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Yoichiro Matsumoto - One of the best experts on this subject based on the ideXlab platform.
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AJK2011-04001 A FULL Eulerian FINITE DIFFERENCE METHOD FOR HYPERELASTIC PARTICLES IN FLUID FLOWS
2020Co-Authors: Kazuyasu Sugiyama, Shintaro Takeuchi, Shu Takagi, Yoichiro MatsumotoAbstract:ABSTRACT A full Eulerian finite difference method has been developed for solving a dynamic interaction problem between Newtonian fluid and hyperelastic material. It facilitates to simulate certain classes of problems, such that an initial and neutral configuration of a multi-component geometry converted from voxel-based data is provided on a fixed Cartesian mesh. A solid volume fraction, which has been widely used for multiphase flow simulations, is applied to describing the multicomponent geometry. The temporal change in the solid deformation is described in the Eulerian Frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for incompressible hyperelastic materials. The present Eulerian approach is confirmed to well reproduce the material deformation in the lid-driven flow and the particle-particle interaction in the Couette flow computed by means of the finite element method. It is applied to a Poiseuille flow containing biconcave neo-Hookean particles. The deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. INTRODUCTION Numerical simulations of Fluid-Structure Interaction (FSI) problems would make it possible to predict the effect of a medical treatment and help one decide the treatment strategy in clinical practice. In particular, a blood flow simulation is expected to contribute to assisting the surgical planning of a cardiovascular disease and a brain aneurysm. Recently, there are growing expectations for its applications along with a progress in imaging and computational technologies. It is also expected to contribute to the field of life science, such as in the understanding of the very essence of life and the demonstration of pathological mechanisms. It is of great importance to develop numerical techniques suitable for the characteristics of body tissues, which are flexible and complicated in shape, when attempting to rationalize and to generalize the fluidstructure coupled analyses. The expectations include the further understandings of the micro/mesoscopic behavior of the flexibly deformable Red Blood Cells (RBCs) in plasma useful for evaluating the macroscopic blood rheology, and the thrombosis formation as aggregation of platelets, of which th
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a full Eulerian finite difference approach for solving fluid structure coupling problems
Journal of Computational Physics, 2011Co-Authors: Kazuyasu Sugiyama, Shintaro Takeuchi, Shu Takagi, Yoichiro MatsumotoAbstract:A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation [Hirt, Nichols, J. Comput. Phys. 39 (1981) 201], which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian Frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.
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Full Eulerian simulations of biconcave neo-Hookean particles in a Poiseuille flow
Computational Mechanics, 2010Co-Authors: Kazuyasu Sugiyama, Satoshi, Shintaro Takeuchi, Shu Takagi, Yoichiro MatsumotoAbstract:For a given initial configuration of a multi-component geometry represented by voxel-based data on a fixed Cartesian mesh, a full Eulerian finite difference method facilitates solution of dynamic interaction problems between Newtonian fluid and hyperelastic material. The solid volume fraction, and the left Cauchy–Green deformation tensor are temporally updated on the Eulerian Frame, respectively, to distinguish the fluid and solid phases, and to describe the solid deformation. The simulation method is applied to two- and three-dimensional motions of two biconcave neo-Hookean particles in a Poiseuille flow. Similar to the numerical study on the red blood cell motion in a circular pipe (Gong et al. in J Biomech Eng 131:074504, 2009), in which Skalak’s constitutive laws of the membrane are considered, the deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. The present Eulerian approach is demonstrated that it has the potential to be easily extended to larger system problems involving a large number of particles of complicated geometries.
Brian K. Kendrick - One of the best experts on this subject based on the ideXlab platform.
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a new method for solving the quantum hydrodynamic equations of motion application to two dimensional reactive scattering
Journal of Chemical Physics, 2004Co-Authors: Denise Pauler, Brian K. KendrickAbstract:The de Broglie–Bohm hydrodynamic equations of motion are solved using a meshless method based on a moving least squares approach and an arbitrary Lagrangian–Eulerian Frame of reference. A regridding algorithm adds and deletes computational points as needed in order to maintain a uniform interparticle spacing, and unitary time evolution is obtained by propagating the wave packet using averaged fields. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. The methodology is applied to a two-dimensional model collinear reaction with an activation barrier. Reaction probabilities are computed as a function of both time and energy, and are in excellent agreement with those based on the quantum trajectory method.
