SAM
https://sam.ensam.eu:443
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http://hdl.handle.net/10985/10242
Parametric solution of the Rayleigh-Benard convection model by using the PGD Application to nanofluids
AGHIGHI, Mohammad Saeid; AMMAR, Amine; METIVIER, Christel; CHINESTA, Francisco
Purpose – The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time. Design/methodology/approach – In this paper both parameters are introduced as model extracoordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily. Findings – Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters. Originality/value – Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/102422015-01-01T00:00:00ZAGHIGHI, Mohammad SaeidAMMAR, AmineMETIVIER, ChristelCHINESTA, FranciscoPurpose – The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time. Design/methodology/approach – In this paper both parameters are introduced as model extracoordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily. Findings – Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters. Originality/value – Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.An overview of the proper generalized decomposition with applications in computational rheology
http://hdl.handle.net/10985/8473
An overview of the proper generalized decomposition with applications in computational rheology
CHINESTA, Francisco; AMMAR, Amine; LEYGUE, Adrien; KEUNINGS, Roland
We review the foundations and applications of the proper generalized decomposition (PGD), a powerful model reduction technique that computes a priori by means of successive enrichment a separated representation of the unknown field. The computational complexity of the PGD scales linearly with the dimension of the space wherein the model is defined, which is in marked contrast with the exponential scaling of standard grid-based methods. First introduced in the context of computational rheology by Ammar et al. [3] and [4], the PGD has since been further developed and applied in a variety of applications ranging from the solution of the Schrödinger equation of quantum mechanics to the analysis of laminate composites. In this paper, we illustrate the use of the PGD in four problem categories related to computational rheology: (i) the direct solution of the Fokker-Planck equation for complex fluids in configuration spaces of high dimension, (ii) the development of very efficient non-incremental algorithms for transient problems, (iii) the fully three-dimensional solution of problems defined in degenerate plate or shell-like domains often encountered in polymer processing or composites manufacturing, and finally (iv) the solution of multidimensional parametric models obtained by introducing various sources of problem variability as additional coordinates.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/84732011-01-01T00:00:00ZCHINESTA, FranciscoAMMAR, AmineLEYGUE, AdrienKEUNINGS, RolandWe review the foundations and applications of the proper generalized decomposition (PGD), a powerful model reduction technique that computes a priori by means of successive enrichment a separated representation of the unknown field. The computational complexity of the PGD scales linearly with the dimension of the space wherein the model is defined, which is in marked contrast with the exponential scaling of standard grid-based methods. First introduced in the context of computational rheology by Ammar et al. [3] and [4], the PGD has since been further developed and applied in a variety of applications ranging from the solution of the Schrödinger equation of quantum mechanics to the analysis of laminate composites. In this paper, we illustrate the use of the PGD in four problem categories related to computational rheology: (i) the direct solution of the Fokker-Planck equation for complex fluids in configuration spaces of high dimension, (ii) the development of very efficient non-incremental algorithms for transient problems, (iii) the fully three-dimensional solution of problems defined in degenerate plate or shell-like domains often encountered in polymer processing or composites manufacturing, and finally (iv) the solution of multidimensional parametric models obtained by introducing various sources of problem variability as additional coordinates.A mesoscopic rheological model of moderately concentrated colloids
http://hdl.handle.net/10985/9962
A mesoscopic rheological model of moderately concentrated colloids
GRMELA, Miroslav; AMMAR, Amine; CHINESTA, Francisco; MAITREJEAN, Guillaume
