Articles de revista
http://hdl.handle.net/2117/79699
2020-07-07T00:32:16ZFluid structure interaction by means of variational multiscale reduced order models
http://hdl.handle.net/2117/189376
Fluid structure interaction by means of variational multiscale reduced order models
Tello Guerra, Alexis; Codina, Ramon; Baiges Aznar, Joan
A reduced order model designed by means of a variational multiscale stabilized formulation has been applied successfully to fluid-structure interaction problems in a strongly coupled partitioned solution scheme. Details of the formulation and the implementation both for the interaction problem and for the reduced models, for both the off-line and on-line phases, are shown. Results are obtained for cases in which both domains are reduced at the same time. Numerical results are presented for a semistationary and a fully transient case.
This is the peer reviewed version of the following article: [ Tello, A, Codina, R, Baiges, J. Fluid structure interaction by means of variational multiscale reduced order models. Int J Numer Methods Eng. 2020; 121: 2601– 2625. https://doi.org/10.1002/nme.6321 ], which has been published in final form at [https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6321]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
2020-05-28T15:28:25ZTello Guerra, AlexisCodina, RamonBaiges Aznar, JoanA reduced order model designed by means of a variational multiscale stabilized formulation has been applied successfully to fluid-structure interaction problems in a strongly coupled partitioned solution scheme. Details of the formulation and the implementation both for the interaction problem and for the reduced models, for both the off-line and on-line phases, are shown. Results are obtained for cases in which both domains are reduced at the same time. Numerical results are presented for a semistationary and a fully transient case.Projection-based reduced order models for flow problems: a variational multiscale approach
http://hdl.handle.net/2117/188114
Projection-based reduced order models for flow problems: a variational multiscale approach
Reyes, Ricardo; Codina, Ramon
In this paper we present a Variational Multi-Scale stabilized formulation for a general projection-based Reduced Order Model. In the stabilized formulation we address techniques already analysed in Variational Multi-Scale-Finite Element methods: time-dependent subscales, non-linearity in the subscales approximation and orthogonality between the solution space and the subscale space. Additionally, we describe a mesh based hyper-Reduced Order Model technique and implement a Petrov–Galerkin projection technique. At the end of the article, we test the proposed Reduced Order Model formulation using the incompressible Navier–Stokes problem.
2020-05-19T15:05:58ZReyes, RicardoCodina, RamonIn this paper we present a Variational Multi-Scale stabilized formulation for a general projection-based Reduced Order Model. In the stabilized formulation we address techniques already analysed in Variational Multi-Scale-Finite Element methods: time-dependent subscales, non-linearity in the subscales approximation and orthogonality between the solution space and the subscale space. Additionally, we describe a mesh based hyper-Reduced Order Model technique and implement a Petrov–Galerkin projection technique. At the end of the article, we test the proposed Reduced Order Model formulation using the incompressible Navier–Stokes problem.Stationary and time-dependent numerical approximation of the lid-driven cavity problem for power-law fluid flows at high Reynolds numbers using a stabilized finite element formulation of the VMS type
http://hdl.handle.net/2117/185480
Stationary and time-dependent numerical approximation of the lid-driven cavity problem for power-law fluid flows at high Reynolds numbers using a stabilized finite element formulation of the VMS type
Aguirre, A.; Castillo, Ernesto; Cruchaga, Marcela A.; Codina, Ramon; Baiges Aznar, Joan
In this work, a variational multiscale finite element formulation is used to approximate numerically the lid-driven cavity flow problem for high Reynolds numbers. For Newtonian fluids, this benchmark case has been extensively studied by many authors for low and moderate Reynolds numbers (up to Re=10,000), giving place to steady flows, using stationary and time-dependent approaches. For more convective flows, the solution becomes unstable, describing an oscillatory behavior. The critical Reynolds number which gives place to this time-dependent fluid dynamics has been defined over a wide range 7, 300 ≲ Re ≲ 35, 000, using different numerical approaches. In the non-Newtonian case, the cavity problem has not been studied deeply for high Reynolds number (Re > 10, 000), specifically, in the oscillatory time-dependent case. A VMS formulation is presented to be validated using existing results, to determine flow conditions at which the instability appears, and lastly, to establish new benchmark solutions for high-Reynolds numbers fluid flows using the power-law model. Obtained results show a good agreement with those reported in the references, and new data related with the oscillatory behavior of the flow has been found for the non-Newtonian case. In this regard, time-dependent flows show dependence on both Reynolds number and power-law index, and the unsteady starting point has been determined for all studied cases. It is determined that the critical Reynolds number (Rec) that defines the first Hopf bifurcation for Newtonian fluid flow is ranged between 8,100 ≲ Rec ≲ 8, 250, whereas for power-law indexes n=0.5 and n=1.5, it is 7,100 ≲ Rec ≲ 7,200 and 18,250 ≲ Rec ≲ 18,500, respectively.
