The central-upwind weighted essentially non-oscillatory (WENO) scheme introduces the downwind substencil to reconstruct the numerical flux, where the smoothness indicator for the downwind substencil is of critical importance in maintaining high order in smooth regions and preserving the essentially non-oscillatory behavior in shock capturing. In this study, we design the smoothness indicator for the downwind substencil by simply summing up all local smoothness indicators and taking the average, which includes the regularity information of the whole stencil. Accordingly the JS-type and Z-type nonlinear weights, based on simple local smoothness indicators, are developed for the fourth-order central-upwind WENO scheme. The accuracy, robustness, and high-resolution properties of our proposed schemes are demonstrated in a variety of one- and two-dimensional problems.
{"title":"JS-type and Z-type weights for fourth-order central-upwind weighted essentially non-oscillatory schemes","authors":"Jiaxi Gu , Xinjuan Chen , Kwanghyuk Park , Jae-Hun Jung","doi":"10.1016/j.compfluid.2025.106867","DOIUrl":"10.1016/j.compfluid.2025.106867","url":null,"abstract":"<div><div>The central-upwind weighted essentially non-oscillatory (WENO) scheme introduces the downwind substencil to reconstruct the numerical flux, where the smoothness indicator for the downwind substencil is of critical importance in maintaining high order in smooth regions and preserving the essentially non-oscillatory behavior in shock capturing. In this study, we design the smoothness indicator for the downwind substencil by simply summing up all local smoothness indicators and taking the average, which includes the regularity information of the whole stencil. Accordingly the JS-type and Z-type nonlinear weights, based on simple local smoothness indicators, are developed for the fourth-order central-upwind WENO scheme. The accuracy, robustness, and high-resolution properties of our proposed schemes are demonstrated in a variety of one- and two-dimensional problems.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106867"},"PeriodicalIF":3.0,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325685","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 : 2025-10-09DOI: 10.1016/j.compfluid.2025.106858
Amareshwara Sainadh Chamarthi
The paper proposes a physically consistent numerical discretization approach for simulating viscous compressible multicomponent flows. It has two main contributions. First, a contact discontinuity (and material interface) detector is developed. In those regions of contact discontinuities, the THINC (Tangent of Hyperbola for INterface Capturing) approach is used for reconstructing appropriate variables (phasic densities). For other flow regions, the variables are reconstructed using the Monotonicity-preserving (MP) scheme (or Weighted essentially non-oscillatory scheme (WENO)). For reconstruction in the characteristic space, the THINC approach is used only for the contact (or entropy) wave and volume fractions. For the reconstruction of primitive variables, the THINC approach is used for phasic densities and volume fractions only, offering an effective solution for reducing dissipation errors near contact discontinuities. The numerical results of the benchmark tests show that the proposed method captured the material interface sharply compared to existing methods. The second contribution is the development of an algorithm that uses a central reconstruction scheme for the tangential velocities, as they are continuous across material interfaces in viscous flows. In this regard, the Ducros sensor (a shock detector that cannot detect material interfaces) is employed to compute the tangential velocities using a central scheme across material interfaces. Using the central scheme does not produce any oscillations at the material interface. The proposed approach is thoroughly validated with several benchmark test cases for compressible multicomponent flows, highlighting its advantages. The physics appropriate approach also shown to prevent spurious vortices, despite being formally second-order accurate for nonlinear problems, on a coarser mesh than a genuinely high-order accurate method.