We extend the Maffettone–Minale model by including non-elliptical shapes of dispersed particles, a new family of internal forces controlling particle deformations, and particle–particle interactions. The last extension is made by transposing the way the chain-chain interactions are mathematically expressed in the reptation theory to suspensions. The particle–particle interactions are regarded as a confinement to cages formed by surrounding particles and by introducing a new dissipative motion (an analog of the reptation motion) inside the cages. Nonlinear responses to imposed shear and elongational flows are found to be in qualitative agreement with available experimental data.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/99622014-01-01T00:00:00ZGRMELA, MiroslavAMMAR, AmineCHINESTA, FranciscoMAITREJEAN, GuillaumeWe extend the Maffettone–Minale model by including non-elliptical shapes of dispersed particles, a new family of internal forces controlling particle deformations, and particle–particle interactions. The last extension is made by transposing the way the chain-chain interactions are mathematically expressed in the reptation theory to suspensions. The particle–particle interactions are regarded as a confinement to cages formed by surrounding particles and by introducing a new dissipative motion (an analog of the reptation motion) inside the cages. Nonlinear responses to imposed shear and elongational flows are found to be in qualitative agreement with available experimental data.On the Model Order Reduction of Confined Plasticity
http://hdl.handle.net/10985/10754
On the Model Order Reduction of Confined Plasticity
NASRI, Mohamed Aziz; AMMAR, Amine; CHINESTA, Francisco; ROBERT, Camille; EL AREM, Saber; MOREL, Franck
Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems. In some processes, plastic deformations remain very localized, for example in the immediate neighborhood of the surface. In that case, the in-plane characteristic dimension is several orders of magnitude higher than the one related to the deepness in which plasticity localizes. In those situations the use of standard mesh-based 3D discretization is challenging because the extremely different characteristic dimensions that to capture all the information requires the use of millions of nodes.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/107542016-01-01T00:00:00ZNASRI, Mohamed AzizAMMAR, AmineCHINESTA, FranciscoROBERT, CamilleEL AREM, SaberMOREL, FranckForming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems. In some processes, plastic deformations remain very localized, for example in the immediate neighborhood of the surface. In that case, the in-plane characteristic dimension is several orders of magnitude higher than the one related to the deepness in which plasticity localizes. In those situations the use of standard mesh-based 3D discretization is challenging because the extremely different characteristic dimensions that to capture all the information requires the use of millions of nodes.Proper general decomposition (PGD) for the resolution of Navier–Stokes equations
http://hdl.handle.net/10985/8469
Proper general decomposition (PGD) for the resolution of Navier–Stokes equations
DUMON, Antoine; ALLERY, Cyrille; AMMAR, Amine
In this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/84692011-01-01T00:00:00ZDUMON, AntoineALLERY, CyrilleAMMAR, AmineIn this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.Proper Generalized Decomposition method for incompressible Navier–Stokes equations with a spectral discretization
http://hdl.handle.net/10985/8487
Proper Generalized Decomposition method for incompressible Navier–Stokes equations with a spectral discretization
DUMON, Antoine; ALLERY, Cyrille; AMMAR, Amine
Proper Generalized Decomposition (PGD) is a method which consists in looking for the solution to a problem in a separate form. This approach has been increasingly used over the last few years to solve mathematical problems. The originality of this work consists in the association of PGD with a spectral collocation method to solve transfer equations as well as Navier–Stokes equations. In the first stage, the PGD method and its association with spectral discretization is detailed. This approach was tested for several problems: the Poisson equation, the Darcy problem, Navier–Stokes equations (the Taylor Green problem and the lid-driven cavity). In the Navier–Stokes problems, the coupling between velocity and pressure was performed using a fractional step scheme and a PN—PN-2 discretization. For all problems considered, the results from PGD simulations were compared with those obtained by a standard solver and/or with the results found in the literature. The simulations performed showed that PGD is as accurate as standard solvers. PGD preserves the spectral behavior of the errors in velocity and pressure when the time step or the space step decreases. Moreover, for a given number of discretization nodes, PGD is faster than the standard solvers.
