We introduce semi‐implicit Lagrangian Voronoi approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier–Stokes equations, which combines the efficiency of semi‐implicit time marching schemes with the robustness of time‐dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection‐based Arbitrary‐Lagrangian‐Eulerian schemes, we need no remapping stage. A semi‐implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence‐free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi‐phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no‐slip and free‐slip boundary conditions.
{"title":"Semi‐implicit Lagrangian Voronoi approximation for the incompressible Navier–Stokes equations","authors":"Ondřej Kincl, Ilya Peshkov, Walter Boscheri","doi":"10.1002/fld.5339","DOIUrl":"https://doi.org/10.1002/fld.5339","url":null,"abstract":"We introduce semi‐implicit Lagrangian Voronoi approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier–Stokes equations, which combines the efficiency of semi‐implicit time marching schemes with the robustness of time‐dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection‐based Arbitrary‐Lagrangian‐Eulerian schemes, we need no remapping stage. A semi‐implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence‐free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi‐phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no‐slip and free‐slip boundary conditions.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The goal of this research is to propose a new modification of a non‐equilibrium effect in the turbulence model to better predict high‐speed turbulent flows. For that, the two local compressibility coefficients are included in the balance production/dissipation terms in a specific dissipation rate equation. The specific dissipation rate reacts to changes in the local Mach number and density through these local coefficients. The developed model is applied to the numerical simulation of the spatial supersonic turbulent airflow with round hydrogen injection. In that, the effects of the proposed turbulence model on the flow field behavior (shock wave and vortex formations, shock wave/boundary layer interaction, and mixture layer) are studied via the solution of three‐dimensional Favre‐averaged Navier–Stokes equations with a third‐order Essentially Non‐Oscillatory scheme. A series of numerical experiments are performed, in which an allowable range of local constants by comparing results with experimental data is obtained. The non‐equilibrium modification by simultaneous decrease of the turbulence kinetic energy and increase of the specific dissipation rate gives a good agreement of the hydrogen depth penetration with experimental data. Also, the numerical experiment of the supersonic airflow with a nitrogen jet shows wall pressure distribution is consistent well with experimental data.
{"title":"A new non‐equilibrium modification of the k−ω$$ k-omega $$ turbulence model for supersonic turbulent flows with transverse jet","authors":"Altynshash Naimanova, Assel Beketaeva","doi":"10.1002/fld.5337","DOIUrl":"https://doi.org/10.1002/fld.5337","url":null,"abstract":"The goal of this research is to propose a new modification of a non‐equilibrium effect in the turbulence model to better predict high‐speed turbulent flows. For that, the two local compressibility coefficients are included in the balance production/dissipation terms in a specific dissipation rate equation. The specific dissipation rate reacts to changes in the local Mach number and density through these local coefficients. The developed model is applied to the numerical simulation of the spatial supersonic turbulent airflow with round hydrogen injection. In that, the effects of the proposed turbulence model on the flow field behavior (shock wave and vortex formations, shock wave/boundary layer interaction, and mixture layer) are studied via the solution of three‐dimensional Favre‐averaged Navier–Stokes equations with a third‐order Essentially Non‐Oscillatory scheme. A series of numerical experiments are performed, in which an allowable range of local constants by comparing results with experimental data is obtained. The non‐equilibrium modification by simultaneous decrease of the turbulence kinetic energy and increase of the specific dissipation rate gives a good agreement of the hydrogen depth penetration with experimental data. Also, the numerical experiment of the supersonic airflow with a nitrogen jet shows wall pressure distribution is consistent well with experimental data.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, the response surface approach was employed to enhance the hydraulic performance of the pump at the rated point. Specifically, an approximate link between the design head and efficiency of the single‐stage centrifugal pump and the parameters of the impeller's design was established. The first step in creating a one‐factor experimental design involved selecting significant geometric variables as factors. Decision variables such as the number of blades, flow rate, and rotation were chosen due to their significant impact on hydraulic performance, while head and efficiency were considered as responses. Subsequently, the best‐optimized values for each level of the parameters were identified using response surface analysis and a central composite design. The impeller schemes of the Design‐Expert software were evaluated for head and efficiency using Computational fluid dynamics, and a total of 20 experiments were conducted. The simulated results were then validated with experimental data. Through the analysis of the individual parameters and the approximation model, the ideal parameter combination that increased head and efficiency by 7.90% and 2.06%, respectively, at the rated value was discovered. It is worth noting that in cases of a high rate of flow, the inner flow was also enhanced.
