Pub Date : 2026-04-15Epub Date: 2026-02-05DOI: 10.1016/j.compfluid.2026.106998
Éloïse D’ayer , Arthur Colombié , François Chedevergne
Aiming at high-fidelity near-wall turbulent flow simulations accounting for roughness effects and heating, an immersed boundary method based on volume penalization was implemented and assessed within a spectral difference framework. A time integration scheme using the Strang splitting operator was used to lower the possible values of the penalization parameter, without consequences for the time step. The resulting algorithm is tested with the reference case of the flow around a cylinder at a low Reynolds number. The results are comparable to those obtained by the body-fitted method. This reference case was already used in the literature to validate a volume penalization method combined with flux reconstruction. The approach is then applied to the direct numerical simulation of near-wall turbulence in two different rough channel configurations, for which reference data are available. The first academic case includes heat transfer, while the second configuration consider a complex surface topography. The good agreement between the body-fitted approach, the immersed boundary method, and the reference computations demonstrate the reliability of the present methodology to generate a database of near-wall turbulent flow over rough surfaces.
{"title":"Immersed boundary conditions using the spectral difference method applied to turbulent flows over rough surfaces","authors":"Éloïse D’ayer , Arthur Colombié , François Chedevergne","doi":"10.1016/j.compfluid.2026.106998","DOIUrl":"10.1016/j.compfluid.2026.106998","url":null,"abstract":"<div><div>Aiming at high-fidelity near-wall turbulent flow simulations accounting for roughness effects and heating, an immersed boundary method based on volume penalization was implemented and assessed within a spectral difference framework. A time integration scheme using the Strang splitting operator was used to lower the possible values of the penalization parameter, without consequences for the time step. The resulting algorithm is tested with the reference case of the flow around a cylinder at a low Reynolds number. The results are comparable to those obtained by the body-fitted method. This reference case was already used in the literature to validate a volume penalization method combined with flux reconstruction. The approach is then applied to the direct numerical simulation of near-wall turbulence in two different rough channel configurations, for which reference data are available. The first academic case includes heat transfer, while the second configuration consider a complex surface topography. The good agreement between the body-fitted approach, the immersed boundary method, and the reference computations demonstrate the reliability of the present methodology to generate a database of near-wall turbulent flow over rough surfaces.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"309 ","pages":"Article 106998"},"PeriodicalIF":3.0,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146154163","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 : 2026-04-15Epub Date: 2026-02-02DOI: 10.1016/j.compfluid.2026.106997
Charbel Ghosn, Thierry Goudon, Sebastian Minjeaud
We introduce muscl reconstructions for schemes designed on staggered grids for the numerical resolution of the Euler system. The proposed scheme works on general polygonal unstructured meshes in 2D. It uses principles based on the Discrete Duality Finite Volume framework for which the structure of the unknowns makes the gradient reconstruction naturally amenable. We develop a multislope approach where gradients and limiters are constructed face-by-face of the control volumes. Since the numerical unknowns are stored on different grids, several reconstruction techniques have to be combined. We study the stability conditions induced by the preservation of the positivity of the density and internal energy. The scheme is challenged against several numerical test cases.