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a new method for solving the quantum hydrodynamic equations of motion application to two dimensional reactive scattering
Journal of Chemical Physics, 2004Co-Authors: Denise Pauler, Brian K. KendrickAbstract:The de Broglie–Bohm hydrodynamic equations of motion are solved using a meshless method based on a moving least squares approach and an arbitrary Lagrangian–Eulerian Frame of reference. A regridding algorithm adds and deletes computational points as needed in order to maintain a uniform interparticle spacing, and unitary time evolution is obtained by propagating the wave packet using averaged fields. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. The methodology is applied to a two-dimensional model collinear reaction with an activation barrier. Reaction probabilities are computed as a function of both time and energy, and are in excellent agreement with those based on the quantum trajectory method.
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a new method for solving the quantum hydrodynamic equations of motion
Journal of Chemical Physics, 2003Co-Authors: Brian K. KendrickAbstract:The quantum hydrodynamic equations associated with the de Broglie–Bohm formulation of quantum mechanics are solved using a meshless method based on a moving least squares approach. An arbitrary Lagrangian–Eulerian Frame of reference is used which significantly improves the accuracy and stability of the method when compared to an approach based on a purely Lagrangian Frame of reference. A regridding algorithm is implemented which adds and deletes points when necessary in order to maintain accurate and stable calculations. It is shown that unitarity in the time evolution of the quantum wave packet is significantly improved by propagating using averaged fields. As nodes in the reflected wave packet start to form, the quantum potential and force become very large and numerical instabilities occur. By introducing artificial viscosity into the equations of motion, these instabilities can be avoided and the stable propagation of the wave packet for very long times becomes possible. Results are presented for the ...
Arif Masud - One of the best experts on this subject based on the ideXlab platform.
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residual based turbulence models and arbitrary lagrangian Eulerian Framework for free surface flows
Mathematical Models and Methods in Applied Sciences, 2015Co-Authors: Ramon Calderer, Lixing Zhu, Richard Gibson, Arif MasudAbstract:We present a residual-based turbulence model for problems with free surfaces. The method is derived based on variational multiscale ideas that assume a decomposition of the solution fields into overlapping scales that are termed as coarse and fine scales. The fine scales are further split hierarchically into fine-scales level-I and fine-scales level-II. The hierarchical variational problems that govern the two fine-scale components are modeled employing bubble functions approach. The model for level-II scales is variationally embedded in the mixed field level-I problem to yield a stable level-I formulation. Subsequently, the model for level-I scales that in fact constitutes the fine-scale turbulence model is then variationally injected in the coarse-scale variational form. A significant feature of the method is that it does not contain any embedded tunable parameters. To accommodate the moving boundaries we cast the formulation in an arbitrary Lagrangian–Eulerian Frame of reference. The free surface boundary condition is imposed weakly which results in a formulation that conserves the volume of the fluid. A variety of benchmark problems show the accuracy and range of applicability of the proposed formulation and results are compared with published data. A wavy bed problem is investigated to show the interaction of turbulence generated at the bottom surface with the free surface thereby leading to irregular free surface elevations.
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Effects of Mesh Motion on the Stability and Convergence of ALE Based Formulations for Moving Boundary Flows
Computational Mechanics, 2006Co-Authors: Arif MasudAbstract:This paper investigates the effects of mesh motion on the stability of fluid-flow equations when written in an Arbitrary Lagrangian–Eulerian Frame for solving moving boundary flow problems. Employing the advection-diffusion equation as a model problem we present a mathematical proof of the destabilizing effects induced by an arbitrary mesh motion on the stability and convergence of an otherwise stable scheme. We show that the satisfaction of the so-called geometric conservation laws is essential to the development of an identity that plays a crucial role in establishing stability. We explicitly show that the advection dominated case is susceptible to growth in error because of the motion of the computational grid. To retain the bound on the growth in error, the mesh motion techniques need to account for a domain based constraint that minimizes the relative mesh velocity. Analysis presented in this work can also be extended to the Navier–Stokes equations when written in an ALE Frame for FSI problems.
Schumacher Jörg - One of the best experts on this subject based on the ideXlab platform.