{"title":"Response surface method‐based hydraulic performance optimization of a single‐stage centrifugal pump","authors":"Durvesh Yadav, Raj Kumar Singh, K. Manjunath","doi":"10.1002/fld.5332","DOIUrl":"https://doi.org/10.1002/fld.5332","url":null,"abstract":"In this article, the response surface approach was employed to enhance the hydraulic performance of the pump at the rated point. Specifically, an approximate link between the design head and efficiency of the single‐stage centrifugal pump and the parameters of the impeller's design was established. The first step in creating a one‐factor experimental design involved selecting significant geometric variables as factors. Decision variables such as the number of blades, flow rate, and rotation were chosen due to their significant impact on hydraulic performance, while head and efficiency were considered as responses. Subsequently, the best‐optimized values for each level of the parameters were identified using response surface analysis and a central composite design. The impeller schemes of the Design‐Expert software were evaluated for head and efficiency using Computational fluid dynamics, and a total of 20 experiments were conducted. The simulated results were then validated with experimental data. Through the analysis of the individual parameters and the approximation model, the ideal parameter combination that increased head and efficiency by 7.90% and 2.06%, respectively, at the rated value was discovered. It is worth noting that in cases of a high rate of flow, the inner flow was also enhanced.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper presents an improved approach for modeling multicomponent gas mixtures based on quasi‐gasdynamic equations. The proposed numerical algorithm is implemented as a reactingQGDFoam solver based on the open‐source OpenFOAM platform. The following problems have been considered for validation: the Riemann problems, the backward facing step problem, the interaction of a shock wave with a heavy and a light gas bubble, the unsteady underexpanded hydrogen jet flow in an air. The stability and convergence parameters of the proposed numerical algorithm are determined. The simulation results are found to be in agreement with analytical solutions and experimental data.
{"title":"Development of a new solver for homogenous mixture based on regularized gas dynamic equation system","authors":"Andrey Epikhin, Ivan But","doi":"10.1002/fld.5333","DOIUrl":"https://doi.org/10.1002/fld.5333","url":null,"abstract":"The paper presents an improved approach for modeling multicomponent gas mixtures based on quasi‐gasdynamic equations. The proposed numerical algorithm is implemented as a reactingQGDFoam solver based on the open‐source OpenFOAM platform. The following problems have been considered for validation: the Riemann problems, the backward facing step problem, the interaction of a shock wave with a heavy and a light gas bubble, the unsteady underexpanded hydrogen jet flow in an air. The stability and convergence parameters of the proposed numerical algorithm are determined. The simulation results are found to be in agreement with analytical solutions and experimental data.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work presents a monolithic finite element strategy for the accurate solution of strongly‐coupled fluid‐structure‐electrostatics interaction problems involving a compressible fluid. The complete set of equations for a compressible fluid is employed within the framework of the arbitrary Lagrangian–Eulerian (ALE) fluid formulation on the reference configuration. The proposed numerical approach incorporates geometric nonlinearities of both the structural and fluid domains, and can thus be used for investigating dynamic pull‐in phenomena and squeeze film damping in high aspect‐ratio micro‐electro‐mechanical systems (MEMS) structures immersed in a compressible fluid. Through various illustrative examples, we demonstrate the significant influence of fluid compressibility on the dynamics of MEMS devices subjected to constrained geometry and/or high‐frequency electrostatic actuation. Moreover, we compare the proposed formulation with the nonlinear compressible Reynolds equation and highlight that, particularly at low pressures and high fluid viscosity, the Reynolds equation fails to provide a reliable approximation to the complete set of equations utilized in our proposed formulation.