{"title":"A muscl-scheme on 2D staggered unstructured grids for the Euler equations","authors":"Charbel Ghosn, Thierry Goudon, Sebastian Minjeaud","doi":"10.1016/j.compfluid.2026.106997","DOIUrl":"10.1016/j.compfluid.2026.106997","url":null,"abstract":"<div><div>We introduce <span>muscl</span> reconstructions for schemes designed on staggered grids for the numerical resolution of the Euler system. The proposed scheme works on general polygonal unstructured meshes in 2<span>D</span>. It uses principles based on the Discrete Duality Finite Volume framework for which the structure of the unknowns makes the gradient reconstruction naturally amenable. We develop a multislope approach where gradients and limiters are constructed face-by-face of the control volumes. Since the numerical unknowns are stored on different grids, several reconstruction techniques have to be combined. We study the stability conditions induced by the preservation of the positivity of the density and internal energy. The scheme is challenged against several numerical test cases.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"309 ","pages":"Article 106997"},"PeriodicalIF":3.0,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146154164","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 : 2026-03-30Epub Date: 2026-01-27DOI: 10.1016/j.compfluid.2026.106988
Yiren Tong, Panagiotis Tsoutsanis
In this paper, we present a multi-dimensional, arbitrary-order hybrid reconstruction framework for compressible flows on unstructured meshes. The proposed method advances state-of-the-art high-resolution schemes by combining the efficiency of linear reconstruction with the robustness of high-order non-oscillatory formulations, activated only where necessary through a novel a priori detection strategy. This approach minimises the use of costly Compact Weighted Essentially Non-Oscillatory (CWENOZ) or Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) reconstructions, thereby substantially reducing computational overhead without compromising accuracy or stability. The framework integrates the strengths of CWENOZ formulations and the Multi-dimensional Optimal Order Detection (MOOD) paradigm, while introducing a redesigned Numerical Admissibility Detector (NAD) that classifies the local flow field in a single step into smooth, weakly non-smooth, and discontinuous regions. Each region is then reconstructed using an optimal method: a high-order linear scheme in smooth areas, CWENOZ in weakly non-smooth zones, and a second-order MUSCL scheme near discontinuities. This targeted, a priori allocation preserves high-order accuracy where possible and guarantees non-oscillatory, stable solutions near shocks and strong gradients. The proposed hybrid strategy is implemented within the open-source unstructured finite-volume solver UCNS3D and supports arbitrary-order reconstructions on mixed-element meshes. Comprehensive two- and three-dimensional benchmark tests demonstrate that the method maintains the designed order of accuracy in smooth regions while significantly enhancing robustness in shock-dominated flows. Owing to the reduced frequency of expensive nonlinear reconstructions, the framework achieves up to a 2.5 × speed-up compared to a CWENOZ scheme of the same order in 3D compressible turbulence simulations. Overall, this hybrid framework brings high-order accuracy closer to in industrial-scale CFD simulations through its combination of reduced computational cost, improved robustness, and reliability.
{"title":"A hybrid finite-volume reconstruction framework for efficient high-order shock-capturing on unstructured meshes","authors":"Yiren Tong, Panagiotis Tsoutsanis","doi":"10.1016/j.compfluid.2026.106988","DOIUrl":"10.1016/j.compfluid.2026.106988","url":null,"abstract":"<div><div>In this paper, we present a multi-dimensional, arbitrary-order hybrid reconstruction framework for compressible flows on unstructured meshes. The proposed method advances state-of-the-art high-resolution schemes by combining the efficiency of linear reconstruction with the robustness of high-order non-oscillatory formulations, activated only where necessary through a novel a priori detection strategy. This approach minimises the use of costly Compact Weighted Essentially Non-Oscillatory (CWENOZ) or Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) reconstructions, thereby substantially reducing computational overhead without compromising accuracy or stability. The framework integrates the strengths of CWENOZ formulations and the Multi-dimensional Optimal Order Detection (MOOD) paradigm, while introducing a redesigned Numerical Admissibility Detector (NAD) that classifies the local flow field in a single step into smooth, weakly non-smooth, and discontinuous regions. Each region is then reconstructed using an optimal method: a high-order linear scheme in smooth areas, CWENOZ in weakly non-smooth zones, and a