Pub Date : 2026-01-15Epub Date: 2025-10-26DOI: 10.1016/j.compfluid.2025.106889
Adil Fahsi , Azzeddine Soulaïmani
We present a second-order semi-implicit time integration scheme for modeling surface tension in capillary-dominated two-phase flows, implemented within a two-dimensional XFEM/level set framework. Traditional explicit methods are constrained by the capillary time-step, requiring prohibitively small increments and leading to long simulations and error accumulation. Semi-implicit strategies relax this limitation by introducing a Laplace-Beltrami operator that acts as a numerical interface viscosity, damping high-frequency interfacial modes and thereby improving stability. While this stabilizing dissipation enables larger time-steps and suppresses spurious currents, it also introduces artificial damping that may distort interfacial dynamics. Our proposed BDF2 formulation reduces this dissipation by a factor of two-thirds compared with the classical first-order variant, thus enhancing fidelity without sacrificing stability. The method is validated on three two-dimensional benchmarks: a static bubble, a rising bubble, and an oscillating bubble demonstrating robust convergence to theoretical and reference solutions. Results confirm that the second-order semi-implicit scheme achieves genuine second-order temporal accuracy with improved efficiency, making it suitable for high-fidelity simulations of capillary-driven two-phase flows.
{"title":"A semi-implicit, second-order time-integration scheme for surface tension modeling in two-dimensional capillary-dominated two-phase flows","authors":"Adil Fahsi , Azzeddine Soulaïmani","doi":"10.1016/j.compfluid.2025.106889","DOIUrl":"10.1016/j.compfluid.2025.106889","url":null,"abstract":"<div><div>We present a second-order semi-implicit time integration scheme for modeling surface tension in capillary-dominated two-phase flows, implemented within a two-dimensional XFEM/level set framework. Traditional explicit methods are constrained by the capillary time-step, requiring prohibitively small increments and leading to long simulations and error accumulation. Semi-implicit strategies relax this limitation by introducing a Laplace-Beltrami operator that acts as a numerical interface viscosity, damping high-frequency interfacial modes and thereby improving stability. While this stabilizing dissipation enables larger time-steps and suppresses spurious currents, it also introduces artificial damping that may distort interfacial dynamics. Our proposed BDF2 formulation reduces this dissipation by a factor of two-thirds compared with the classical first-order variant, thus enhancing fidelity without sacrificing stability. The method is validated on three two-dimensional benchmarks: a static bubble, a rising bubble, and an oscillating bubble demonstrating robust convergence to theoretical and reference solutions. Results confirm that the second-order semi-implicit scheme achieves genuine second-order temporal accuracy with improved efficiency, making it suitable for high-fidelity simulations of capillary-driven two-phase flows.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"304 ","pages":"Article 106889"},"PeriodicalIF":3.0,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464295","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 : 2026-01-15Epub Date: 2025-10-17DOI: 10.1016/j.compfluid.2025.106881
A.R. Kocharina , D.V. Chirkov
The incompressible Navier-Stokes equations are solved using the finite-volume artificial compressibility method. A Godunov-type scheme with an exact Riemann solver is developed for the evaluation of inviscid fluxes across cell faces. To this end, the exact solution of the one-dimensional Riemann problem for the artificial compressibility equations is obtained using the method of -diagrams. The uniqueness of the solution is rigorously proven. The method is then extended to the multidimensional case. Two approaches for evaluation of the tangential velocity component are examined and discussed. A high-order variant of the Godunov scheme based on third-order MUSCL interpolation is proposed. At that, non-uniformity of the grid is taken into account. An implicit formulation of the scheme is developed, and the linearization process is described in detail. The proposed scheme is compared with the well-established Roe scheme through a series of steady-state two-dimensional benchmark problems, including inviscid and viscous flows around a circular cylinder and the 2D lid-driven cavity flow. The performance of the schemes on non-orthogonal grids is also investigated. Finally, both Roe and Godunov schemes are applied to the simulation of a three-dimensional turbulent flow in a hydraulic turbine flow passage. The results show that while both schemes exhibit comparable accuracy and convergence, the Godunov scheme offers advantages for inviscid simulations on highly non-orthogonal grids.
