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Cassio M. Oishi - One of the best experts on this subject based on the ideXlab platform.
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Numerical study of the Stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids
Physics of Fluids, 2019Co-Authors: Jonathan D. Evans, J. A. Cuminato, I. L. Palhares Junior, Cassio M. OishiAbstract:Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives improved convergence results both temporally and spatially near to the singularity while maintaining the same global flow characteristics as the Cartesian.Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives...
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Numerical study of the Stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids
Physics of Fluids, 2019Co-Authors: Jonathan D. Evans, J. A. Cuminato, I. L. Palhares Junior, Cassio M. OishiAbstract:Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives...
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Application of the Natural Stress formulation for solving unsteady viscoelastic contraction flows
Journal of Computational Physics, 2019Co-Authors: Jonathan D. Evans, Hugo L. França, Cassio M. OishiAbstract:Abstract We present a numerical scheme for a previously unexploited formulation of the equations for unsteady viscoelastic flow. The formulation aligns the polymer Stress along particle paths/streamlines, utilising the characteristic curves associated with the hyperbolic part of the constitutive equations. We illustrate the approach for the Oldroyd-B model in the benchmark 4:1 contraction for moderate elasticity numbers. We show that the scheme is able to accurately capture the re-entrant corner singularity for the polymer Stresses and the pressure, the latter variable being inaccurately determined by schemes using the traditional formulation in terms of Cartesian polymer Stresses. A space-step restriction for stability is derived, which can be numerically limiting in certain recirculation regions. This contrasts with the equivalent space-step restriction for the formulation in Cartesian Stresses, which is limiting in flow regions of high velocity gradients, for example, at sharp corners in contraction flows.
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Transient computations using the Natural Stress formulation for solving sharp corner flows
Journal of Non-Newtonian Fluid Mechanics, 2017Co-Authors: Jonathan D. Evans, Cassio M. OishiAbstract:Abstract In this short communication, we analyse the potential of the Natural Stress formulation (NSF) (i.e. aligning the Stress basis along streamlines) for computing planar flows of an Oldroyd-B fluid around sharp corners. This is the first attempt to combine the NSF into a numerical strategy for solving a transient fluid flow problem considering the momentum equation in Navier–Stokes form (the elastic Stress entering as a source term) and using the constitutive equations for Natural Stress variables. Preliminary results of the NSF are motivating in the sense that accuracy of the numerical solution for the extra Stress tensor is improved near to the sharp corner. Comparison studies among the NSF and the Cartesian Stress formulation (CSF) (i.e. using a fixed Cartesian Stress basis) are conducted in a typical benchmark viscoelastic fluid flow involving a sharp corner: the 4 : 1 contraction. The CSF needs a mesh approximately 10 times smaller to capture similar near singularity results to the NSF.
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Testing viscoelastic numerical schemes using the Oldroyd-B fluid in Newtonian kinematics
Applied Mathematics and Computation, 1Co-Authors: Jonathan D. Evans, I. L. Palhares Junior, H.l. França, Cassio M. OishiAbstract:Abstract We focus here on using a Newtonian velocity field to evaluate numerical schemes for two different formulations of viscoelastic flow. The two distinct formulations we consider, correspond to either using a fixed basis for the elastic Stress or one that uses the flow directions or streamlines. The former is the traditional Cartesian Stress formulation, whilst the later may be referred to as the Natural Stress formulation of the equations. We choose the Oldroyd-B fluid and three benchmarks in computational rheology: the 4:1 contraction flow, the stick-slip and cross-slot problems. In the context of the contraction flow, fixing the kinematics as Newtonian, actually gives a larger Stress singularity at the re-entrant corner, the matched asymptotics of which are presented here. Numerical results for temporal and spatial convergence of the two formulations are compared first in this decoupled velocity and elastic Stress situation, to assess the performance of the two approaches. This may be regarded as an intermediate test case before proceeding to the far more difficult fully coupled velocity and Stress situation. We also present comparison results between numerics and asymptotics for the stick-slip problem. Finally, the Natural Stress formulation is used to investigate the cross-slot problem, again in a Newtonian velocity field.