second-order MUSCL scheme near discontinuities. This targeted, a priori allocation preserves high-order accuracy where possible and guarantees non-oscillatory, stable solutions near shocks and strong gradients. The proposed hybrid strategy is implemented within the open-source unstructured finite-volume solver UCNS3D and supports arbitrary-order reconstructions on mixed-element meshes. Comprehensive two- and three-dimensional benchmark tests demonstrate that the method maintains the designed order of accuracy in smooth regions while significantly enhancing robustness in shock-dominated flows. Owing to the reduced frequency of expensive nonlinear reconstructions, the framework achieves up to a 2.5 × speed-up compared to a CWENOZ scheme of the same order in 3D compressible turbulence simulations. Overall, this hybrid framework brings high-order accuracy closer to in industrial-scale CFD simulations through its combination of reduced computational cost, improved robustness, and reliability.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"308 ","pages":"Article 106988"},"PeriodicalIF":3.0,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076190","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 : 2026-03-30Epub Date: 2026-01-18DOI: 10.1016/j.compfluid.2026.106975
Prashant Kumar, Rajesh Ranjan
Shock waves are a ubiquitous phenomenon in high Mach number compressible flows, but their numerical prediction remains challenging. Traditional computational fluid dynamics (CFD) methods employ well-established shock-capturing schemes, but physics-informed machine learning approaches struggle to predict shocks accurately in the absence of data, even when enforcing governing equations and boundary conditions as constraints. This work addresses this challenge by developing a data-free Physics-Informed Neural Network (PINN) framework that integrates multiple features to enhance robustness and generalizability across a wide range of compressible flows. The framework employs the non-dimensional compressible Euler equations with vanishing artificial viscosity, ν, ensuring physical consistency in shock predictions. Instead of treating ν as a fixed hyperparameter, it is learned jointly with the flow variables. Two formulations are developed: a global model, where ν is optimized in parallel with flow variables via a decoupled update, and a local model, where ν varies spatially and is predicted using either a shared network (L-NN1) or an auxiliary network (L-NN2). To enhance generalization and training consistency across different flow conditions, the framework standardizes input spaces using their mean and standard deviations, and also employs a predefined learning rate decay. The framework is evaluated on a range of supersonic cases, including Sod and Lax shock tubes, compression and expansion corners, shock reflection, and 2D Riemann problems, showing accurate prediction of shock locations and strengths with close agreement to high-fidelity CFD. The global formulation exhibits higher diffusion at discontinuities, while the auxiliary-network local formulation (L-NN2) yields the sharpest resolution. The shared-network formulation (L-NN1) provides limited improvement due to coupled learning dynamics with primary flow variables. Overall, the proposed framework demonstrates that PINNs can achieve physically consistent predictions for strongly nonlinear compressible flows while reducing reliance on data and extensive hyperparameter tuning, thus paving the way for broader adoption of physics-informed machine learning in aerodynamics and fluid mechanics.
{"title":"A robust data-free physics-informed neural network for compressible flows with shocks","authors":"Prashant Kumar, Rajesh Ranjan","doi":"10.1016/j.compfluid.2026.106975","DOIUrl":"10.1016/j.compfluid.2026.106975","url":null,"abstract":"<div><div>Shock waves are a ubiquitous phenomenon in high Mach number compressible flows, but their numerical prediction remains challenging. Traditional computational fluid dynamics (CFD) methods employ well-established shock-capturing schemes, but physics-informed machine learning approaches struggle to predict shocks accurately in the absence of data, even when enforcing governing equations and boundary conditions as constraints. This work addresses this challenge by developing a data-free Physics-Informed Neural Network (PINN) framework that integrates multiple features to enhance robustness and generalizability across a wide range of compressible flows. The framework employs the non-dimensional compressible Euler equations with vanishing artificial viscosity, <em>ν</em>, ensuring physical consistency in shock predictions. Instead of treating <em>ν</em> as a fixed hyperparameter, it is learned jointly with the flow variables. Two formulations are developed: a global model, where <em>ν</em> is optimized in parallel with flow variables via a decoupled update, and a local