2020-04-28T15:36:31ZAguirre, A.Castillo, ErnestoCruchaga, Marcela A.Codina, RamonBaiges Aznar, JoanIn this work, a variational multiscale finite element formulation is used to approximate numerically the lid-driven cavity flow problem for high Reynolds numbers. For Newtonian fluids, this benchmark case has been extensively studied by many authors for low and moderate Reynolds numbers (up to Re=10,000), giving place to steady flows, using stationary and time-dependent approaches. For more convective flows, the solution becomes unstable, describing an oscillatory behavior. The critical Reynolds number which gives place to this time-dependent fluid dynamics has been defined over a wide range 7, 300 ≲ Re ≲ 35, 000, using different numerical approaches. In the non-Newtonian case, the cavity problem has not been studied deeply for high Reynolds number (Re > 10, 000), specifically, in the oscillatory time-dependent case. A VMS formulation is presented to be validated using existing results, to determine flow conditions at which the instability appears, and lastly, to establish new benchmark solutions for high-Reynolds numbers fluid flows using the power-law model. Obtained results show a good agreement with those reported in the references, and new data related with the oscillatory behavior of the flow has been found for the non-Newtonian case. In this regard, time-dependent flows show dependence on both Reynolds number and power-law index, and the unsteady starting point has been determined for all studied cases. It is determined that the critical Reynolds number (Rec) that defines the first Hopf bifurcation for Newtonian fluid flow is ranged between 8,100 ≲ Rec ≲ 8, 250, whereas for power-law indexes n=0.5 and n=1.5, it is 7,100 ≲ Rec ≲ 7,200 and 18,250 ≲ Rec ≲ 18,500, respectively.Logarithmic conformation reformulation in viscoelastic flow problems approximated by a VMS-type stabilized finite element formulation
http://hdl.handle.net/2117/185034
Logarithmic conformation reformulation in viscoelastic flow problems approximated by a VMS-type stabilized finite element formulation
Moreno Martínez, Laura; Codina, Ramon; Baiges Aznar, Joan; Castillo, Ernesto
The log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers which are impossible to solve with the typical three-field formulation. By following this approach, in this work we develop a new stabilized finite element formulation based on the logarithmic reformulation using the Variational Multiscale (VMS) method as stabilization technique, together with a modified log-conformation formulation. Our approach follows the term-by-term stabilization proposed by Castillo and Codina (2014) for the standard formulation, which is more effective when there are stress singularities. The formulation can be used when the relaxation parameter is set to zero, and permits a direct steady numerical resolution. The formulation is validated in the classical benchmark flow past a cylinder and in the well-known planar contraction 4:1, achieving very accurate, stable and mesh independent results for highly elastic fluids.
2020-04-24T13:27:57ZMoreno Martínez, LauraCodina, RamonBaiges Aznar, JoanCastillo, ErnestoThe log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers which are impossible to solve with the typical three-field formulation. By following this approach, in this work we develop a new stabilized finite element formulation based on the logarithmic reformulation using the Variational Multiscale (VMS) method as stabilization technique, together with a modified log-conformation formulation. Our approach follows the term-by-term stabilization proposed by Castillo and Codina (2014) for the standard formulation, which is more effective when there are stress singularities. The formulation can be used when the relaxation parameter is set to zero, and permits a direct steady numerical resolution. The formulation is validated in the classical benchmark flow past a cylinder and in the well-known planar contraction 4:1, achieving very accurate, stable and mesh independent results for highly elastic fluids.A fractional step method for computational aeroacoustics using weak imposition of Dirichlet boundary conditions
http://hdl.handle.net/2117/180697
A fractional step method for computational aeroacoustics using weak imposition of Dirichlet boundary conditions
Parada Bustelo, Samuel; Baiges Aznar, Joan; Codina, Ramon
In this work we consider the approximation of the isentropic Navier–Stokes equations. The model we present is capable of taking into account acoustic and flow scales at once. After space and time discretizations have been chosen, it is very convenient from the computational point of view to design fractional step schemes in time so as to permit a segregated calculation of the problem unknowns. While these segregation schemes are well established for incompressible flows, much less is known in the case of isentropic flows. We discuss this issue in this article and, furthermore, we study the way to weakly impose Dirichlet boundary conditions via Nitsche’s method. In order to avoid spurious reflections of the acoustic waves, Nitsche’s method is combined with a non-reflecting boundary condition. Employing a purely algebraic approach to discuss the problem, some of the boundary contributions are treated explicitly and we explain how these are included in the different steps of the final algorithm. Numerical evidence shows that this explicit treatment does not have a significant impact on the convergence rate of the resulting time integration scheme. The equations of the formulation are solved using a subgrid scale technique based on a term-by-term stabilization.