{"title":"Godunov scheme for numerical solution of incompressible Navier-Stokes equations","authors":"A.R. Kocharina , D.V. Chirkov","doi":"10.1016/j.compfluid.2025.106881","DOIUrl":"10.1016/j.compfluid.2025.106881","url":null,"abstract":"<div><div>The incompressible Navier-Stokes equations are solved using the finite-volume artificial compressibility method. A Godunov-type scheme with an exact Riemann solver is developed for the evaluation of inviscid fluxes across cell faces. To this end, the exact solution of the one-dimensional Riemann problem for the artificial compressibility equations is obtained using the method of <span><math><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>p</mi><mo>)</mo></mrow></math></span>-diagrams. The uniqueness of the solution is rigorously proven. The method is then extended to the multidimensional case. Two approaches for evaluation of the tangential velocity component are examined and discussed. A high-order variant of the Godunov scheme based on third-order MUSCL interpolation is proposed. At that, non-uniformity of the grid is taken into account. An implicit formulation of the scheme is developed, and the linearization process is described in detail. The proposed scheme is compared with the well-established Roe scheme through a series of steady-state two-dimensional benchmark problems, including inviscid and viscous flows around a circular cylinder and the 2D lid-driven cavity flow. The performance of the schemes on non-orthogonal grids is also investigated. Finally, both Roe and Godunov schemes are applied to the simulation of a three-dimensional turbulent flow in a hydraulic turbine flow passage. The results show that while both schemes exhibit comparable accuracy and convergence, the Godunov scheme offers advantages for inviscid simulations on highly non-orthogonal grids.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"304 ","pages":"Article 106881"},"PeriodicalIF":3.0,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145360932","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 : 2026-01-15Epub Date: 2025-10-24DOI: 10.1016/j.compfluid.2025.106883
S. Bennie , M. Fossati
Presented in the following work is a comprehensive analysis of wake vortex encounters with residential structures. From the results of high fidelity LES simulations, the dynamics and underlying flow structures which govern these potentially damaging encounters have been identified. Through evaluation of the pressure loads transmitted to the roof surface, the potential for damage to occur to a residential structure as a result of wake vortex exposure has been evaluated for a variety of cases. Regarding the building’s design, structures possessing larger pitch angles and thus steeper roofs have been found to sustain the largest peak loads for their encounter with an identical wake vortex system as compared to their flatter roofed counterparts. Similarly, upon assessing the effect of the environmental conditions it was observed that for increasingly turbulent atmospheres, the wake vortex encounter would occur sooner and with a reduced intensity compared to more neutral conditions. These behaviours have been attributed to the effects of secondary flow structures formed from the shedding of vorticity from the building surface or from wake vortex interactions with the eddies that comprise the atmospheric environment. These secondary flow structures energise wake vortex instability mechanisms thus leading to the variations in pressure loads sustained by the roof. With respect to the impact orientation, we note that there exists a minimal difference on the pressure loads generated during a wake vortex encounter for small angular offsets up to .