model, where <em>ν</em> varies spatially and is predicted using either a shared network (L-NN1) or an auxiliary network (L-NN2). To enhance generalization and training consistency across different flow conditions, the framework standardizes input spaces using their mean and standard deviations, and also employs a predefined learning rate decay. The framework is evaluated on a range of supersonic cases, including Sod and Lax shock tubes, compression and expansion corners, shock reflection, and 2D Riemann problems, showing accurate prediction of shock locations and strengths with close agreement to high-fidelity CFD. The global formulation exhibits higher diffusion at discontinuities, while the auxiliary-network local formulation (L-NN2) yields the sharpest resolution. The shared-network formulation (L-NN1) provides limited improvement due to coupled learning dynamics with primary flow variables. Overall, the proposed framework demonstrates that PINNs can achieve physically consistent predictions for strongly nonlinear compressible flows while reducing reliance on data and extensive hyperparameter tuning, thus paving the way for broader adoption of physics-informed machine learning in aerodynamics and fluid mechanics.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"308 ","pages":"Article 106975"},"PeriodicalIF":3.0,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015793","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 : 2026-03-30Epub Date: 2026-01-22DOI: 10.1016/j.compfluid.2026.106986
Luca Damiola , Jan Decuyper , Mark C. Runacres , Tim De Troyer
Dynamic stall is an unsteady aerodynamic phenomenon which temporarily enhances lift and delays flow separation on a lifting surface, but is also associated with large load fluctuations that may compromise the structural integrity of the system. The present work, based on transient computational fluid dynamics (CFD) simulations, proposes a methodology to mitigate the undesired effects of dynamic stall on a pitching NACA 0018 aerofoil undergoing a large-amplitude sinusoidal oscillation. The study aims to alleviate the post-stall load fluctuations by introducing small modifications to the pitching kinematics of the aerofoil. The approach relies on the construction of a nonlinear data-driven model of the system, which is capable of predicting the time-varying lift, drag, and moment coefficients from a given angle-of-attack time series. This fast and accurate nonlinear model, based on neural networks, is coupled with a multi-objective genetic algorithm designed to optimise two competing objectives: the negative peak pitching moment coefficient and the mean lift coefficient. The optimised pitching parameters are identified by modifying the original sinusoidal motion through the superposition of two higher harmonics, with their amplitudes and phases being the design variables. The optimised aerofoil motion proposed by the genetic algorithm is subsequently evaluated through CFD analysis to verify the accuracy of the model predictions. Results show good agreement between the predicted and the actual transient aerodynamic coefficients, demonstrating that small adjustments to the pitching trajectory can lead to substantial reduction of the peak loads during deep dynamic stall. The obtained results further underscore the usefulness of nonlinear data-driven models, which are particularly well-suited for integration into optimisation and control frameworks that require both accuracy and a fast evaluation time.
{"title":"Dynamic stall mitigation of a pitching aerofoil using a data-driven model","authors":"Luca Damiola , Jan Decuyper , Mark C. Runacres , Tim De Troyer","doi":"10.1016/j.compfluid.2026.106986","DOIUrl":"10.1016/j.compfluid.2026.106986","url":null,"abstract":"<div><div>Dynamic stall is an unsteady aerodynamic phenomenon which temporarily enhances lift and delays flow separation on a lifting surface, but is also associated with large load fluctuations that may compromise the structural integrity of the system. The present work, based on transient computational fluid dynamics (CFD) simulations, proposes a methodology to mitigate the undesired effects of dynamic stall on a pitching NACA 0018 aerofoil undergoing a large-amplitude sinusoidal oscillation. The study aims to alleviate the post-stall load fluctuations by introducing small modifications to the pitching kinematics of the aerofoil. The approach relies on the construction of a nonlinear data-driven model of the system, which is capable of predicting the time-varying lift, drag, and moment coefficients from a given angle-of-attack time series. This fast and accurate nonlinear model, based on neural networks, is coupled with a multi-objective genetic algorithm designed to optimise two competing objectives: the negative peak pitching moment coefficient and the mean lift coefficient. The optimised pitching parameters are identified by