2020-03-20T10:28:22ZParada Bustelo, SamuelBaiges Aznar, JoanCodina, RamonIn this work we consider the approximation of the isentropic Navier–Stokes equations. The model we present is capable of taking into account acoustic and flow scales at once. After space and time discretizations have been chosen, it is very convenient from the computational point of view to design fractional step schemes in time so as to permit a segregated calculation of the problem unknowns. While these segregation schemes are well established for incompressible flows, much less is known in the case of isentropic flows. We discuss this issue in this article and, furthermore, we study the way to weakly impose Dirichlet boundary conditions via Nitsche’s method. In order to avoid spurious reflections of the acoustic waves, Nitsche’s method is combined with a non-reflecting boundary condition. Employing a purely algebraic approach to discuss the problem, some of the boundary contributions are treated explicitly and we explain how these are included in the different steps of the final algorithm. Numerical evidence shows that this explicit treatment does not have a significant impact on the convergence rate of the resulting time integration scheme. The equations of the formulation are solved using a subgrid scale technique based on a term-by-term stabilization.A finite element reduced-order model based on adaptive mesh refinement and artificial neural networks
http://hdl.handle.net/2117/177510
A finite element reduced-order model based on adaptive mesh refinement and artificial neural networks
Baiges Aznar, Joan; Codina, Ramon; Castañar Pérez, Inocencio; Castillo, Ernesto
In this work, a reduced-order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN-ROM) is presented. The idea is to run a high-fidelity simulation by using an adaptively refined finite element mesh and compare the results obtained with those of a coarse mesh finite element model. From this comparison, a correction forcing term can be computed for each training configuration. A model for the correction term is built by using an artificial neural network, and the final reduced-order model is obtained by putting together the coarse mesh finite element model, plus the artificial neural network model for the correction forcing term. The methodology is applied to nonlinear solid mechanics problems, transient quasi-incompressible flows, and a fluid-structure interaction problem. The results of the numerical examples show that the FAN-ROM is capable of improving the simulation results obtained in coarse finite element meshes at a reduced computational cost.
This is the accepted version of the following article: [ Baiges, J, Codina, R, Castañar, I, Castillo, E. A finite element reduced‐order model based on adaptive mesh refinement and artificial neural networks. Int J Numer Methods Eng. 2020; 121: 588– 601. https://doi.org/10.1002/nme.6235], which has been published in final form at https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6235.
2020-02-11T18:23:33ZBaiges Aznar, JoanCodina, RamonCastañar Pérez, InocencioCastillo, ErnestoIn this work, a reduced-order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN-ROM) is presented. The idea is to run a high-fidelity simulation by using an adaptively refined finite element mesh and compare the results obtained with those of a coarse mesh finite element model. From this comparison, a correction forcing term can be computed for each training configuration. A model for the correction term is built by using an artificial neural network, and the final reduced-order model is obtained by putting together the coarse mesh finite element model, plus the artificial neural network model for the correction forcing term. The methodology is applied to nonlinear solid mechanics problems, transient quasi-incompressible flows, and a fluid-structure interaction problem. The results of the numerical examples show that the FAN-ROM is capable of improving the simulation results obtained in coarse finite element meshes at a reduced computational cost.Numerical modelling of heat transfer and experimental validation in powder-bed fusion with the virtual domain approximation
http://hdl.handle.net/2117/172674
Numerical modelling of heat transfer and experimental validation in powder-bed fusion with the virtual domain approximation
Miranda Neiva, Eric; Chiumenti, Michèle; Cervera Ruiz, Miguel; Salsi, Emilio; Piscopo, Gabriele; Badia, Santiago; Martín Huertas, Alberto Francisco; Chen, Zhuoer; Lee, Caroline; Davies, Christopher
Among metal additive manufacturing technologies, powder-bed fusion features very thin layers and rapid solidification rates, leading to long build jobs and a highly localized process. Many efforts are being devoted to accelerate simulation times for practical industrial applications. The new approach suggested here, the virtual domain approximation, is a physics-based rationale for spatial reduction of the domain in the thermal finite-element analysis at the part scale. Computational experiments address, among others, validation against a large physical experiment of 17.5[cm3]of deposited volume in 647 layers. For fast and automatic parameter estimation at such level of complexity, a high-performance computing framework is employed. It couples FEMPAR-AM,a specialized parallel finite-element software, with Dakota, for the parametric exploration. Compared to previous state-of-the-art, this formulation provides higher accuracy at the same computational cost. This sets the path to a fully virtualized model, considering an upwards-moving domain covering the last printed layers.