{"title":"Aircraft wake vortex encounters with residential structures","authors":"S. Bennie , M. Fossati","doi":"10.1016/j.compfluid.2025.106883","DOIUrl":"10.1016/j.compfluid.2025.106883","url":null,"abstract":"<div><div>Presented in the following work is a comprehensive analysis of wake vortex encounters with residential structures. From the results of high fidelity LES simulations, the dynamics and underlying flow structures which govern these potentially damaging encounters have been identified. Through evaluation of the pressure loads transmitted to the roof surface, the potential for damage to occur to a residential structure as a result of wake vortex exposure has been evaluated for a variety of cases. Regarding the building’s design, structures possessing larger pitch angles and thus steeper roofs have been found to sustain the largest peak loads for their encounter with an identical wake vortex system as compared to their flatter roofed counterparts. Similarly, upon assessing the effect of the environmental conditions it was observed that for increasingly turbulent atmospheres, the wake vortex encounter would occur sooner and with a reduced intensity compared to more neutral conditions. These behaviours have been attributed to the effects of secondary flow structures formed from the shedding of vorticity from the building surface or from wake vortex interactions with the eddies that comprise the atmospheric environment. These secondary flow structures energise wake vortex instability mechanisms thus leading to the variations in pressure loads sustained by the roof. With respect to the impact orientation, we note that there exists a minimal difference on the pressure loads generated during a wake vortex encounter for small angular offsets up to <span><math><msup><mn>20</mn><mo>∘</mo></msup></math></span>.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"304 ","pages":"Article 106883"},"PeriodicalIF":3.0,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464296","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 : 2026-01-15Epub Date: 2025-10-24DOI: 10.1016/j.compfluid.2025.106877
Spencer H. Bryngelson
Ensemble-averaged polydisperse bubbly flow models require statistical moments of the evolving bubble size distribution. Under step forcing, these moments reach statistical equilibrium in finite time. However, the transitional phase before equilibrium and cases with time-dependent forcing are required to predict flow in engineering applications. Computing these moments is expensive because the integrands are highly oscillatory, even when the bubble dynamics are linear. Ensemble-averaged models compute these moments at each grid point and time step, making cost reduction important for large-scale bubbly flow simulations. Traditional methods evaluate the integrals via traditional quadrature rules. This approach requires a large number of quadrature nodes in the equilibrium bubble size, each equipped with its own advection partial differential equation (PDE), resulting in significant computational expense. We formulate a Levin collocation method to reduce this cost. Given the differential equation associated with the integrand, or moment, the method approximates it by evaluating its derivative via polynomial collocation. The differential matrix and amplitude function are well-suited to numerical differentiation via collocation, and so the computation is comparatively cheap. For an example excited polydisperse bubble population, the first moment is computed with the presented method at relative error with 100 times fewer quadrature nodes than the trapezoidal rule. The gap increases for smaller target relative errors: the Levin method requires times fewer points for a relative error of . The formulated method maintains constant cost as the integrands become more oscillatory with time, making it particularly attractive for long-time simulations. Mechanistically, the transient behavior of the moments is set by two effects: resonance detuning across bubble sizes, which causes phase mixing of oscillations, and viscous damping, which removes radial kinetic energy. The proposed formulation isolates the oscillations while keeping the remaining terms smooth, so accuracy does not deteriorate at late times.
{"title":"Fast integration method for averaging polydisperse bubble population dynamics","authors":"Spencer H. Bryngelson","doi":"10.1016/j.compfluid.2025.106877","DOIUrl":"10.1016/j.compfluid.2025.106877","url":null,"abstract":"<div><div>Ensemble-averaged polydisperse bubbly flow models require statistical moments of the evolving bubble size distribution. Under step forcing, these moments reach statistical equilibrium in finite time. However, the transitional phase before equilibrium and cases with time-dependent forcing are required to predict flow in engineering applications. Computing these moments is expensive because the integrands are highly oscillatory, even when the bubble dynamics are linear. Ensemble-averaged models compute these moments at each grid point and time step, making cost reduction important for large-scale bubbly flow simulations. Traditional methods evaluate the integrals via traditional quadrature rules. This approach requires a large number of quadrature nodes in the equilibrium bubble size, each equipped with its own advection partial differential equation (PDE), resulting in significant computational expense. We formulate a Levin collocation method to reduce this cost. Given the differential equation associated with the integrand, or moment, the method approximates it by evaluating its derivative via polynomial collocation. The differential matrix and amplitude function are well-suited to numerical differentiation via collocation, and so the