{"title":"Monolithic finite element modeling of compressible fluid‐structure‐electrostatics interactions in MEMS devices","authors":"Suman Dutta, C. S. Jog","doi":"10.1002/fld.5329","DOIUrl":"https://doi.org/10.1002/fld.5329","url":null,"abstract":"This work presents a monolithic finite element strategy for the accurate solution of strongly‐coupled fluid‐structure‐electrostatics interaction problems involving a compressible fluid. The complete set of equations for a compressible fluid is employed within the framework of the arbitrary Lagrangian–Eulerian (ALE) fluid formulation on the reference configuration. The proposed numerical approach incorporates geometric nonlinearities of both the structural and fluid domains, and can thus be used for investigating dynamic pull‐in phenomena and squeeze film damping in high aspect‐ratio micro‐electro‐mechanical systems (MEMS) structures immersed in a compressible fluid. Through various illustrative examples, we demonstrate the significant influence of fluid compressibility on the dynamics of MEMS devices subjected to constrained geometry and/or high‐frequency electrostatic actuation. Moreover, we compare the proposed formulation with the nonlinear compressible Reynolds equation and highlight that, particularly at low pressures and high fluid viscosity, the Reynolds equation fails to provide a reliable approximation to the complete set of equations utilized in our proposed formulation.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A nonlinear correction technique for finite element methods of advection‐diffusion problems on general triangular meshes is introduced. The classic linear finite element method is modified, and the resulting scheme satisfies discrete strong extremum principle unconditionally, which means that it is unnecessary to impose the well‐known restrictions on diffusion coefficients and geometry of mesh‐cell (e.g., “acute angle” condition), and we need not to perform upwind treatment on the advection term separately. Moreover, numerical example shows that when a discrete scheme does not satisfy the strong extremum principle, even if it maintains the global physical bound, non‐physical numerical oscillations may still occur within local regions where no numerical result is beyond the physical bound. Thus, it is worth to point out that our new nonlinear finite element scheme can avoid non‐physical oscillations around sharp layers in advection‐dominate regions, due to maintaining discrete strong extremum principle. Convergence rates are verified by numerical tests for both diffusion‐dominate and advection‐dominate problems.
{"title":"Discrete strong extremum principles for finite element solutions of advection‐diffusion problems with nonlinear corrections","authors":"Shuai Wang, Guangwei Yuan","doi":"10.1002/fld.5330","DOIUrl":"https://doi.org/10.1002/fld.5330","url":null,"abstract":"A nonlinear correction technique for finite element methods of advection‐diffusion problems on general triangular meshes is introduced. The classic linear finite element method is modified, and the resulting scheme satisfies discrete strong extremum principle unconditionally, which means that it is unnecessary to impose the well‐known restrictions on diffusion coefficients and geometry of mesh‐cell (e.g., “acute angle” condition), and we need not to perform upwind treatment on the advection term separately. Moreover, numerical example shows that when a discrete scheme does not satisfy the strong extremum principle, even if it maintains the global physical bound, non‐physical numerical oscillations may still occur within local regions where no numerical result is beyond the physical bound. Thus, it is worth to point out that our new nonlinear finite element scheme can avoid non‐physical oscillations around sharp layers in advection‐dominate regions, due to maintaining discrete <jats:italic>strong</jats:italic> extremum principle. Convergence rates are verified by numerical tests for both diffusion‐dominate and advection‐dominate problems.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a high‐order compact finite difference method in general curvilinear coordinates is proposed for solving unsteady incompressible Navier‐Stokes equations. By constructing the fourth‐order spatial discretization schemes for all partial derivative terms of the pure streamfunction formulation in general curvilinear coordinates, especially for the fourth‐order mixed derivative terms, and applying a Crank‐Nicolson scheme for the second‐order temporal discretization, we extend the unsteady high‐order pure streamfunction algorithm to flow problems with more general non‐conformal grids. Furthermore, the stability of the newly proposed method for the linear model is validated by von‐Neumann linear stability analysis. Five numerical experiments are conducted to verify the accuracy and robustness of the proposed method. The results show that our method not only effectively solves problems with non‐conformal grids, but also allows grid generation and local refinement using commercial software. The solutions are in good agreement with the established numerical and experimental results.
