Pub Date : 2026-01-19DOI: 10.1016/j.compfluid.2026.106978
G. de Romémont , F. Renac , J. Nunez , D. Gueyffier , F. Chinesta
This paper presents a data-driven finite volume method for solving 1D and 2D hyperbolic partial differential equations. This work builds upon prior research [5, 27, 75] incorporating a data-driven finite-difference approximation of smooth solutions of scalar conservation laws, where optimal coefficients of neural networks approximating space derivatives are learned based on accurate, but cumbersome solutions to these equations. We extend this approach to MUSCL-type finite volume approximations of hyperbolic scalar and systems of conservation laws. We also train the discretization to efficiently capture discontinuous solutions with shock and contact waves, as well as to the application of boundary conditions. The learning procedure of the data-driven model is extended through the definition of a new loss with added regularizers, paddings and adequate training databases. These new ingredients guarantee computational stability, preserve the accuracy of fine-grid solutions, and enhance overall performance. Numerical experiments using test cases from the literature in both one and two-dimensional spaces demonstrate that the learned model accurately reproduces fine-grid results on very coarse meshes achieving 20–50% gains in accuracy.
{"title":"A data-driven learned discretization approach in finite volume schemes for hyperbolic conservation laws and varying boundary conditions","authors":"G. de Romémont , F. Renac , J. Nunez , D. Gueyffier , F. Chinesta","doi":"10.1016/j.compfluid.2026.106978","DOIUrl":"10.1016/j.compfluid.2026.106978","url":null,"abstract":"<div><div>This paper presents a data-driven finite volume method for solving 1D and 2D hyperbolic partial differential equations. This work builds upon prior research [5, 27, 75] incorporating a data-driven finite-difference approximation of smooth solutions of scalar conservation laws, where optimal coefficients of neural networks approximating space derivatives are learned based on accurate, but cumbersome solutions to these equations. We extend this approach to MUSCL-type finite volume approximations of hyperbolic scalar and systems of conservation laws. We also train the discretization to efficiently capture discontinuous solutions with shock and contact waves, as well as to the application of boundary conditions. The learning procedure of the data-driven model is extended through the definition of a new loss with added regularizers, paddings and adequate training databases. These new ingredients guarantee computational stability, preserve the accuracy of fine-grid solutions, and enhance overall performance. Numerical experiments using test cases from the literature in both one and two-dimensional spaces demonstrate that the learned model accurately reproduces fine-grid results on very coarse meshes achieving 20–50% gains in accuracy.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"307 ","pages":"Article 106978"},"PeriodicalIF":3.0,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034934","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 : 2026-01-18DOI: 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":"2026-01-18","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 : 2026-01-17DOI: 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":"2026-01-17","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 : 2026-01-17DOI: 10.1016/j.compfluid.2026.106977
Jingchao Zhang , Yue Zhang , Song Chen , Guanxin Hong
Numerical simulations of chemically reacting flows often suffer from stiffness arising from the large disparities in time scales among advection, diffusion, and chemical reactions, which severely limits computational efficiency. To address this challenge, this study proposes a hybrid implicit-explicit component-splitting method that decomposes the governing equations into two subsystems: a flow subsystem handling advection-viscous terms through explicit time integration, and a component subsystem treating diffusion-reaction terms via implicit time integration. This framework effectively combines the accuracy of explicit methods with the efficiency and stability of implicit schemes. In regions exhibiting strong stiffness, the local time step of the component subsystem is adaptively reduced by an appropriately chosen divisor to improve numerical stability and robustness. Furthermore, a species-invariance criterion based on local mass-fraction gradients and reaction activity is incorporated to selectively update the component subsystem, thereby reducing redundant computations. For unsteady flows, the proposed method permits significantly larger time steps than explicit Runge-Kutta schemes, while for steady flows it increases the maximum stable Courant-Friedrichs-Lewy number and reduces time cost per iteration. Several test cases, including hydrogen-air detonations and hypersonic non-equilibrium flows, demonstrate the method’s effectiveness: it maintains stability at large time steps, accurately captures the complex interactions between shock and detonation waves, and shows excellent agreement with high-order Runge-Kutta simulations. Overall, the proposed implicit-explicit method enables efficient, accurate, and robust simulations of chemically reacting flows with stiff chemistry.