http://dx.doi.org/10.1016/j.amc.2013.02.022
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/84872013-01-01T00:00:00ZDUMON, AntoineALLERY, CyrilleAMMAR, AmineProper Generalized Decomposition (PGD) is a method which consists in looking for the solution to a problem in a separate form. This approach has been increasingly used over the last few years to solve mathematical problems. The originality of this work consists in the association of PGD with a spectral collocation method to solve transfer equations as well as Navier–Stokes equations. In the first stage, the PGD method and its association with spectral discretization is detailed. This approach was tested for several problems: the Poisson equation, the Darcy problem, Navier–Stokes equations (the Taylor Green problem and the lid-driven cavity). In the Navier–Stokes problems, the coupling between velocity and pressure was performed using a fractional step scheme and a PN—PN-2 discretization. For all problems considered, the results from PGD simulations were compared with those obtained by a standard solver and/or with the results found in the literature. The simulations performed showed that PGD is as accurate as standard solvers. PGD preserves the spectral behavior of the errors in velocity and pressure when the time step or the space step decreases. Moreover, for a given number of discretization nodes, PGD is faster than the standard solvers.Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions
http://hdl.handle.net/10985/8467
Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions
AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco
The numerical solution of the chemical master equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task owing to its complexity, exponentially growing with the number of species involved. Although most of the existing techniques rely on the use of Monte Carlo-like techniques, we present here a new technique based on the approximation of the unknown variable (the probability of having a particular chemical state) in terms of a finite sum of separable functions. In this framework, the complexity of the CME grows only linearly with the number of state space dimensions. This technique generalizes the so-called Hartree approximation, by using terms as needed in the finite sums decomposition for ensuring convergence. But noteworthy, the ease of the approximation allows for an easy treatment of unknown parameters (as is frequently the case when modeling gene regulatory networks, for instance). These unknown parameters can be considered as new space dimensions. In this way, the proposed method provides solutions for any value of the unknown parameters (within some interval of arbitrary size) in one execution of the program.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/84672012-01-01T00:00:00ZAMMAR, AmineCUETO, EliasCHINESTA, FranciscoThe numerical solution of the chemical master equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task owing to its complexity, exponentially growing with the number of species involved. Although most of the existing techniques rely on the use of Monte Carlo-like techniques, we present here a new technique based on the approximation of the unknown variable (the probability of having a particular chemical state) in terms of a finite sum of separable functions. In this framework, the complexity of the CME grows only linearly with the number of state space dimensions. This technique generalizes the so-called Hartree approximation, by using terms as needed in the finite sums decomposition for ensuring convergence. But noteworthy, the ease of the approximation allows for an easy treatment of unknown parameters (as is frequently the case when modeling gene regulatory networks, for instance). These unknown parameters can be considered as new space dimensions. In this way, the proposed method provides solutions for any value of the unknown parameters (within some interval of arbitrary size) in one execution of the program.Degradation modes and tool wear mechanisms in finish and rough machining of Ti17 Titanium alloy under high-pressure water jet assistance
http://hdl.handle.net/10985/8608
Degradation modes and tool wear mechanisms in finish and rough machining of Ti17 Titanium alloy under high-pressure water jet assistance
AYED, Yessine; GERMAIN, Guénaël; AMMAR, Amine; FURET, Benoit
This article presents the results of an experimental study on the Ti17 titanium alloy, which was carried out to analyze tool wear and the degradation mechanisms of an uncoated tungsten carbide tool insert. Two machining conditions, roughing and finishing, have been studied under different lubrication conditions. The experimental procedure included measurement of the cutting forces and the surface roughness. Different techniques have been used to explain the tool wear mechanisms. Distribution maps of the elemental composition of the titanium alloy and the tool inserts have been created using Energy Dispersive X-ray Spectroscopy (EDS). An area of material deposition on the tool rake face, characterized by a high titanium concentration has been observed. The width of this area and the concentration of titanium, decrease when increasing water jet pressure. The study shows that wear mechanisms, with and without high-pressure water jet assistance (HPWJA) are not the same. For example, for the roughing condition using conventional lubrication, the temperature in the cutting area becomes very high, this causes plastic deformation of the cutting edge which results in its rapid collapse. By contrast, this problem disappears when machining with HPWJA. In addition, the evolution of flank wear (VB) is stabilized with high-pressure lubrication. In this case, the most critical degradation mode is due to notch wear (VBn) leading to the sudden rupture of the cutting edge.