{"title":"Physics appropriate interface capturing reconstruction approach for viscous compressible multicomponent flows","authors":"Amareshwara Sainadh Chamarthi","doi":"10.1016/j.compfluid.2025.106858","DOIUrl":"10.1016/j.compfluid.2025.106858","url":null,"abstract":"<div><div>The paper proposes a physically consistent numerical discretization approach for simulating viscous compressible multicomponent flows. It has two main contributions. First, a contact discontinuity (and material interface) detector is developed. In those regions of contact discontinuities, the THINC (Tangent of Hyperbola for INterface Capturing) approach is used for reconstructing appropriate variables (phasic densities). For other flow regions, the variables are reconstructed using the Monotonicity-preserving (MP) scheme (or Weighted essentially non-oscillatory scheme (WENO)). For reconstruction in the characteristic space, the THINC approach is used only for the contact (or entropy) wave and volume fractions. For the reconstruction of primitive variables, the THINC approach is used for phasic densities and volume fractions only, offering an effective solution for reducing dissipation errors near contact discontinuities. The numerical results of the benchmark tests show that the proposed method captured the material interface sharply compared to existing methods. The second contribution is the development of an algorithm that uses a central reconstruction scheme for the tangential velocities, as they are continuous across material interfaces in viscous flows. In this regard, the Ducros sensor (a shock detector that cannot detect material interfaces) is employed to compute the tangential velocities using a central scheme across material interfaces. Using the central scheme does not produce any oscillations at the material interface. The proposed approach is thoroughly validated with several benchmark test cases for compressible multicomponent flows, highlighting its advantages. The physics appropriate approach also shown to prevent spurious vortices, despite being formally second-order accurate for nonlinear problems, on a coarser mesh than a genuinely high-order accurate method.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106858"},"PeriodicalIF":3.0,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145264410","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 : 2025-10-08DOI: 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":"2025-10-08","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 : 2025-10-08DOI: 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":"2025-10-08","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}
Pub Date : 2025-10-08DOI: 10.1016/j.compfluid.2025.106856
Takahito Asaga , Yuichi Kuya
This paper proposes numerical methods to obtain converged flow solutions by quantum annealing. The proposed quantum annealing methods are developed for lattice gas automata (LGA) and finite difference methods (FDMs). The quadratic unconstrained binary optimization (QUBO) model for LGA consists of the cost functions for the steady-state flow condition, collision law condition, boundary condition, and flow field condition. In contrast, the QUBO model for FDMs is built directly from the discretized governing equations expressed in a binary form. In the numerical experiments of channel flows, both proposed methods successfully extract the converged velocity profiles from a large number of flow state combinations by quantum annealing. The obtained solutions closely match those obtained by the conventional or analytical approach. Since, due to the difference in characteristics between LGA and FDMs, FDMs can reduce the scale of combinatorial optimization problems more efficiently than LGA, the proposed FDM-based method obtains more accurate solutions than the proposed LGA-based method.
{"title":"Obtaining converged flow solutions using quantum annealing","authors":"Takahito Asaga , Yuichi Kuya","doi":"10.1016/j.compfluid.2025.106856","DOIUrl":"10.1016/j.compfluid.2025.106856","url":null,"abstract":"<div><div>This paper proposes numerical methods to obtain converged flow solutions by quantum annealing. The proposed quantum annealing methods are developed for lattice gas automata (LGA) and finite difference methods (FDMs). The quadratic unconstrained binary optimization (QUBO) model for LGA consists of the cost functions for the steady-state flow condition, collision law condition, boundary condition, and flow field condition. In contrast, the QUBO model for FDMs is built directly from the discretized governing equations expressed in a binary form. In the numerical experiments of channel flows, both proposed methods successfully extract the converged velocity profiles from a large number of flow state combinations by quantum annealing. The obtained solutions closely match those obtained by the conventional or analytical approach. Since, due to the difference in characteristics between LGA and FDMs, FDMs can reduce the scale of combinatorial optimization problems more efficiently than LGA, the proposed FDM-based method obtains more accurate solutions than the proposed LGA-based method.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106856"},"PeriodicalIF":3.0,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325681","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 : 2025-10-08DOI: 10.1016/j.compfluid.2025.106857
Shashi Shekhar Roy , S.V. Raghurama Rao
In this paper, we present a kinetic model with flexible velocities that satisfy positivity preservation conditions for the Euler equations. Our 1D kinetic model consists of two velocities and employs both the asymmetrical and symmetrical models. Switching between the two models is governed by our formulation of kinetic relative entropy, together with an additional criterion that ensures a robust and accurate scheme yielding entropic results. In 2D, we introduce a novel three-velocity kinetic model, defined to ensure a locally one-dimensional formulation for the resulting macroscopic normal flux. For first order accuracy, we also obtain a limit on the time step that ensures positivity preservation. The resulting numerical scheme captures grid-aligned steady shocks exactly. Several benchmark compressible flow test cases are solved in 1D and 2D to demonstrate the efficacy of the proposed solver.