computation is comparatively cheap. For an example excited polydisperse bubble population, the first moment is computed with the presented method at <span><math><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math></span> relative error with 100 times fewer quadrature nodes than the trapezoidal rule. The gap increases for smaller target relative errors: the Levin method requires <span><math><msup><mn>10</mn><mn>4</mn></msup></math></span> times fewer points for a relative error of <span><math><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></math></span>. The formulated method maintains constant cost as the integrands become more oscillatory with time, making it particularly attractive for long-time simulations. Mechanistically, the transient behavior of the moments is set by two effects: resonance detuning across bubble sizes, which causes phase mixing of oscillations, and viscous damping, which removes radial kinetic energy. The proposed formulation isolates the oscillations while keeping the remaining terms smooth, so accuracy does not deteriorate at late times.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"304 ","pages":"Article 106877"},"PeriodicalIF":3.0,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145414646","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 : 2025-12-15Epub Date: 2025-09-29DOI: 10.1016/j.compfluid.2025.106852
Sen Zhang, Yuxuan Zhang, Dingxi Wang
This paper presents the algorithm development of a Jacobian-free Newton–Krylov (JFNK) solver for turbomachinery steady aerodynamic analysis, based on the three-dimensional Favre-averaged Navier–Stokes (FANS) equations. The Jacobian-free approach achieves accurate Jacobian-vector calculation using automatic differentiation, avoiding the complexity of explicitly forming a full Jacobian matrix. A lower–upper Symmetric-Gauss–Seidel (LU-SGS) preconditioner and a geometric multigrid preconditioner are proposed in this work to further enhance convergence. The two preconditioners are also compared with the standard incomplete LU factorization (ILU) preconditioner. The LU-SGS preconditioner does not rely on any explicit matrix, resulting in a fully matrix-free Newton–Krylov solver, while both the ILU and multigrid preconditioners require the explicit formation of an approximate Jacobian matrix. The performance of the developed JFNK solver is benchmarked against that of a standalone multigrid solver, which employs a multistage Runge–Kutta time-stepping scheme with an LU-SGS residual smoother. Two transonic compressor test cases are used for performance evaluation. Numerical results consistently reveal that the multigrid-preconditioned JFNK solver achieves a faster convergence rate than the standalone multigrid solver, while the other preconditioning cases require significantly more computational time. These findings demonstrate the effectiveness and robustness of the proposed multigrid preconditioner.
{"title":"Jacobian-free Newton–Krylov methods for turbomachinery steady aerodynamic analysis","authors":"Sen Zhang, Yuxuan Zhang, Dingxi Wang","doi":"10.1016/j.compfluid.2025.106852","DOIUrl":"10.1016/j.compfluid.2025.106852","url":null,"abstract":"<div><div>This paper presents the algorithm development of a Jacobian-free Newton–Krylov (JFNK) solver for turbomachinery steady aerodynamic analysis, based on the three-dimensional Favre-averaged Navier–Stokes (FANS) equations. The Jacobian-free approach achieves accurate Jacobian-vector calculation using automatic differentiation, avoiding the complexity of explicitly forming a full Jacobian matrix. A lower–upper Symmetric-Gauss–Seidel (LU-SGS) preconditioner and a geometric multigrid preconditioner are proposed in this work to further enhance convergence. The two preconditioners are also compared with the standard incomplete LU factorization (ILU) preconditioner. The LU-SGS preconditioner does not rely on any explicit matrix, resulting in a fully matrix-free Newton–Krylov solver, while both the ILU and multigrid preconditioners require the explicit formation of an approximate Jacobian matrix. The performance of the developed JFNK solver is benchmarked against that of a standalone multigrid solver, which employs a multistage Runge–Kutta time-stepping scheme with an LU-SGS residual smoother. Two transonic compressor test cases are used for performance evaluation. Numerical results consistently reveal that the multigrid-preconditioned JFNK solver achieves a faster convergence rate than the standalone multigrid solver, while the other preconditioning cases require significantly more computational time. These findings demonstrate the effectiveness and robustness of the proposed multigrid preconditioner.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106852"},"PeriodicalIF":3.0,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145264409","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 : 2025-12-15Epub Date: 2025-09-30DOI: 10.1016/j.compfluid.2025.106853
Victor Michel-Dansac, Andrea Thomann
The present work concerns the derivation of a fully well-balanced Godunov-type finite volume scheme for the Euler equations with a gravitational potential based on an approximate Riemann solver in a one-dimensional framework. It is an extension to general equations of states of the entropy-stable and fully well-balanced scheme for ideal gases recently forwarded in Berthon et al., (2025). A second-order extension preserving the properties of the first-order scheme is given. The scheme is provably entropy-stable and positivity-preserving for all thermodynamic variables. Numerical test cases illustrate the performance and entropy stability of the new scheme, using six different equations of state as examples, four analytic and two tabulated ones.