modifying the original sinusoidal motion through the superposition of two higher harmonics, with their amplitudes and phases being the design variables. The optimised aerofoil motion proposed by the genetic algorithm is subsequently evaluated through CFD analysis to verify the accuracy of the model predictions. Results show good agreement between the predicted and the actual transient aerodynamic coefficients, demonstrating that small adjustments to the pitching trajectory can lead to substantial reduction of the peak loads during deep dynamic stall. The obtained results further underscore the usefulness of nonlinear data-driven models, which are particularly well-suited for integration into optimisation and control frameworks that require both accuracy and a fast evaluation time.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"308 ","pages":"Article 106986"},"PeriodicalIF":3.0,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076124","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 : 2026-03-30Epub Date: 2026-01-19DOI: 10.1016/j.compfluid.2026.106980
Fu Ling , Yonggang Zhang , Binghai Wen
The nucleation behavior of nanobubbles and nanodroplets is highly sensitive to how the liquid-gas surface tension depends on temperature and curvature, and accurately modeling this dependence is crucial for understanding and predicting micro/nano-scale phase transition processes. We establish a dimensional transformation and use a chemical-potential multiphase lattice Boltzmann method to systematically study the effects of temperature and curvature on surface tension and Tolman length for two typical fluids: water and methane. The Tolman length is used to quantify the deviation of interfacial tension from the flat interface limit. The simulation results show that both water and methane exhibit exponential changes in surface tension with temperature at a flat interface. An equation for predicting surface tension is then derived by considering the effects of temperature and curvature. Further analysis reveals that as curvature increases, the surface tension of nanobubbles increases while the Tolman length decreases, whereas nanodroplets exhibit the opposite trends.
{"title":"Effect of temperature and curvature on surface tension and Tolman length in the multiphase lattice Boltzmann method","authors":"Fu Ling , Yonggang Zhang , Binghai Wen","doi":"10.1016/j.compfluid.2026.106980","DOIUrl":"10.1016/j.compfluid.2026.106980","url":null,"abstract":"<div><div>The nucleation behavior of nanobubbles and nanodroplets is highly sensitive to how the liquid-gas surface tension depends on temperature and curvature, and accurately modeling this dependence is crucial for understanding and predicting micro/nano-scale phase transition processes. We establish a dimensional transformation and use a chemical-potential multiphase lattice Boltzmann method to systematically study the effects of temperature and curvature on surface tension and Tolman length for two typical fluids: water and methane. The Tolman length is used to quantify the deviation of interfacial tension from the flat interface limit. The simulation results show that both water and methane exhibit exponential changes in surface tension with temperature at a flat interface. An equation for predicting surface tension is then derived by considering the effects of temperature and curvature. Further analysis reveals that as curvature increases, the surface tension of nanobubbles increases while the Tolman length decreases, whereas nanodroplets exhibit the opposite trends.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"308 ","pages":"Article 106980"},"PeriodicalIF":3.0,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076121","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}
This study presents an enhancement of Reynolds-averaged Navier-Stokes (RANS) simulations for predicting the flow around a simplified notchback car model by incorporating experimental data from global luminescent oil film (GLOF) measurements. The simulations employ the SST k-ω turbulence model, with a particular focus on improving predictions of flow separation in the rear regions of the car model, including the rear window and rear side surfaces. To achieve this, the parameter a1 of the SST k-ω turbulence model is zonally optimized using an ensemble Kalman filter (EnKF), ensuring that the predicted separation locations align locally with near-wall flow features captured by the GLOF measurements. The data assimilation framework is first validated through a numerical data assimilation experiment (twin experiment) that mimics GLOF measurements within the RANS simulation. Following this validation, the system is applied to actual GLOF measurements. The resulting GLOF-informed distribution yields near-wall flow patterns that closely match those observed in the experiment, demonstrating the effectiveness of the proposed approach.