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Lagrangian heat transport in turbulent three-dimensional convection
'American Physical Society (APS)', 2021Co-Authors: Vieweg, Philipp P., Schneide Christiane, Padberg-gehle Kathrin, Schumacher JörgAbstract:Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-B\'{e}nard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CS) which we investigate here in direct numerical simulations in convection cells with square cross section of aspect ratio $\Gamma = 16$, Rayleigh number $Ra = 10^{5}$, and Prandtl numbers $Pr = 0.1, 0.7$ and $7$. The analysis is based on $N=524,288$ Lagrangian tracer particles which are advected in the time-dependent flow. Clusters of trajectories are identified by a graph Laplacian with a diffusion kernel, which quantifies the connectivity of trajectory segments, and a subsequent sparse eigenbasis approximation (SEBA) for cluster detection. The combination of graph Laplacian and SEBA leads to a significantly improved cluster identification that is compared with the large-scale patterns in the Eulerian Frame of reference. We show that the detected CS contribute by a third less to the global turbulent heat transport for all investigated $Pr$ compared to the trajectories in the spatial complement. This is realized by monitoring Nusselt numbers along the tracer trajectory ensembles, a dimensionless local measure of heat transfer.Comment: 8 pages, 5 figure
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Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-B\'enard convection flows
2021Co-Authors: Schneide Christiane, Vieweg, Philipp P., Schumacher Jörg, Padberg-gehle KathrinAbstract:We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless fluid tracers that are advected in the flow. Coherent sets result from trajectories that stay closely together under the dynamics of the turbulent flow. For longer times, they are always destroyed by the intrinsic turbulent dispersion of material transport. Here, this constraint is overcome by the application of evolutionary clustering algorithms that add a time memory to the coherent set detection and allow individual trajectories to leak in or out of evolving clusters. Evolutionary clustering thus also opens the possibility to monitor the splits and mergers of coherent sets. These rare dynamic events leave clear footprints in the evolving eigenvalue spectrum of the Laplacian matrix of the trajectory network in both convection flows. The Lagrangian trajectories reveal the individual pathways of convective heat transfer across the fluid layer. We identify the long-term coherent sets as those fluid flow regions that contribute least to heat transfer. Thus, our evolutionary Framework defines a complementary perspective on the slow dynamics of turbulent superstructure patterns in convection flows that were recently discussed in the Eulerian Frame of reference. The presented Framework might be well suited for studies in natural flows which are typically based on sparse information from drifters and probes
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Lagrangian coherent sets in turbulent Rayleigh-B\'enard convection
'American Physical Society (APS)', 2019Co-Authors: Schneide Christiane, Padberg-gehle Kathrin, Stahn Martin, Pandey Ambrish, Junge Oliver, Koltai Péter, Schumacher JörgAbstract:Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh--B\'{e}nard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number ${\rm Ra}=10^6$ and at a Prandtl number ${\rm Pr}=10$. Three different Lagrangian analysis techniques based on graph Laplacians -- distance spectral trajectory clustering, time-averaged diffusion maps and finite-element based dynamic Laplacian discretization -- are used to monitor the turbulent fields along trajectories of massless Lagrangian particles in the evolving turbulent convection flow. The three methods are compared to each other and the obtained coherent sets are related to results from an analysis in the Eulerian Frame of reference. We show that the results of these methods agree with each other and that Lagrangian and Eulerian coherent sets form basically a disjoint union of the flow domain. Additionally, a windowed time-averaging of variable interval length is performed to study the degree of coherence as a function of this additional coarse graining which removes small-scale fluctuations that cause trajectories to disperse quickly. Finally, the coherent set Framework is extended to study heat transport
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Lagrangian coherent sets in turbulent Rayleigh-Bénard convection
