network framework for predicting flow-induced vibrations in freely oscillating cylinders. The surrogate architecture transforms unstructured computational meshes into node-element hypergraphs that encode higher-order spatial relationships through element-based connectivity, preserving the geometric and topological structure of the underlying finite-element discretization. The temporal evolution of the fluid-structure interaction is modeled via a modular partitioned architecture: a complex-valued, proper orthogonal decomposition-based sub-network predicts mesh deformation using a low-rank representation of Arbitrary Lagrangian-Eulerian (ALE) grid displacements, while a hypergraph-based message-passing network predicts the unsteady flow field using geometry-aware node, element, and hybrid edge features. High-fidelity ALE-based simulations provide training and evaluation data across a range of Reynolds numbers and reduced velocities for isolated and tandem cylinder configurations. The framework demonstrates stable rollouts and accurately captures the nonlinear variation of oscillation amplitudes with respect to reduced velocity, a key challenge in surrogate modeling of flow-induced vibrations. In the tandem configuration, the model successfully resolves complex wake-body interactions and multi-scale coupling effects, enabling prediction of pressure and velocity fields under strong wake interference conditions. Our results show high fidelity in reproducing force statistics, dominant frequencies, and flow-field dynamics, supporting the framework’s potential as a robust surrogate model for digital twin applications.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"307 ","pages":"Article 106930"},"PeriodicalIF":3.0,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145883380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-12-15DOI: 10.1016/j.compfluid.2025.106943
Manuel A. Ramirez-Cabrera , Eduardo Ramos , Manira E. Narvaez-Saucedo , Patricio J. Valades-Pelayo
We present a Monte Carlo method for the incompressible Navier-Stokes equations, enforcing divergence-free solutions through a probabilistic projection framework. Using short random walks embedded in Markov matrices, the method sequentially solves diffusion, convection, and pressure projection steps at each timestep. The method achieves near-linear CPU scaling (O(N1.18)) for transient simulations through pre-computed transition probability matrices for linear operators, with Multi-Level Monte Carlo acceleration improving steady-state convergence to (O(N1.58)). Validation on lid-driven cavity flows (Re=100, 1000) shows differences below 3 % versus benchmarks. Additionally, the mesh-free nature of the Monte Carlo approach handles complex geometries simply by tagging random walkers within non-conforming obstacles, bypassing traditional meshing requirements. The method combines accuracy, unconditional stability, and inherent parallelizability, offering a compelling alternative to deterministic approaches.
{"title":"A Markov matrix iterative splitting algorithm for incompressible flow","authors":"Manuel A. Ramirez-Cabrera , Eduardo Ramos , Manira E. Narvaez-Saucedo , Patricio J. Valades-Pelayo","doi":"10.1016/j.compfluid.2025.106943","DOIUrl":"10.1016/j.compfluid.2025.106943","url":null,"abstract":"<div><div>We present a Monte Carlo method for the incompressible Navier-Stokes equations, enforcing divergence-free solutions through a probabilistic projection framework. Using short random walks embedded in Markov matrices, the method sequentially solves diffusion, convection, and pressure projection steps at each timestep. The method achieves near-linear CPU scaling (<em>O</em>(<em>N</em><sup>1.18</sup>)) for transient simulations through pre-computed transition probability matrices for linear operators, with Multi-Level Monte Carlo acceleration improving steady-state convergence to (<em>O</em>(<em>N</em><sup>1.58</sup>)). Validation on lid-driven cavity flows (Re=100, 1000) shows differences below 3 % versus benchmarks. Additionally, the mesh-free nature of the Monte Carlo approach handles complex geometries simply by tagging random walkers within non-conforming obstacles, bypassing traditional meshing requirements. The method combines accuracy, unconditional stability, and inherent parallelizability, offering a compelling alternative to deterministic approaches.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"306 ","pages":"Article 106943"},"PeriodicalIF":3.0,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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