{"title":"A hybrid implicit-explicit time integration for stiff chemically reacting flows based on adaptive component-splitting method","authors":"Jingchao Zhang , Yue Zhang , Song Chen , Guanxin Hong","doi":"10.1016/j.compfluid.2026.106977","DOIUrl":"10.1016/j.compfluid.2026.106977","url":null,"abstract":"<div><div>Numerical simulations of chemically reacting flows often suffer from stiffness arising from the large disparities in time scales among advection, diffusion, and chemical reactions, which severely limits computational efficiency. To address this challenge, this study proposes a hybrid implicit-explicit component-splitting method that decomposes the governing equations into two subsystems: a flow subsystem handling advection-viscous terms through explicit time integration, and a component subsystem treating diffusion-reaction terms via implicit time integration. This framework effectively combines the accuracy of explicit methods with the efficiency and stability of implicit schemes. In regions exhibiting strong stiffness, the local time step of the component subsystem is adaptively reduced by an appropriately chosen divisor to improve numerical stability and robustness. Furthermore, a species-invariance criterion based on local mass-fraction gradients and reaction activity is incorporated to selectively update the component subsystem, thereby reducing redundant computations. For unsteady flows, the proposed method permits significantly larger time steps than explicit Runge-Kutta schemes, while for steady flows it increases the maximum stable Courant-Friedrichs-Lewy number and reduces time cost per iteration. Several test cases, including hydrogen-air detonations and hypersonic non-equilibrium flows, demonstrate the method’s effectiveness: it maintains stability at large time steps, accurately captures the complex interactions between shock and detonation waves, and shows excellent agreement with high-order Runge-Kutta simulations. Overall, the proposed implicit-explicit method enables efficient, accurate, and robust simulations of chemically reacting flows with stiff chemistry.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"307 ","pages":"Article 106977"},"PeriodicalIF":3.0,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034933","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 : 2026-01-14DOI: 10.1016/j.compfluid.2026.106973
Antonio Blanco-Casares, Daniel Mira, Oriol Lehmkuhl
This work presents a low-dissipative numerical method to solve the scalar transport equation with an exhaustive analysis of its application to reacting flows in the limit of perfectly premixed combustion with a low-Mach number formulation. A tabulated flamelet model is used to simplify the chemical reactions. The proposed method is presented for a generic conservation law and its property-preserving capability is proved on linear advection tests, in which it proves the preservation of strong gradients and the ability of controlling overshoots-undershoots. Even though the TVD property is not guaranteed, the numerical oscillations are greatly reduced. Then, the method is adapted to solve the convection-diffusion transport scalar equation with source terms, which is the core of any reacting flow simulation. The implementation is validated with the one-dimensional flame problem and then is tested in a turbulent combustion case. The comparison between the results obtained with conventional methods based on high-dissipation and the proposed low-dissipative approach shows clear benefits of the later, the interfaces are sharper and there is an improvement in the representation of the flame front. This formulation also shows capability to capture much more flow structures which make the simulation a closer representation of the actual physics.