{"title":"A kinetic scheme based on positivity preservation with exact shock capture","authors":"Shashi Shekhar Roy , S.V. Raghurama Rao","doi":"10.1016/j.compfluid.2025.106857","DOIUrl":"10.1016/j.compfluid.2025.106857","url":null,"abstract":"<div><div>In this paper, we present a kinetic model with flexible velocities that satisfy positivity preservation conditions for the Euler equations. Our 1D kinetic model consists of two velocities and employs both the asymmetrical and symmetrical models. Switching between the two models is governed by our formulation of kinetic relative entropy, together with an additional criterion that ensures a robust and accurate scheme yielding entropic results. In 2D, we introduce a novel three-velocity kinetic model, defined to ensure a locally one-dimensional formulation for the resulting macroscopic normal flux. For first order accuracy, we also obtain a limit on the time step that ensures positivity preservation. The resulting numerical scheme captures grid-aligned steady shocks exactly. Several benchmark compressible flow test cases are solved in 1D and 2D to demonstrate the efficacy of the proposed solver.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106857"},"PeriodicalIF":3.0,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325684","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 : 2025-10-03DOI: 10.1016/j.compfluid.2025.106855
N. Smirnova , S. Utyuzhnikov , V. Titarev , M. Petrov
In turbulence modeling the resolution of near-wall boundary layer requires most of computing time. The near-wall domain decomposition (NDD) approach proved to be efficient in tackling this problem. It represents a trade-off between computing time and accuracy. In this method, the computational domain is divided into two non-overlapping subdomains: the inner layer and region outside. The interface boundary conditions of Robin type are set by transferring the boundary conditions from the wall to the interface boundary. In contrast to the exact NDD, in the approximate NDD a simplified system of equations is solved in the near-wall subdomain. In the current paper a variant of the exact NDD is proposed, that uses an operator corresponding to the approximate NDD approach as a preconditioner. To improve the efficiency of NDD methods the GMRES method is applied. The efficacy of NDD algorithms are compared against for the low-Reynolds-number model.
{"title":"Convergence acceleration algorithms for non-overlapping domain decomposition in near-wall turbulence modeling","authors":"N. Smirnova , S. Utyuzhnikov , V. Titarev , M. Petrov","doi":"10.1016/j.compfluid.2025.106855","DOIUrl":"10.1016/j.compfluid.2025.106855","url":null,"abstract":"<div><div>In turbulence modeling the resolution of near-wall boundary layer requires most of computing time. The near-wall domain decomposition (NDD) approach proved to be efficient in tackling this problem. It represents a trade-off between computing time and accuracy. In this method, the computational domain is divided into two non-overlapping subdomains: the inner layer and region outside. The interface boundary conditions of Robin type are set by transferring the boundary conditions from the wall to the interface boundary. In contrast to the exact NDD, in the approximate NDD a simplified system of equations is solved in the near-wall subdomain. In the current paper a variant of the exact NDD is proposed, that uses an operator corresponding to the approximate NDD approach as a preconditioner. To improve the efficiency of NDD methods the GMRES method is applied. The efficacy of NDD algorithms are compared against for the low-Reynolds-number model.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106855"},"PeriodicalIF":3.0,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145263969","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 : 2025-10-03DOI: 10.1016/j.compfluid.2025.106859
Tibing Xu , Gang Zhao , Yee-Chung Jin
The mixture theory coupled with a mesh-free method can describe movable grains caused by violent free surface flows such as dam-break flow. In the method, discretized mixture particles involve a fraction of both solid and fluid with two sets of velocity fields. In a pure Lagrangian method, the particles should move by incorporating the two sets of velocity fields. In this study, a mixture moving particle scheme is proposed to simulate dam-break flows interacting with different granular materials. In the simulations, various grain properties including density of the granular material, mean diameter, and friction angle are investigated. The simulated free surface and interface are in good agreement with the experimental measurements. The impact of dam-break flows over a movable granular bed is also simulated by the proposed mixture moving particle scheme and the impacting pressure on the solid wall is reproduced.
{"title":"Mixture moving particle scheme to simulate interactions between fluid and granular material","authors":"Tibing Xu , Gang Zhao , Yee-Chung Jin","doi":"10.1016/j.compfluid.2025.106859","DOIUrl":"10.1016/j.compfluid.2025.106859","url":null,"abstract":"<div><div>The mixture theory coupled with a mesh-free method can describe movable grains caused by violent free surface flows such as dam-break flow. In the method, discretized mixture particles involve a fraction of both solid and fluid with two sets of velocity fields. In a pure Lagrangian method, the particles should move by incorporating the two sets of velocity fields. In this study, a mixture moving particle scheme is proposed to simulate dam-break flows interacting with different granular materials. In the simulations, various grain properties including density of the granular material, mean diameter, and friction angle are investigated. The simulated free surface and interface are in good agreement with the experimental measurements. The impact of dam-break flows over a movable granular bed is also simulated by the proposed mixture moving particle scheme and the impacting pressure on the solid wall is reproduced.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"303 ","pages":"Article 106859"},"PeriodicalIF":3.0,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145264407","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 : 2025-09-30DOI: 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":"2025-09-30","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 : 2025-09-30DOI: 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":"2025-09-30","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}
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