{"title":"Flow separation prediction in a simplified notchback car model by assimilating global luminescent oil film measurements","authors":"Takashi Misaka , Takuji Nakashima , Keigo Shimizu , Masato Hijikuro , Masayuki Anyoji , Yoshiyuki Furukawa","doi":"10.1016/j.compfluid.2026.106983","DOIUrl":"10.1016/j.compfluid.2026.106983","url":null,"abstract":"<div><div>This study presents an enhancement of Reynolds-averaged Navier-Stokes (RANS) simulations for predicting the flow around a simplified notchback car model by incorporating experimental data from global luminescent oil film (GLOF) measurements. The simulations employ the SST <em>k</em>-<em>ω</em> turbulence model, with a particular focus on improving predictions of flow separation in the rear regions of the car model, including the rear window and rear side surfaces. To achieve this, the parameter <em>a</em><sub>1</sub> of the SST <em>k</em>-<em>ω</em> turbulence model is zonally optimized using an ensemble Kalman filter (EnKF), ensuring that the predicted separation locations align locally with near-wall flow features captured by the GLOF measurements. The data assimilation framework is first validated through a numerical data assimilation experiment (twin experiment) that mimics GLOF measurements within the RANS simulation. Following this validation, the system is applied to actual GLOF measurements. The resulting GLOF-informed <span><math><msub><mi>a</mi><mn>1</mn></msub></math></span> distribution yields near-wall flow patterns that closely match those observed in the experiment, demonstrating the effectiveness of the proposed approach.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"308 ","pages":"Article 106983"},"PeriodicalIF":3.0,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076126","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 : 2026-03-30Epub Date: 2026-01-17DOI: 10.1016/j.compfluid.2026.106976
Afaf Bouharguane , Angelo Iollo , Alexis Tardieu
This paper proposes to solve numerically the two dimensional nonlinear advection-diffusion equation. The space discretization relies on a classical Discontinuous Galerkin (DG) method. This scheme is combined together with an Arbitrary high order DERivatives (ADER) approach to ensure the same high order of accuracy in time compared to the precision in space. More precisely, two different methods are compared regarding the computational cost, the error and the order of convergence: the Symmetric Interior Penalty Galerkin (SIPG) and the Cattaneo relaxation methods. The viscosity of the medium, the mesh and the approximation degree being fixed, we aim at determining whether the penalty or the relaxation scheme is to be preferred. Numerical examples are provided to illustrate and quantify this comparison. We show that both approaches ensure to reach an arbitrary high precision and present an interest from an implementation perspective.
{"title":"Nonlinear advection-diffusion equation: ADER-DG penalty vs. relaxation schemes","authors":"Afaf Bouharguane , Angelo Iollo , Alexis Tardieu","doi":"10.1016/j.compfluid.2026.106976","DOIUrl":"10.1016/j.compfluid.2026.106976","url":null,"abstract":"<div><div>This paper proposes to solve numerically the two dimensional nonlinear advection-diffusion equation. The space discretization relies on a classical Discontinuous Galerkin (DG) method. This scheme is combined together with an Arbitrary high order DERivatives (ADER) approach to ensure the same high order of accuracy in time compared to the precision in space. More precisely, two different methods are compared regarding the computational cost, the error and the order of convergence: the Symmetric Interior Penalty Galerkin (SIPG) and the Cattaneo relaxation methods. The viscosity of the medium, the mesh and the approximation degree being fixed, we aim at determining whether the penalty or the relaxation scheme is to be preferred. Numerical examples are provided to illustrate and quantify this comparison. We show that both approaches ensure to reach an arbitrary high precision and present an interest from an implementation perspective.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"308 ","pages":"Article 106976"},"PeriodicalIF":3.0,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036612","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 : 2026-03-30Epub Date: 2026-01-23DOI: 10.1016/j.compfluid.2026.106984
G.G. Kokkinakis, A.I. Delis
This paper presents a novel symmetry-aware troubled-cell indicator (TCI) for high-order ADER Discontinuous Galerkin (ADER-DG) schemes, designed to improve robustness and generalization in the presence of discontinuities on unstructured triangular meshes. The proposed method leverages a Siamese Convolutional Neural Network (SCNN-TCI) that explicitly encodes invariance to geometric transformations-rotations and reflections-by design. Six transformed versions of each input patch are processed through identical CNN branches with shared weights, and their features are fused using pixel-wise max-pooling to achieve transformation-invariant classification. This approach eliminates the need for extensive data augmentation and ensures consistent predictions across varying mesh orientations. Numerical experiments on analytical functions, as well as the two-dimensional Burgers and Euler equations, demonstrate that the SCNN-TCI accurately detects both sharp gradients and shock regions, while preserving rotational and reflectional symmetry. The architecture integrates seamlessly with the ADER-DG solver, triggering sub-cell limiting only when necessary, and represents a compact, interpretable, and computationally efficient alternative to existing ML-based TCIs.