{"title":"A low-dissipation continuous Galerkin formulation for turbulent premixed combustion","authors":"Antonio Blanco-Casares, Daniel Mira, Oriol Lehmkuhl","doi":"10.1016/j.compfluid.2026.106973","DOIUrl":"10.1016/j.compfluid.2026.106973","url":null,"abstract":"<div><div>This work presents a low-dissipative numerical method to solve the scalar transport equation with an exhaustive analysis of its application to reacting flows in the limit of perfectly premixed combustion with a low-Mach number formulation. A tabulated flamelet model is used to simplify the chemical reactions. The proposed method is presented for a generic conservation law and its property-preserving capability is proved on linear advection tests, in which it proves the preservation of strong gradients and the ability of controlling overshoots-undershoots. Even though the TVD property is not guaranteed, the numerical oscillations are greatly reduced. Then, the method is adapted to solve the convection-diffusion transport scalar equation with source terms, which is the core of any reacting flow simulation. The implementation is validated with the one-dimensional flame problem and then is tested in a turbulent combustion case. The comparison between the results obtained with conventional methods based on high-dissipation and the proposed low-dissipative approach shows clear benefits of the later, the interfaces are sharper and there is an improvement in the representation of the flame front. This formulation also shows capability to capture much more flow structures which make the simulation a closer representation of the actual physics.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"307 ","pages":"Article 106973"},"PeriodicalIF":3.0,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974158","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 : 2026-01-14DOI: 10.1016/j.compfluid.2026.106972
Mustafa Ishak Benzaza , David Uystepruyst , François Beaubert , Damien Méresse , François Delcourt , Céline Morin
This work investigates both experimentally and numerically the turbulent flow within cyclonic separators using DES and VLES turbulence methods. Numerical predictions are validated against Hoekstra’s experimental data, showing that DES accurately captures the tangential velocity and pressure drop, but struggles to reproduce the axial velocity, particularly near the vortex core. Several outlet boundary conditions, including the addition of an obstacle, are tested to improve flow representation. A mapped pressure boundary condition offers a more physically consistent solution. Furthermore, spectral analysis is used to identify the end of the unsteady transient regime and the dominant flow frequencies. The effect of cyclone body height is also investigated both experimentally and numerically by comparing two industrial configurations. Shorter cyclone bodies lead to lower velocities and higher swirl numbers at the cyclone body and near the outlet, while taller cyclones significantly mitigate the Precessing Vortex Core effect and reduce vortex intensity at the outlet region.
{"title":"Modeling and analysis of swirling flow in cyclone separators using various hybrid scale-resolving approaches","authors":"Mustafa Ishak Benzaza , David Uystepruyst , François Beaubert , Damien Méresse , François Delcourt , Céline Morin","doi":"10.1016/j.compfluid.2026.106972","DOIUrl":"10.1016/j.compfluid.2026.106972","url":null,"abstract":"<div><div>This work investigates both experimentally and numerically the turbulent flow within cyclonic separators using DES and VLES turbulence methods. Numerical predictions are validated against Hoekstra’s experimental data, showing that DES accurately captures the tangential velocity and pressure drop, but struggles to reproduce the axial velocity, particularly near the vortex core. Several outlet boundary conditions, including the addition of an obstacle, are tested to improve flow representation. A mapped pressure boundary condition offers a more physically consistent solution. Furthermore, spectral analysis is used to identify the end of the unsteady transient regime and the dominant flow frequencies. The effect of cyclone body height is also investigated both experimentally and numerically by comparing two industrial configurations. Shorter cyclone bodies lead to lower velocities and higher swirl numbers at the cyclone body and near the outlet, while taller cyclones significantly mitigate the Precessing Vortex Core effect and reduce vortex intensity at the outlet region.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"307 ","pages":"Article 106972"},"PeriodicalIF":3.0,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034932","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 : 2026-01-13DOI: 10.1016/j.compfluid.2026.106974
Shaoqiang Han , Xiaogang Deng , Wenping Song , Zhonghua Han
The classic fifth-order weighted compact nonlinear scheme (WCNS) suffers from excessive numerical dissipation and an accuracy mismatch between its nonlinear interpolation and flux differences. Although the sixth-order central/upwind WCNS (WCNS-CU6) resolves the accuracy mismatch, it compromises stability. In this paper, an alternative sixth-order WCNS based on nonpolynomial interpolation (WCNS-NP6) is proposed to enhance accuracy and resolution while maintaining stability. The basic framework of WCNS-NP6 relies on the nonlinear weighting of three-point substencils, similar to the classic fifth-order WCNS. However, in WCNS-NP6, a radial basis function (RBF) is used to interpolate variables from point-based stencils to midpoints, and information from a global six-point stencil is integrated through the shape parameter of the RBF to achieve sixth-order accuracy. A novel measurement function is constructed to assess the smoothness of the six-point stencil. Near discontinuities, the measurement function adaptively removes the shape parameter, reverting WCNS-NP6 to the classic fifth-order WCNS and thereby ensuring stability. In smooth regions, the measurement function confines the active range of the nonlinear weights, thereby mitigating the impact of nonlinear mechanisms on spectral properties. Furthermore, a stencil rotation method is presented to ensure that WCNS-NP6 maintains its nominal sixth-order accuracy for solutions containing arbitrary numbers and orders of critical points. The numerical tests demonstrate that WCNS-NP6 outperforms classic fifth-order and sixth-order WCNSs in terms of numerical dissipation, resolution, and accuracy, particularly at high-order critical points. Notably, the WCNS-NP6 scheme demonstrates better stability than the classical sixth-order WCNS-CU6 scheme, while the computational cost increases by only 19% in 2D benchmark inviscid cases and remains below 10% in a 3D viscous case in engineering.