{"title":"Towards a fully well-balanced and entropy-stable scheme for the Euler equations with gravity: General equations of state","authors":"Victor Michel-Dansac, Andrea Thomann","doi":"10.1016/j.compfluid.2025.106853","DOIUrl":"10.1016/j.compfluid.2025.106853","url":null,"abstract":"<div><div>The present work concerns the derivation of a fully well-balanced Godunov-type finite volume scheme for the Euler equations with a gravitational potential based on an approximate Riemann solver in a one-dimensional framework. It is an extension to general equations of states of the entropy-stable and fully well-balanced scheme for ideal gases recently forwarded in Berthon et al., (2025). A second-order extension preserving the properties of the first-order scheme is given. The scheme is provably entropy-stable and positivity-preserving for all thermodynamic variables. Numerical test cases illustrate the performance and entropy stability of the new scheme, using six different equations of state as examples, four analytic and two tabulated ones.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106853"},"PeriodicalIF":3.0,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145204237","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 : 2025-12-15Epub Date: 2025-10-08DOI: 10.1016/j.compfluid.2025.106870
Aaron English , Renato Vacondio , Susanna Dazzi , José M. Domínguez
In this work, Smoothed Particle Hydrodynamics (SPH) is assessed for the modelling of flow past bridges. An improved pressure extrapolation method and a no-slip extension for the widely used modified Dynamic Boundary Condition (mDBC) are presented. The no-slip condition is validated with benchmark test cases of Poiseuille flow and flow past a cylinder. The ability to simulate river flows past bridges is assessed by comparing with experimental measurements for two model bridges with multiple discharges. The results are also evaluated against numerical results from 2D Shallow Water Equation (SWE) simulations, which is the leading approach for this kind of flow. While both methods shows good agreement with the experimental data away from the bridge, the SWE assumptions fail in the immediate vicinity of the bridge. In this region, the SPH method demonstrates higher accuracy, captures additional flow features and offers deeper insight into local hydraulic behaviour. A new SPH restart procedure has been developed that enables high-resolution simulations to be initialized using results from lower-resolution simulations. This greatly reduces simulation run times for large and complex transient flow such as rivers. Advanced DualSPHysics boundary generation and pre-processing tools allow for easier creation of boundaries through STL files, and GPU acceleration on the latest hardware allow for faster simulation with larger domains. With all these features, the first full-scale SPH simulation of a real river flow past a bridge is presented, including the riverbed bathymetry and model of Ponte Vecchio on the Arno River (Italy).