Jonathan D. Evans - One of the best experts on this subject based on the ideXlab platform.
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Numerical study of the Stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids
Physics of Fluids, 2019Co-Authors: Jonathan D. Evans, J. A. Cuminato, I. L. Palhares Junior, Cassio M. OishiAbstract:Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives...
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Numerical study of the Stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids
Physics of Fluids, 2019Co-Authors: Jonathan D. Evans, J. A. Cuminato, I. L. Palhares Junior, Cassio M. OishiAbstract:Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives improved convergence results both temporally and spatially near to the singularity while maintaining the same global flow characteristics as the Cartesian.Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives...
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Application of the Natural Stress formulation for solving unsteady viscoelastic contraction flows
Journal of Computational Physics, 2019Co-Authors: Jonathan D. Evans, Hugo L. França, Cassio M. OishiAbstract:Abstract We present a numerical scheme for a previously unexploited formulation of the equations for unsteady viscoelastic flow. The formulation aligns the polymer Stress along particle paths/streamlines, utilising the characteristic curves associated with the hyperbolic part of the constitutive equations. We illustrate the approach for the Oldroyd-B model in the benchmark 4:1 contraction for moderate elasticity numbers. We show that the scheme is able to accurately capture the re-entrant corner singularity for the polymer Stresses and the pressure, the latter variable being inaccurately determined by schemes using the traditional formulation in terms of Cartesian polymer Stresses. A space-step restriction for stability is derived, which can be numerically limiting in certain recirculation regions. This contrasts with the equivalent space-step restriction for the formulation in Cartesian Stresses, which is limiting in flow regions of high velocity gradients, for example, at sharp corners in contraction flows.
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Transient computations using the Natural Stress formulation for solving sharp corner flows
Journal of Non-Newtonian Fluid Mechanics, 2017Co-Authors: Jonathan D. Evans, Cassio M. OishiAbstract:Abstract In this short communication, we analyse the potential of the Natural Stress formulation (NSF) (i.e. aligning the Stress basis along streamlines) for computing planar flows of an Oldroyd-B fluid around sharp corners. This is the first attempt to combine the NSF into a numerical strategy for solving a transient fluid flow problem considering the momentum equation in Navier–Stokes form (the elastic Stress entering as a source term) and using the constitutive equations for Natural Stress variables. Preliminary results of the NSF are motivating in the sense that accuracy of the numerical solution for the extra Stress tensor is improved near to the sharp corner. Comparison studies among the NSF and the Cartesian Stress formulation (CSF) (i.e. using a fixed Cartesian Stress basis) are conducted in a typical benchmark viscoelastic fluid flow involving a sharp corner: the 4 : 1 contraction. The CSF needs a mesh approximately 10 times smaller to capture similar near singularity results to the NSF.
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Re-entrant corner flow for PTT fluids in the Natural Stress basis
Journal of Non-newtonian Fluid Mechanics, 2008Co-Authors: Jonathan D. Evans, David N. SibleyAbstract:Abstract We revisit the situation of steady planar flow of Phan–Thien–Tanner (PTT) fluids around re-entrant corners of angles π / α where 1 / 2 ≤ α 1 . The model is considered in the absence of a solvent viscosity, under which a class of self-similar solutions has been identified with Stress singularities of O ( r − 2 ( 1 − α ) ) and stream function behaviour O ( r α ( 1 + α ) ) (r being the radial distance from the corner). The asymptotic analysis is completed by providing a solution for the downstream boundary layer using Natural Stress variables. We show that the matching of the outer (core) solution into the downstream boundary layer imposes a restriction on the range of α ∈ ( 2 / 3 , 1 ) for which these self-similar solutions are applicable, i.e. they only hold for corner angles between 180 ° and 270 ° .