{"title":"A high‐order pure streamfunction method in general curvilinear coordinates for unsteady incompressible viscous flow with complex geometry","authors":"Bo Wang, Peixiang Yu, Xin Tong, Hua Ouyang","doi":"10.1002/fld.5331","DOIUrl":"https://doi.org/10.1002/fld.5331","url":null,"abstract":"In this paper, a high‐order compact finite difference method in general curvilinear coordinates is proposed for solving unsteady incompressible Navier‐Stokes equations. By constructing the fourth‐order spatial discretization schemes for all partial derivative terms of the pure streamfunction formulation in general curvilinear coordinates, especially for the fourth‐order mixed derivative terms, and applying a Crank‐Nicolson scheme for the second‐order temporal discretization, we extend the unsteady high‐order pure streamfunction algorithm to flow problems with more general non‐conformal grids. Furthermore, the stability of the newly proposed method for the linear model is validated by von‐Neumann linear stability analysis. Five numerical experiments are conducted to verify the accuracy and robustness of the proposed method. The results show that our method not only effectively solves problems with non‐conformal grids, but also allows grid generation and local refinement using commercial software. The solutions are in good agreement with the established numerical and experimental results.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A local and hierarchical Koopman spectral analysis is proposed to extend Koopman spectral analysis typically used in a linear system or an ergodic process to its application in general nonlinear dynamics. The continuous and analytic Koopman eigenfunctions and eigenvalues, derived from operator perturbation theory, are capable of dealing with a nonlinear transition process with mathematical rigorousness. A proliferation rule is identified to derive high‐order eigenvalues and eigenfunctions from lower‐order ones, thus various spectral patterns may be generated through recursive proliferations. The locally linear map around each state constructs base local Koopman eigenvalues and eigenfunctions from an algebraic eigenvalue problem, and high‐order ones are generated via the proliferation rule to express the systematic nonlinearity. The aforementioned hierarchy simplifies the Koopman spectral analysis and is verified by studying the development of Kármán vortex streets. The triangular chain and the lattice distribution of Koopman eigenvalues confirm the critical role of the proliferation rule and the hierarchy structure of Koopman eigenvalues. The local spectral analysis on the transition process shows that the periodic flow forms as the growth rates of the critical Koopman modes reduce to zero, and meanwhile, the Koopman modes at the same frequency superpose on each other to form the well‐known Fourier or Floquet modes, where the latter are the enhanced nonlinear motions due to the alignment of Koopman eigenvalues with the critical ones.
{"title":"A local and hierarchical Koopman spectral analysis of fluid dynamics","authors":"Wei Zhang, Mingjun Wei","doi":"10.1002/fld.5327","DOIUrl":"https://doi.org/10.1002/fld.5327","url":null,"abstract":"A local and hierarchical Koopman spectral analysis is proposed to extend Koopman spectral analysis typically used in a linear system or an ergodic process to its application in general nonlinear dynamics. The continuous and analytic Koopman eigenfunctions and eigenvalues, derived from operator perturbation theory, are capable of dealing with a nonlinear transition process with mathematical rigorousness. A proliferation rule is identified to derive high‐order eigenvalues and eigenfunctions from lower‐order ones, thus various spectral patterns may be generated through recursive proliferations. The locally linear map around each state constructs base local Koopman eigenvalues and eigenfunctions from an algebraic eigenvalue problem, and high‐order ones are generated via the proliferation rule to express the systematic nonlinearity. The aforementioned hierarchy simplifies the Koopman spectral analysis and is verified by studying the development of Kármán vortex streets. The triangular chain and the lattice distribution of Koopman eigenvalues confirm the critical role of the proliferation rule and the hierarchy structure of Koopman eigenvalues. The local spectral analysis on the transition process shows that the periodic flow forms as the growth rates of the critical Koopman modes reduce to zero, and meanwhile, the Koopman modes at the same frequency superpose on each other to form the well‐known Fourier or Floquet modes, where the latter are the enhanced nonlinear motions due to the alignment of Koopman eigenvalues with the critical ones.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work presents a comprehensive framework for the sensitivity analysis of the Navier–Stokes equations, with an emphasis on the stability estimate of the discretized first‐order sensitivity of the Navier–Stokes equations. The first‐order sensitivity of the Navier–Stokes equations is defined using the polynomial chaos method, and a finite element‐volume numerical scheme for the Navier–Stokes equations is suggested. This numerical method is integrated into the open‐source industrial code TrioCFD developed by the CEA. The finite element‐volume discretization is extended to the first‐order sensitivity Navier–Stokes equations, and the most significant and original point is the discretization of the nonlinear term. A stability estimate for continuous and discrete Navier–Stokes equations is established. Finally, numerical tests are presented to evaluate the polynomial chaos method and to compare it to the Monte Carlo and Taylor expansion methods.