'American Physical Society (APS)', 2019Co-Authors: Ch. Schneide, Padberg-gehle Kathrin, Stahn Martin, Junge Oliver, Koltai Péter, Pandey A., Schumacher JörgAbstract:Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh-Bénard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number Ra=10^6 and at a Prandtl number Pr=10. Three different Lagrangian analysis techniques based on graph Laplacians (distance spectral trajectory clustering, time-averaged diffusion maps, and finite-element based dynamic Laplacian discretization) are used to monitor the turbulent fields along trajectories of massless Lagrangian particles in the evolving turbulent convection flow. The three methods are compared to each other and the obtained coherent sets are related to results from an analysis in the Eulerian Frame of reference. We show that the results of these methods agree with each other and that Lagrangian and Eulerian coherent sets form basically a disjoint union of the flow domain. Additionally, a windowed time averaging of variable interval length is performed to study the degree of coherence as a function of this additional coarse graining which removes small-scale fluctuations that cause trajectories to disperse quickly. Finally, the coherent set Framework is extended to study heat transport
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Comparison of Lagrangian and Eulerian Frames of passive scalar turbulent mixing
'American Physical Society (APS)', 2019Co-Authors: Götzfried Paul, Emran Mohammad, Villermaux Emmanuel, Schumacher JörgAbstract:International audienceThe mixing of a passive scalar in a three-dimensional, statistically stationary turbulent Navier-Stokes flow at a constant and moderate Taylor microscale Reynolds number R λ = 42 is studied by means of direct numerical simulations for Schmidt numbers between 1 and 64. The freely decaying passive scalar is represented in two different ways: (1) in the Lagrangian Frame of reference as a cloud of up to 4.8 billion individually advected massless tracer particles subject to a stochastic Wiener process along the tracer tracks that describes scalar diffusion or (2) in the standard Eulerian Frame of reference as an advection-diffusion equation of the continuum concentration field. In both cases, the scalar is initially seeded in a small cubic subvolume. The mean mixing time t s is determined by the mean compressive strain rate λ 3 < 0 which is obtained from the probability density functions of the local finite-time Lyapunov exponents in the Lagrangian Frame, λ i (t) with i = 1, 2 and 3. The direct comparison of freely decaying Lagrangian and Eulerian passive scalars gives a good agreement of the scalar variance for times t 10 t s and for the probability density functions P(, t) taken with respect to the whole simulation domain. We also show how the multilayer aggregations of scalar filaments and sheets in the Lagrangian Frame are increasingly influenced by the noise due to discreteness with progressing dilution of the initially high tracer particle concentration. This limits the Lagrangian approach in its present form and for the obtainable Schmidt numbers to studies of shorter time periods. A simple one-dimensional advection-diffusion model of a solitary strip is finally applied to the problem at hand to derive the probability density function of the scalar concentration, P(, t), from the one of the compressive local finite-time Lyapunov exponent, p(λ 3 , t). Model prediction with and without self-convolution and numerical data of the scalar distributions agree qualitatively, however with quantitative differences particularly for small scalar concentrations. The present Lagrangian approach to passive scalar mixing in turbulence opens the application of more flexible passive scalar injection and boundary conditions and allows to relax the resolution constraints for high-Schmidt number mixing studies
Jungho Hwang - One of the best experts on this subject based on the ideXlab platform.
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numerical investigation of particle transport hydrodynamics and coal combustion in an industrial scale circulating fluidized bed combustor effects of coal feeder positions and coal feeding rates
Fuel, 2017Co-Authors: Massoud Massoudi Farid, Hyo Jae Jeong, Keun Ho Kim, Jongmi Lee, Dongwo Kim, Jungho HwangAbstract:Abstract This study investigates particle transport hydrodynamics and coal combustion in an industrial-scale circulating fluidized bed (CFB) combustor using the dense discrete phase model (DDPM). DDPM is an extension of the discrete phase model (DPM); however, unlike the standard formulation of DPM, DDPM considers the solid volume fraction when solving the Navier–Stokes equations for the gas phase. In the DDPM, the kinetic theory of granular flows is used to calculate the particle interaction in the Eulerian Frame of reference. This interaction is then mapped to the particles in the Lagrangian Frame of reference. In this study, user defined functions (UDFs) were used to extend the ANSYS FLUENT original code. These UDFs were used to reinject particles into to the combustor (cyclones were not modeled), calculate the pressure drop, circulation rate, and combustor mass load control. Various operation indexes such as distributions of gas temperature, solid volume fraction, pressure, and mass fractions of combustion products were displayed, and the selected indexes were compared with operating data obtained from a 340 MWe CFB combustor located in Yeosu, South Korea. The effects of both coal feeder positions and coal feeding rates on operation indexes were investigated.