2019-11-19T00:15:21ZMiranda Neiva, EricChiumenti, MichèleCervera Ruiz, MiguelSalsi, EmilioPiscopo, GabrieleBadia, SantiagoMartín Huertas, Alberto FranciscoChen, ZhuoerLee, CarolineDavies, ChristopherAmong metal additive manufacturing technologies, powder-bed fusion features very thin layers and rapid solidification rates, leading to long build jobs and a highly localized process. Many efforts are being devoted to accelerate simulation times for practical industrial applications. The new approach suggested here, the virtual domain approximation, is a physics-based rationale for spatial reduction of the domain in the thermal finite-element analysis at the part scale. Computational experiments address, among others, validation against a large physical experiment of 17.5[cm3]of deposited volume in 647 layers. For fast and automatic parameter estimation at such level of complexity, a high-performance computing framework is employed. It couples FEMPAR-AM,a specialized parallel finite-element software, with Dakota, for the parametric exploration. Compared to previous state-of-the-art, this formulation provides higher accuracy at the same computational cost. This sets the path to a fully virtualized model, considering an upwards-moving domain covering the last printed layers.Pseudoplastic fluid flows for different Prandtl numbers: steady and time-dependent solutions
http://hdl.handle.net/2117/167057
Pseudoplastic fluid flows for different Prandtl numbers: steady and time-dependent solutions
Aguirre, A.; Castillo, Ernesto; Cruchaga, Marcela A.; Codina, Ramon; Baiges Aznar, Joan
In this work, a variational multiscale (VMS) finite element formulation is used to approximate numerically the natural convection in square cavity with differentially heated from sidewalls problem for Newtonian and power-law fluids. The problem is characterized for going through a Hopf bifurcation when reaching high enough Rayleigh numbers, which initiates the transition between steady and time dependent behavior, however, results found in the literature are only for air Prandtl number. The presented VMS formulation is validated using existing results, and is used to study highly convective cases, to determine the flow conditions at which it becomes time dependent, and to establish new benchmark solutions for non-Newtonian fluid flows for different Pr and power-law indexes n. The range of solutions were found in the range 0.6<n<1 and 0.01<Pr<1,000, and the critical Rayleigh number (Rac) where Hopf bifurcations appear were identified for all cases. Obtained results have good agreement with those previously reported in the specific literature, and new data related to the heat transfer capabilities of pseudoplastic fluids and its oscillatory behavior was identified. This non-Newtonian influence of the fluid is later checked in a 3D model of a simplified heat exchanger, where the capability of pseudoplastic fluids for energy transport proved to be enhanced when compared to the Newtonian case.
2019-07-29T22:31:16ZAguirre, A.Castillo, ErnestoCruchaga, Marcela A.Codina, RamonBaiges Aznar, JoanIn this work, a variational multiscale (VMS) finite element formulation is used to approximate numerically the natural convection in square cavity with differentially heated from sidewalls problem for Newtonian and power-law fluids. The problem is characterized for going through a Hopf bifurcation when reaching high enough Rayleigh numbers, which initiates the transition between steady and time dependent behavior, however, results found in the literature are only for air Prandtl number. The presented VMS formulation is validated using existing results, and is used to study highly convective cases, to determine the flow conditions at which it becomes time dependent, and to establish new benchmark solutions for non-Newtonian fluid flows for different Pr and power-law indexes n. The range of solutions were found in the range 0.6<n<1 and 0.01<Pr<1,000, and the critical Rayleigh number (Rac) where Hopf bifurcations appear were identified for all cases. Obtained results have good agreement with those previously reported in the specific literature, and new data related to the heat transfer capabilities of pseudoplastic fluids and its oscillatory behavior was identified. This non-Newtonian influence of the fluid is later checked in a 3D model of a simplified heat exchanger, where the capability of pseudoplastic fluids for energy transport proved to be enhanced when compared to the Newtonian case.Maximum-principle preserving space–time isogeometric analysis
http://hdl.handle.net/2117/134634
Maximum-principle preserving space–time isogeometric analysis
Bonilla de Toro, Jesús; Badia, Santiago
In this work we propose a nonlinear stabilization technique for convection–diffusion–reaction and pure transport problems discretized with space–time isogeometric analysis. The stabilization is based on a graph-theoretic artificial diffusion operator and a novel shock detector for isogeometric analysis. Stabilization in time and space directions are performed similarly, which allow us to use high-order discretizations in time without any CFL-like condition. The method is proven to yield solutions that satisfy the discrete maximum principle (DMP) unconditionally for arbitrary order. In addition, the stabilization is linearity preserving in a space–time sense. Moreover, the scheme is proven to be Lipschitz continuous ensuring that the nonlinear problem is well-posed. Solving large problems using a space–time discretization can become highly costly. Therefore, we also propose a partitioned space–time scheme that allows us to select the length of every time slab, and solve sequentially for every subdomain. As a result, the computational cost is reduced while the stability and convergence properties of the scheme remain unaltered. In addition, we propose a twice differentiable version of the stabilization scheme, which enjoys the same stability properties while the nonlinear convergence is significantly improved. Finally, the proposed schemes are assessed with numerical experiments. In particular, we considered steady and transient pure convection and convection–diffusion problems in one and two dimensions.