本研究提出了纳维-斯托克斯方程灵敏度分析的综合框架，重点是纳维-斯托克斯方程离散一阶灵敏度的稳定性估计。利用多项式混沌法定义了纳维-斯托克斯方程的一阶灵敏度，并提出了纳维-斯托克斯方程的有限元体积数值方案。该数值方法已集成到 CEA 开发的开源工业代码 TrioCFD 中。有限元素-体积离散化扩展到一阶敏感 Navier-Stokes 方程，最重要和最新颖的一点是非线性项的离散化。建立了连续和离散 Navier-Stokes 方程的稳定性估计。最后，通过数值测试评估了多项式混沌法，并将其与蒙特卡罗法和泰勒展开法进行了比较。
{"title":"Stability of a continuous/discrete sensitivity model for the Navier–Stokes equations","authors":"N. Nouaime, B. Després, M. A. Puscas, C. Fiorini","doi":"10.1002/fld.5324","DOIUrl":"https://doi.org/10.1002/fld.5324","url":null,"abstract":"This work presents a comprehensive framework for the sensitivity analysis of the Navier–Stokes equations, with an emphasis on the stability estimate of the discretized first‐order sensitivity of the Navier–Stokes equations. The first‐order sensitivity of the Navier–Stokes equations is defined using the polynomial chaos method, and a finite element‐volume numerical scheme for the Navier–Stokes equations is suggested. This numerical method is integrated into the open‐source industrial code TrioCFD developed by the CEA. The finite element‐volume discretization is extended to the first‐order sensitivity Navier–Stokes equations, and the most significant and original point is the discretization of the nonlinear term. A stability estimate for continuous and discrete Navier–Stokes equations is established. Finally, numerical tests are presented to evaluate the polynomial chaos method and to compare it to the Monte Carlo and Taylor expansion methods.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ahmed Jan, Muhammad Mushtaq, Muhammad Imran Khan, Umer Farooq
The current study investigates the boundary layer flow of Carreau‐Yasuda (C‐Y) ternary hybrid nanofluid model in a porous medium across curved surface stretching at linear rate under the influence of applied radial magnetic field. , and are nanoparticles and ethylene glycol is considered as base fluid. The effects of viscous dissipation and ohmic heating are present in the energy equation. The governing partial differential equation (PDEs) is nondimensionalized using non‐similarity transformations. They can be treated as ordinary differential equations (ODEs) using local non‐similarity method and solutions are obtained via bvp4c MATLAB tools. The results are evaluated by introducing computational intelligence approach utilizing the AI‐based Levenberg–Marquardt scheme with a backpropagation neural network (LMS‐BPNN) to investigate flow stability. The authors intend to use AI‐based LMS‐BPNN is to optimize the behavior of the hybrid nanofluid (HNF) flow of Carreau‐Yasuda fluid across a stretching curved sheet. Initial/reference solutions are obtained through bvp4c function (an embedded MATLAB function designed to solve systems of ODEs) by systematically adjusting input parameters as demonstrated in Scenarios 1–5. There are three options to divide the numerical data: 80% for training, 10% for testing, and an additional 10% for validation. The LMS‐BPNN is used for approximate solutions of Scenario 1–5. The efficiency and reliability of LMS‐BPNN are validated through fitness curves based on correlation index (R), error, and regression analysis. The velocity and temperature profiles asymptotically satisfy boundary conditions of Scenario 1–5 with LMS‐BPNN.
{"title":"Integrated artificial intelligence and non‐similar analysis for forced convection of radially magnetized ternary hybrid nanofluid of Carreau‐Yasuda fluid model over a curved stretching surface","authors":"Ahmed Jan, Muhammad Mushtaq, Muhammad Imran Khan, Umer Farooq","doi":"10.1002/fld.5325","DOIUrl":"https://doi.org/10.1002/fld.5325","url":null,"abstract":"The current study investigates the boundary layer flow of Carreau‐Yasuda (C‐Y) ternary hybrid nanofluid model in a porous medium across curved surface stretching at linear rate under the influence of applied radial magnetic field. , and are nanoparticles and ethylene glycol is considered as base fluid. The effects of viscous dissipation and ohmic heating are present in the energy equation. The governing partial differential equation (PDEs) is nondimensionalized using non‐similarity transformations. They can be treated as ordinary differential equations (ODEs) using local non‐similarity method and solutions are obtained via bvp4c MATLAB tools. The results are evaluated by introducing computational intelligence approach utilizing the AI‐based Levenberg–Marquardt scheme with a backpropagation neural network (LMS‐BPNN) to investigate flow stability. The authors intend to use AI‐based LMS‐BPNN is to optimize the behavior of the hybrid nanofluid (HNF) flow of Carreau‐Yasuda fluid across a stretching curved sheet. Initial/reference solutions are obtained through bvp4c function (an embedded MATLAB function designed to solve systems of ODEs) by systematically adjusting input parameters as demonstrated in Scenarios 1–5. There are three options to divide the numerical data: 80% for training, 10% for testing, and an additional 10% for validation. The LMS‐BPNN is used for approximate solutions of Scenario 1–5. The efficiency and reliability of LMS‐BPNN are validated through fitness curves based on correlation index (R), error, and regression analysis. The velocity and temperature profiles asymptotically satisfy boundary conditions of Scenario 1–5 with LMS‐BPNN.","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：