{"title":"A sixth-order WCNS based on nonpolynomial interpolation with enhanced accuracy and resolution","authors":"Shaoqiang Han , Xiaogang Deng , Wenping Song , Zhonghua Han","doi":"10.1016/j.compfluid.2026.106974","DOIUrl":"10.1016/j.compfluid.2026.106974","url":null,"abstract":"<div><div>The classic fifth-order weighted compact nonlinear scheme (WCNS) suffers from excessive numerical dissipation and an accuracy mismatch between its nonlinear interpolation and flux differences. Although the sixth-order central/upwind WCNS (WCNS-CU6) resolves the accuracy mismatch, it compromises stability. In this paper, an alternative sixth-order WCNS based on nonpolynomial interpolation (WCNS-NP6) is proposed to enhance accuracy and resolution while maintaining stability. The basic framework of WCNS-NP6 relies on the nonlinear weighting of three-point substencils, similar to the classic fifth-order WCNS. However, in WCNS-NP6, a radial basis function (RBF) is used to interpolate variables from point-based stencils to midpoints, and information from a global six-point stencil is integrated through the shape parameter of the RBF to achieve sixth-order accuracy. A novel measurement function is constructed to assess the smoothness of the six-point stencil. Near discontinuities, the measurement function adaptively removes the shape parameter, reverting WCNS-NP6 to the classic fifth-order WCNS and thereby ensuring stability. In smooth regions, the measurement function confines the active range of the nonlinear weights, thereby mitigating the impact of nonlinear mechanisms on spectral properties. Furthermore, a stencil rotation method is presented to ensure that WCNS-NP6 maintains its nominal sixth-order accuracy for solutions containing arbitrary numbers and orders of critical points. The numerical tests demonstrate that WCNS-NP6 outperforms classic fifth-order and sixth-order WCNSs in terms of numerical dissipation, resolution, and accuracy, particularly at high-order critical points. Notably, the WCNS-NP6 scheme demonstrates better stability than the classical sixth-order WCNS-CU6 scheme, while the computational cost increases by only 19% in 2D benchmark inviscid cases and remains below 10% in a 3D viscous case in engineering.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"307 ","pages":"Article 106974"},"PeriodicalIF":3.0,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974157","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 : 2026-01-10DOI: 10.1016/j.compfluid.2026.106969
Matteo Savino, Alessia Ferrari, Renato Vacondio, Paolo Mignosa
In this work, we introduce a novel fully implicit numerical scheme for the two-dimensional Vertically Averaged and Moment (VAM) system of equations. The method combines a Discontinuous Galerkin (DG) discretization of the homogeneous system with a local Taylor-based reconstruction of the non-conservative terms, ensuring stability without the need for empirical tuning parameters. The full set of equations is advanced in time, following a third-order accurate linear implicit Runge-Kutte (LIRK) method, through a single implicit step, where the fluxes and source terms are linearized via a Taylor-series expansion, thus avoiding computationally expensive iterative solvers. The effectiveness of the approach is demonstrated against experimental benchmarks, showing excellent agreement in both steady and unsteady flow regimes. Notably, the scheme remains robust for Courant-Friedrichs-Lewy (CFL) numbers up to 10, underscoring its potential for efficient large-scale simulations. Most importantly, the proposed formulation enables the simulation of non-hydrostatic pressure flows within a two-dimensional grid, thereby capturing essential three-dimensional effects without the prohibitive cost of fully 3D solvers.