2019-06-18T07:25:16ZBonilla de Toro, JesúsBadia, SantiagoIn this work we propose a nonlinear stabilization technique for convection–diffusion–reaction and pure transport problems discretized with space–time isogeometric analysis. The stabilization is based on a graph-theoretic artificial diffusion operator and a novel shock detector for isogeometric analysis. Stabilization in time and space directions are performed similarly, which allow us to use high-order discretizations in time without any CFL-like condition. The method is proven to yield solutions that satisfy the discrete maximum principle (DMP) unconditionally for arbitrary order. In addition, the stabilization is linearity preserving in a space–time sense. Moreover, the scheme is proven to be Lipschitz continuous ensuring that the nonlinear problem is well-posed. Solving large problems using a space–time discretization can become highly costly. Therefore, we also propose a partitioned space–time scheme that allows us to select the length of every time slab, and solve sequentially for every subdomain. As a result, the computational cost is reduced while the stability and convergence properties of the scheme remain unaltered. In addition, we propose a twice differentiable version of the stabilization scheme, which enjoys the same stability properties while the nonlinear convergence is significantly improved. Finally, the proposed schemes are assessed with numerical experiments. In particular, we considered steady and transient pure convection and convection–diffusion problems in one and two dimensions.Scalable solvers for complex electromagnetics problems
http://hdl.handle.net/2117/132678
Scalable solvers for complex electromagnetics problems
Badia, Santiago; Martín Huertas, Alberto Francisco; Olm Serra, Marc
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce the continuity across subdomains of the method, we use a partition of the interface objects (edges and faces) into sub-objects determined by the variation of the physical coefficients of the problem. For multi-material problems, a constant coefficient condition is enough to define this sub-partition of the objects. For arbitrarily heterogeneous problems, a relaxed version of the method is defined, where we only require that the maximal contrast of the physical coefficient in each object is smaller than a predefined threshold. Besides, the addition of perturbation terms to the preconditioner is empirically shown to be effective in order to deal with the case where the two coefficients of the model problem jump simultaneously across the interface. The new method, in contrast to existing approaches for problems in curl-conforming spaces does not require spectral information whilst providing robustness with regard to coefficient jumps and heterogeneous materials. A detailed set of numerical experiments, which includes the application of the preconditioner to 3D realistic cases, shows excellent weak scalability properties of the implementation of the proposed algorithms.
2019-05-07T22:12:34ZBadia, SantiagoMartín Huertas, Alberto FranciscoOlm Serra, MarcIn this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce the continuity across subdomains of the method, we use a partition of the interface objects (edges and faces) into sub-objects determined by the variation of the physical coefficients of the problem. For multi-material problems, a constant coefficient condition is enough to define this sub-partition of the objects. For arbitrarily heterogeneous problems, a relaxed version of the method is defined, where we only require that the maximal contrast of the physical coefficient in each object is smaller than a predefined threshold. Besides, the addition of perturbation terms to the preconditioner is empirically shown to be effective in order to deal with the case where the two coefficients of the model problem jump simultaneously across the interface. The new method, in contrast to existing approaches for problems in curl-conforming spaces does not require spectral information whilst providing robustness with regard to coefficient jumps and heterogeneous materials. A detailed set of numerical experiments, which includes the application of the preconditioner to 3D realistic cases, shows excellent weak scalability properties of the implementation of the proposed algorithms.