{"title":"Smoothed particle hydrodynamics modelling of river flows past bridges","authors":"Aaron English , Renato Vacondio , Susanna Dazzi , José M. Domínguez","doi":"10.1016/j.compfluid.2025.106870","DOIUrl":"10.1016/j.compfluid.2025.106870","url":null,"abstract":"<div><div>In this work, Smoothed Particle Hydrodynamics (SPH) is assessed for the modelling of flow past bridges. An improved pressure extrapolation method and a no-slip extension for the widely used modified Dynamic Boundary Condition (mDBC) are presented. The no-slip condition is validated with benchmark test cases of Poiseuille flow and flow past a cylinder. The ability to simulate river flows past bridges is assessed by comparing with experimental measurements for two model bridges with multiple discharges. The results are also evaluated against numerical results from 2D Shallow Water Equation (SWE) simulations, which is the leading approach for this kind of flow. While both methods shows good agreement with the experimental data away from the bridge, the SWE assumptions fail in the immediate vicinity of the bridge. In this region, the SPH method demonstrates higher accuracy, captures additional flow features and offers deeper insight into local hydraulic behaviour. A new SPH restart procedure has been developed that enables high-resolution simulations to be initialized using results from lower-resolution simulations. This greatly reduces simulation run times for large and complex transient flow such as rivers. Advanced DualSPHysics boundary generation and pre-processing tools allow for easier creation of boundaries through STL files, and GPU acceleration on the latest hardware allow for faster simulation with larger domains. With all these features, the first full-scale SPH simulation of a real river flow past a bridge is presented, including the riverbed bathymetry and model of Ponte Vecchio on the Arno River (Italy).</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106870"},"PeriodicalIF":3.0,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325686","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 : 2025-12-15Epub Date: 2025-09-30DOI: 10.1016/j.compfluid.2025.106849
Yao-Hsuan Tsai , Hsiao-Tung Juan , Pao-Hsiung Chiu , Chao-An Lin
Physics-Informed Neural Networks (PINNs) have emerged as a promising methodology for solving partial differential equations (PDEs), gaining significant attention in computer science and various physics-related fields. Despite demonstrating the ability to incorporate physical laws for versatile applications, PINNs still struggle with challenging problems that are stiff to solve and/or have high-frequency components in their solutions, resulting in accuracy and convergence issues. These problems not only increase computational costs but may also lead to accuracy loss or solution divergence in the worst-case scenario. In this study, we introduce a novel PINN framework, dubbed MLD-PINN, to mitigate the above-mentioned problems. Inspired by the multigrid method in the CFD community, the underlying idea of our approach is to efficiently remove different frequency errors by training with different levels of training samples. This provides a simpler way to improve training accuracy without spending time fine-tuning neural network structures, loss weights, or hyperparameters. To demonstrate the efficacy of our approach, we first investigate a canonical 1D ODE with high-frequency components and a 2D convection–diffusion equation using a V-cycle training strategy. Finally, we apply our method to the classical benchmark problem of steady lid-driven cavity flows at different Reynolds numbers (Re) to examine its applicability and efficacy for problems involving multiple modes of high and low frequencies. Through various training sequence modes, our predictions achieve 30% to 60% accuracy improvement. We also investigate the synergy between our method and transfer learning techniques for more challenging problems (i.e., higher cases). The present results reveal that our framework can produce good predictions even for the case of , demonstrating its ability to solve complex high-frequency PDEs.
{"title":"MLD-PINN: A multi-level datasets training method in Physics-Informed Neural Networks","authors":"Yao-Hsuan Tsai , Hsiao-Tung Juan , Pao-Hsiung Chiu , Chao-An Lin","doi":"10.1016/j.compfluid.2025.106849","DOIUrl":"10.1016/j.compfluid.2025.106849","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINNs) have emerged as a promising methodology for solving partial differential equations (PDEs), gaining significant attention in computer science and various physics-related fields. Despite demonstrating the ability to incorporate physical laws for versatile applications, PINNs still struggle with challenging problems that are stiff to solve and/or have high-frequency components in their solutions, resulting in accuracy and convergence issues. These problems not only increase computational costs but may also lead to accuracy loss or solution divergence in the worst-case scenario. In this study, we introduce a novel PINN framework, dubbed MLD-PINN, to mitigate the above-mentioned problems. Inspired by the multigrid method in the CFD community, the underlying idea of our approach is to efficiently remove different frequency errors by training with different levels of training samples. This provides a simpler way to improve training accuracy without spending time fine-tuning neural network structures, loss weights, or hyperparameters. To demonstrate the efficacy of our approach, we first investigate a canonical 1D ODE with high-frequency components and a 2D convection–diffusion equation using a V-cycle training strategy. Finally, we apply our method to the classical benchmark problem of steady lid-driven cavity flows at different Reynolds numbers (Re) to examine its applicability and efficacy for problems involving multiple modes of high and low frequencies. Through various training sequence modes, our predictions achieve 30% to 60% accuracy improvement. We also investigate the synergy between our method and transfer learning techniques for more challenging problems (i.e., higher <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span> cases). The present results reveal that our framework can produce good predictions even for the case of <span><math><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>5000</mn></mrow></math></span>, demonstrating its ability to solve complex high-frequency PDEs.