{"title":"Symmetry-preserving neural indicators for discontinuity detection in high-order discontinuous Galerkin solvers","authors":"G.G. Kokkinakis, A.I. Delis","doi":"10.1016/j.compfluid.2026.106984","DOIUrl":"10.1016/j.compfluid.2026.106984","url":null,"abstract":"<div><div>This paper presents a novel symmetry-aware troubled-cell indicator (TCI) for high-order ADER Discontinuous Galerkin (ADER-DG) schemes, designed to improve robustness and generalization in the presence of discontinuities on unstructured triangular meshes. The proposed method leverages a Siamese Convolutional Neural Network (SCNN-TCI) that explicitly encodes invariance to geometric transformations-rotations and reflections-by design. Six transformed versions of each input patch are processed through identical CNN branches with shared weights, and their features are fused using pixel-wise max-pooling to achieve transformation-invariant classification. This approach eliminates the need for extensive data augmentation and ensures consistent predictions across varying mesh orientations. Numerical experiments on analytical functions, as well as the two-dimensional Burgers and Euler equations, demonstrate that the SCNN-TCI accurately detects both sharp gradients and shock regions, while preserving rotational and reflectional symmetry. The architecture integrates seamlessly with the ADER-DG solver, triggering sub-cell limiting only when necessary, and represents a compact, interpretable, and computationally efficient alternative to existing ML-based TCIs.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"308 ","pages":"Article 106984"},"PeriodicalIF":3.0,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076123","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 : 2026-03-30Epub Date: 2026-01-24DOI: 10.1016/j.compfluid.2026.106982
Xiang Qiu , Yujie Wen , Xueqin Zhou , Yulu Liu
This study introduces a new Bayesian uncertainty quantification and calibration method, employing a hybrid surrogate model for parameter calibration and uncertainty analysis in turbulence modeling. The proposed method integrates three surrogate modeling techniques, including Gaussian Process Regression, Polynomial Chaos Expansion and BackPropagation neural networks, by employing a weighted averaging approach to construct a high-accuracy and robust hybrid surrogate model. To optimize model performance, an adaptive sampling method is employed, adjusting the distribution of samples dynamically based on output uncertainty and dispersion. This approach improves model fitting accuracy and predictive capability while reducing computational costs. Validation of the surrogate modeling method is carried out through mathematical function fitting, demonstrating its ability to improve accuracy and decrease sample requirements. Furthermore, the method is applied to two representative turbulence cases: periodic hill flow and backward-facing step flow. In the periodic hill case, model calibration performance is assessed using high-fidelity Direct Numerical Simulation data, showing that the calibrated model reduces prediction errors in the recirculation zone. In the backward-facing step case, the model’s applicability in separated turbulence is further verified through parameter calibration and posterior uncertainty quantification. The simulation reveals that the refined model effectively improves consistency with experimental data, reducing errors in predicting key flow characteristics, especially in regions with intense flow variations.
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