I. L. Palhares Junior - One of the best experts on this subject based on the ideXlab platform.
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Numerical study of the Stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids
Physics of Fluids, 2019Co-Authors: Jonathan D. Evans, J. A. Cuminato, I. L. Palhares Junior, Cassio M. OishiAbstract:Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives improved convergence results both temporally and spatially near to the singularity while maintaining the same global flow characteristics as the Cartesian.Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives...
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Numerical study of the Stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids
Physics of Fluids, 2019Co-Authors: Jonathan D. Evans, J. A. Cuminato, I. L. Palhares Junior, Cassio M. OishiAbstract:Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives...
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Testing viscoelastic numerical schemes using the Oldroyd-B fluid in Newtonian kinematics
Applied Mathematics and Computation, 1Co-Authors: Jonathan D. Evans, I. L. Palhares Junior, H.l. França, Cassio M. OishiAbstract:Abstract We focus here on using a Newtonian velocity field to evaluate numerical schemes for two different formulations of viscoelastic flow. The two distinct formulations we consider, correspond to either using a fixed basis for the elastic Stress or one that uses the flow directions or streamlines. The former is the traditional Cartesian Stress formulation, whilst the later may be referred to as the Natural Stress formulation of the equations. We choose the Oldroyd-B fluid and three benchmarks in computational rheology: the 4:1 contraction flow, the stick-slip and cross-slot problems. In the context of the contraction flow, fixing the kinematics as Newtonian, actually gives a larger Stress singularity at the re-entrant corner, the matched asymptotics of which are presented here. Numerical results for temporal and spatial convergence of the two formulations are compared first in this decoupled velocity and elastic Stress situation, to assess the performance of the two approaches. This may be regarded as an intermediate test case before proceeding to the far more difficult fully coupled velocity and Stress situation. We also present comparison results between numerics and asymptotics for the stick-slip problem. Finally, the Natural Stress formulation is used to investigate the cross-slot problem, again in a Newtonian velocity field.
J. A. Cuminato - One of the best experts on this subject based on the ideXlab platform.
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Numerical study of the Stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids
Physics of Fluids, 2019Co-Authors: Jonathan D. Evans, J. A. Cuminato, I. L. Palhares Junior, Cassio M. OishiAbstract:Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives improved convergence results both temporally and spatially near to the singularity while maintaining the same global flow characteristics as the Cartesian.Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives...
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Numerical study of the Stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids
Physics of Fluids, 2019Co-Authors: Jonathan D. Evans, J. A. Cuminato, I. L. Palhares Junior, Cassio M. OishiAbstract:Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer Stress behavior around the Stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and Natural Stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The Natural Stress formulation gives...
Z. Y. Yang - One of the best experts on this subject based on the ideXlab platform.
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A Natural Stress boundary integral equation for calculating the near boundary Stress field
Computers & Structures, 2011Co-Authors: Changzheng Cheng, Zhongrong Niu, Naman Récho, Z. Y. YangAbstract:The Stress computational accuracy of internal points by conventional boundary element method becomes more and more deteriorate as the points approach to the boundary due to the nearly singular integrals including nearly strong singularity and hyper-singularity. For calculating the boundary Stress, a Natural boundary integral equation in which the boundary variables are the displacements, tractions and Natural boundary variables was established in the authors' previous work. Herein, a Natural Stress boundary integral equation (NSBIE) is further proposed by introducing the Natural variables to analyze the Stress field of interior points. There are only nearly strong singular integrals in the NSBIE, i.e., the singularity is reduced by one order. The regularization algorithm proposed by the authors is taken over to deal with these singular integrals. Consequently, the NSBIE can analyze the Stress field closer to the boundary. Numerical examples demonstrated that two orders of magnitude improvement in reducing the approaching degree can be achieved by NSBIE compared to the conventional one when the near boundary Stress field is evaluated. Furthermore, this new way is extended to the multi-domain elasticity problem to calculate the Stress field near the boundary and interface.