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/86082013-01-01T00:00:00ZAYED, YessineGERMAIN, GuénaëlAMMAR, AmineFURET, BenoitThis article presents the results of an experimental study on the Ti17 titanium alloy, which was carried out to analyze tool wear and the degradation mechanisms of an uncoated tungsten carbide tool insert. Two machining conditions, roughing and finishing, have been studied under different lubrication conditions. The experimental procedure included measurement of the cutting forces and the surface roughness. Different techniques have been used to explain the tool wear mechanisms. Distribution maps of the elemental composition of the titanium alloy and the tool inserts have been created using Energy Dispersive X-ray Spectroscopy (EDS). An area of material deposition on the tool rake face, characterized by a high titanium concentration has been observed. The width of this area and the concentration of titanium, decrease when increasing water jet pressure. The study shows that wear mechanisms, with and without high-pressure water jet assistance (HPWJA) are not the same. For example, for the roughing condition using conventional lubrication, the temperature in the cutting area becomes very high, this causes plastic deformation of the cutting edge which results in its rapid collapse. By contrast, this problem disappears when machining with HPWJA. In addition, the evolution of flank wear (VB) is stabilized with high-pressure lubrication. In this case, the most critical degradation mode is due to notch wear (VBn) leading to the sudden rupture of the cutting edge.Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation
http://hdl.handle.net/10985/8462
Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation
BERGAMASCO, Luca; IZQUIERDO, Salvador; AMMAR, Amine
Micro–macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro–macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation by a lattice-Boltzmann one. The kinetic model is given by molecular analogy with a finitely extensible non-linear elastic (FENE) dumbbell and is deterministically solved through an equivalent Fokker–Planck equation. The key features of the proposed approach are: (i) a proper scaling and coupling between the micro lattice-Boltzmann solution and the macro finite-volume one; (ii) a fast microscopic solver thanks to an implementation for Graphic Processing Unit (GPU) and the local adaptivity of the lattice-Boltzmann mesh; (iii) an operator-splitting algorithm for the convection of the macroscopic viscoelastic stresses instead of the whole probability density of the dumbbell configuration. This latter feature allows the application of the proposed method to non-homogeneous flow conditions with low memory-storage requirements. The model optimization is achieved through an extensive analysis of the lattice-Boltzmann solution, which finally provides control on the numerical error and on the computational time. The resulting micro–macro model is validated against the benchmark problem of a viscoelastic flow past a confined cylinder and the results obtained confirm the validity of the approach.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/84622013-01-01T00:00:00ZBERGAMASCO, LucaIZQUIERDO, SalvadorAMMAR, AmineMicro–macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro–macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation by a lattice-Boltzmann one. The kinetic model is given by molecular analogy with a finitely extensible non-linear elastic (FENE) dumbbell and is deterministically solved through an equivalent Fokker–Planck equation. The key features of the proposed approach are: (i) a proper scaling and coupling between the micro lattice-Boltzmann solution and the macro finite-volume one; (ii) a fast microscopic solver thanks to an implementation for Graphic Processing Unit (GPU) and the local adaptivity of the lattice-Boltzmann mesh; (iii) an operator-splitting algorithm for the convection of the macroscopic viscoelastic stresses instead of the whole probability density of the dumbbell configuration. This latter feature allows the application of the proposed method to non-homogeneous flow conditions with low memory-storage requirements. The model optimization is achieved through an extensive analysis of the lattice-Boltzmann solution, which finally provides control on the numerical error and on the computational time. The resulting micro–macro model is validated against the benchmark problem of a viscoelastic flow past a confined cylinder and the results obtained confirm the validity of the approach.On the solution of the multidimensional Langer’s equation using the proper generalized decomposition method for modeling phase transitions
http://hdl.handle.net/10985/8479
On the solution of the multidimensional Langer’s equation using the proper generalized decomposition method for modeling phase transitions
LAMARI, Hajer; AMMAR, Amine; LEYGUE, Adrien; CHINESTA, Francisco
The dynamics of phase transition in a binary mixture occurring during a quench is studied taking into account composition fluctuations by solving Langer’s equation in a domain composed of a certain number of micro-domains. The resulting Langer’s equation governing the evolution of the distribution function becomes multidimensional. Circumventing the curse of dimensionality the proper generalized decomposition is applied. The influence of the interaction parameter in the vicinity of the critical point is analyzed. First we address the case of a system composed of a single micro-domain in which phase transition occurs by a simple symmetry change. Next, we consider a system composed of two micro-domains in which phase transition occurs by phase separation, with special emphasis on the effect of the Landau free energy non-local term. Finally, some systems consisting of many micro-domains are considered.
http://dx.doi.org/10.1088/0965-0393/20/1/015007
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/84792012-01-01T00:00:00ZLAMARI, HajerAMMAR, AmineLEYGUE, AdrienCHINESTA, FranciscoThe dynamics of phase transition in a binary mixture occurring during a quench is studied taking into account composition fluctuations by solving Langer’s equation in a domain composed of a certain number of micro-domains. The resulting Langer’s equation governing the evolution of the distribution function becomes multidimensional. Circumventing the curse of dimensionality the proper generalized decomposition is applied. The influence of the interaction parameter in the vicinity of the critical point is analyzed. First we address the case of a system composed of a single micro-domain in which phase transition occurs by a simple symmetry change. Next, we consider a system composed of two micro-domains in which phase transition occurs by phase separation, with special emphasis on the effect of the Landau free energy non-local term. Finally, some systems consisting of many micro-domains are considered.