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106849"},"PeriodicalIF":3.0,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219066","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 : 2025-12-15Epub Date: 2025-10-17DOI: 10.1016/j.compfluid.2025.106869
Gino I. Montecinos , Eleuterio F. Toro
The WENO-DK reconstruction [M. Dumbser and M. Käser, JCOMP.221:693-723, (2007)] is a type of WENO procedure in which, for the one-dimensional case only the leftmost, centered and rightmost stencils are involved. For even orders the central stencil contains more elements than degrees of freedom and an overdetermined system is solved by means of a least-squares approach. Here, it is numerically investigated the impact of choosing the smallest and largest central stencil around the cell of interests and proposed two variants to obtain the central polynomial where the solution of overdetermined systems is not needed. Implementations of the proposed approaches in the framework of fully discrete ADER schemes for the linear advection equation and the Euler equations of gas dynamics are reported. Comparisons with conventional WENO and conventional WENO-DK confirm that the proposed variants of WENO-DK are a suitable compromise between simplicity and accuracy in the context of ADER schemes, implemented up to the tenth order of accuracy in space and time.
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Pub Date : 2025-12-15Epub Date: 2025-10-08DOI: 10.1016/j.compfluid.2025.106868
Naman Bartwal , Somnath Roy , Surya Pratap Vanka
Mixed convection is ubiquitous in nature and industrial processes that involve the combination of both natural and forced convective flows. It plays an important role in broad range of engineering applications such as in cooling of electronics, heat exchangers, HVAC systems, etc. Optimizing the thermal management systems is crucial for achieving effective cooling or heating in industrial equipments. By comprehending and utilizing the phenomenon of mixed convection, one can effectively design thermal systems that attain superior overall performance. Here, we present detailed investigations on the influence of four rotating circular cylinders on mixed convection within a square cavity. We investigate the effects of various parameters such as Richardson number (Ri), Reynolds number (Re) and location and direction of rotation of cylinders. These factors are shown to influence the heat transfer rates significantly, which is shown via streamlines and isotherms pattern within the cavity for varying values of Re and Ri. A radial basis function based meshless method is developed for the simulation of mixed convection scenarios. High-order accuracy is demonstrated by first simulating the benchmark case of cylindrical Couette flow. We have also provided detailed validation and verification for thermal convection problems by comparing our findings to experimental and numerical results in the published literature.
{"title":"Application of a high-order meshless method to study mixed convection heat transfer in a cavity with rotating circular cylinders","authors":"Naman Bartwal , Somnath Roy , Surya Pratap Vanka","doi":"10.1016/j.compfluid.2025.106868","DOIUrl":"10.1016/j.compfluid.2025.106868","url":null,"abstract":"<div><div>Mixed convection is ubiquitous in nature and industrial processes that involve the combination of both natural and forced convective flows. It plays an important role in broad range of engineering applications such as in cooling of electronics, heat exchangers, HVAC systems, etc. Optimizing the thermal management systems is crucial for achieving effective cooling or heating in industrial equipments. By comprehending and utilizing the phenomenon of mixed convection, one can effectively design thermal systems that attain superior overall performance. Here, we present detailed investigations on the influence of four rotating circular cylinders on mixed convection within a square cavity. We investigate the effects of various parameters such as Richardson number (Ri), Reynolds number (Re) and location and direction of rotation of cylinders. These factors are shown to influence the heat transfer rates significantly, which is shown via streamlines and isotherms pattern within the cavity for varying values of Re and Ri. A radial basis function based meshless method is developed for the simulation of mixed convection scenarios. High-order accuracy is demonstrated by first simulating the benchmark case of cylindrical Couette flow. We have also provided detailed validation and verification for thermal convection problems by comparing our findings to experimental and numerical results in the published literature.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106868"},"PeriodicalIF":3.0,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325682","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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