{"title":"A fully implicit Discontinuous Galerkin finite element scheme for the 2D vertically averaged and moment equations","authors":"Matteo Savino, Alessia Ferrari, Renato Vacondio, Paolo Mignosa","doi":"10.1016/j.compfluid.2026.106969","DOIUrl":"10.1016/j.compfluid.2026.106969","url":null,"abstract":"<div><div>In this work, we introduce a novel fully implicit numerical scheme for the two-dimensional Vertically Averaged and Moment (VAM) system of equations. The method combines a Discontinuous Galerkin (DG) discretization of the homogeneous system with a local Taylor-based reconstruction of the non-conservative terms, ensuring stability without the need for empirical tuning parameters. The full set of equations is advanced in time, following a third-order accurate linear implicit Runge-Kutte (LIRK) method, through a single implicit step, where the fluxes and source terms are linearized via a Taylor-series expansion, thus avoiding computationally expensive iterative solvers. The effectiveness of the approach is demonstrated against experimental benchmarks, showing excellent agreement in both steady and unsteady flow regimes. Notably, the scheme remains robust for Courant-Friedrichs-Lewy (CFL) numbers up to 10, underscoring its potential for efficient large-scale simulations. Most importantly, the proposed formulation enables the simulation of non-hydrostatic pressure flows within a two-dimensional grid, thereby capturing essential three-dimensional effects without the prohibitive cost of fully 3D solvers.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"307 ","pages":"Article 106969"},"PeriodicalIF":3.0,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974155","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 : 2026-01-09DOI: 10.1016/j.compfluid.2026.106970
Jang Min Park
In this study, the diffuse-interface method is employed to model a Boussinesq-Scriven interface that incorporates surface viscosity alongside surface tension. This method differs from the sharp-interface approach in its continuous treatment of the additional surface stress in the momentum conservation equation. The finite element formulation and numerical results are presented. Convergence tests are carried out by using the method of manufactured solution, and optimal convergence rates are observed in both time and space. For a two-dimensional droplet deformation problem, the results show that the diffuse-interface method converges to the sharp-interface method as the diffuse-interface thickness decreases. The present formulation is also applied to a two-dimensional droplet coalescence problem to investigate the effect of surface viscosity.
{"title":"Diffuse-interface modeling of two-phase flows with a Boussinesq-Scriven interface","authors":"Jang Min Park","doi":"10.1016/j.compfluid.2026.106970","DOIUrl":"10.1016/j.compfluid.2026.106970","url":null,"abstract":"<div><div>In this study, the diffuse-interface method is employed to model a Boussinesq-Scriven interface that incorporates surface viscosity alongside surface tension. This method differs from the sharp-interface approach in its continuous treatment of the additional surface stress in the momentum conservation equation. The finite element formulation and numerical results are presented. Convergence tests are carried out by using the method of manufactured solution, and optimal convergence rates are observed in both time and space. For a two-dimensional droplet deformation problem, the results show that the diffuse-interface method converges to the sharp-interface method as the diffuse-interface thickness decreases. The present formulation is also applied to a two-dimensional droplet coalescence problem to investigate the effect of surface viscosity.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"307 ","pages":"Article 106970"},"PeriodicalIF":3.0,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974153","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 : 2026-01-08DOI: 10.1016/j.compfluid.2025.106958
Wenzhuo Xu, Madhav Karthikeyakannan, Christopher McComb, Noelia Grande Gutiérrez
Machine learning (ML) based surrogate models offer the potential to accelerate real-world engineering simulations involving millions of elements by bypassing the need for full-scale numerical simulations. However, current model capacities and available GPU memory often impose severe constraints, limiting our ability to accurately represent the highly variant physical dynamics encountered in complex systems. In traditional numerical methods, these computational limitations are mitigated using domain decomposition. The computational domain is split up to enable parallelization of the computation and reduce memory load. Similarly, ML models can benefit from decomposing the domain into subdomains. However, domain decomposition alone is insufficient to guarantee model performance and accuracy when physical dynamics vary spatially. We introduce the Adaptive Local Domain Decomposition (ALDD) method, which features two key innovations. First, it utilizes domain decomposition to improve the training efficiency of the ML model, with time reduction scaling almost linearly with the number of parallel GPUs. Second, ALDD adaptively partitions the domain and schedules appropriate models by segmenting the physics domain into subdomains based on physical dynamics features. Different ML models explicitly trained to solve different physical dynamics are then strategically assigned to these subdomains, encoding boundary information to ensure a smooth transition at the subdomain interface. This is accomplished by analyzing the energy spectrum of each subdomain and applying k-means clustering on the Wasserstein distances to identify physically coherent regions. We demonstrate superior performance and accuracy compared to baseline ML surrogate models for transitional boundary layer flow and recurrent temporal predictions with over 6 million elements.
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