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Henrik Bruus - One of the best experts on this subject based on the ideXlab platform.
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a numerical study of two phase Stokes Flow in an axisymmetric Flow focusing device
Physics of Fluids, 2006Co-Authors: Mads Jakob Herring Jensen, Howard A Stone, Henrik BruusAbstract:We present a numerical investigation of the time-dependent dynamics of the creation of gas bubbles in an axisymmetric Flow-focusing device. The liquid motion is treated as a Stokes Flow, and using a generic framework we implement a second-order time-integration scheme and a free-surface model in MATLAB, which interfaces with the finite-element software FEMLAB. We derive scaling laws for the volume of a created bubble and for the gas Flow rate, and confirm them numerically. Our results are consistent with existing experimental results by Garstecki et al. [Phys. Rev. Lett. 94, 164501 (2005)], and predict a scaling yet to be observed: the bubble volume scales with the outlet channel radius to the power of 4 and the surface tension. Our axisymmetric simulations further show that the collapse of the gas thread before bubble snap-off is different from the recent experimental results. We suggest that this difference is caused by differences in geometry between experiments and the simulations.
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a high level programming language implementation of topology optimization applied to steady state navier Stokes Flow
International Journal for Numerical Methods in Engineering, 2006Co-Authors: Laurits Hojgaard Olesen, Fridolin Okkels, Henrik BruusAbstract:We present a versatile high-level programming-language implementation of non-linear topology optimization. Our implementation is based on the commercial software package FEMLAB, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier–Stokes Flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes Flow (Int. J. Num. Meth. Fluids 2003; 41:77–107). We analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as FEMLAB code in an appendix. Copyright © 2005 John Wiley & Sons, Ltd.
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a high level programming language implementation of topology optimization applied to steady state navier Stokes Flow
International Journal for Numerical Methods in Engineering, 2006Co-Authors: Laurits Hojgaard Olesen, Fridolin Okkels, Henrik BruusAbstract:We present a versatile high-level programming-language implementation of non-linear topology optimization. Our implementation is based on the commercial software package FEMLAB, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier–Stokes Flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes Flow (Int. J. Num. Meth. Fluids 2003; 41:77–107). We analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as FEMLAB code in an appendix. Copyright © 2005 John Wiley & Sons, Ltd.
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a high level programming language implementation of topology optimization applied to steady state navier Stokes Flow
arXiv: Fluid Dynamics, 2004Co-Authors: Laurits Hojgaard Olesen, Fridolin Okkels, Henrik BruusAbstract:We present a versatile high-level programming-language implementation of nonlinear topology optimization. Our implementation is based on the commercial software package Femlab, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier-Stokes Flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes Flow [Int. J. Num. Meth. Fluids 2003; 41:77--107]. We analyze the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as Femlab code in an appendix.
Laurits Hojgaard Olesen - One of the best experts on this subject based on the ideXlab platform.
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a high level programming language implementation of topology optimization applied to steady state navier Stokes Flow
International Journal for Numerical Methods in Engineering, 2006Co-Authors: Laurits Hojgaard Olesen, Fridolin Okkels, Henrik BruusAbstract:We present a versatile high-level programming-language implementation of non-linear topology optimization. Our implementation is based on the commercial software package FEMLAB, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier–Stokes Flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes Flow (Int. J. Num. Meth. Fluids 2003; 41:77–107). We analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as FEMLAB code in an appendix. Copyright © 2005 John Wiley & Sons, Ltd.
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a high level programming language implementation of topology optimization applied to steady state navier Stokes Flow
International Journal for Numerical Methods in Engineering, 2006Co-Authors: Laurits Hojgaard Olesen, Fridolin Okkels, Henrik BruusAbstract:We present a versatile high-level programming-language implementation of non-linear topology optimization. Our implementation is based on the commercial software package FEMLAB, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier–Stokes Flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes Flow (Int. J. Num. Meth. Fluids 2003; 41:77–107). We analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as FEMLAB code in an appendix. Copyright © 2005 John Wiley & Sons, Ltd.
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a high level programming language implementation of topology optimization applied to steady state navier Stokes Flow
arXiv: Fluid Dynamics, 2004Co-Authors: Laurits Hojgaard Olesen, Fridolin Okkels, Henrik BruusAbstract:We present a versatile high-level programming-language implementation of nonlinear topology optimization. Our implementation is based on the commercial software package Femlab, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier-Stokes Flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes Flow [Int. J. Num. Meth. Fluids 2003; 41:77--107]. We analyze the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as Femlab code in an appendix.
Fridolin Okkels - One of the best experts on this subject based on the ideXlab platform.
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a high level programming language implementation of topology optimization applied to steady state navier Stokes Flow
International Journal for Numerical Methods in Engineering, 2006Co-Authors: Laurits Hojgaard Olesen, Fridolin Okkels, Henrik BruusAbstract:We present a versatile high-level programming-language implementation of non-linear topology optimization. Our implementation is based on the commercial software package FEMLAB, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier–Stokes Flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes Flow (Int. J. Num. Meth. Fluids 2003; 41:77–107). We analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as FEMLAB code in an appendix. Copyright © 2005 John Wiley & Sons, Ltd.
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a high level programming language implementation of topology optimization applied to steady state navier Stokes Flow
International Journal for Numerical Methods in Engineering, 2006Co-Authors: Laurits Hojgaard Olesen, Fridolin Okkels, Henrik BruusAbstract:We present a versatile high-level programming-language implementation of non-linear topology optimization. Our implementation is based on the commercial software package FEMLAB, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier–Stokes Flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes Flow (Int. J. Num. Meth. Fluids 2003; 41:77–107). We analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as FEMLAB code in an appendix. Copyright © 2005 John Wiley & Sons, Ltd.
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a high level programming language implementation of topology optimization applied to steady state navier Stokes Flow
arXiv: Fluid Dynamics, 2004Co-Authors: Laurits Hojgaard Olesen, Fridolin Okkels, Henrik BruusAbstract:We present a versatile high-level programming-language implementation of nonlinear topology optimization. Our implementation is based on the commercial software package Femlab, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier-Stokes Flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes Flow [Int. J. Num. Meth. Fluids 2003; 41:77--107]. We analyze the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as Femlab code in an appendix.
Mikito Furuichi - One of the best experts on this subject based on the ideXlab platform.
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implicit solution of the material transport in Stokes Flow simulation toward thermal convection simulation surrounded by free surface
Computer Physics Communications, 2015Co-Authors: Mikito FuruichiAbstract:Abstract We present implicit time integration schemes suitable for modeling free surface Stokes Flow dynamics with marker in cell (MIC) based spatial discretization. Our target is for example thermal convection surrounded by deformable surface boundaries to simulate the long term planetary formation process. The numerical system becomes stiff when the dynamical balancing time scale for the increasing/decreasing load by surface deformation is very short compared with the time scale associated with thermal convection. Any explicit time integration scheme will require very small time steps; otherwise, serious numerical oscillation (spurious solutions) will occur. The implicit time integration scheme possesses a wider stability region than the explicit method; therefore, it is suitable for stiff problems. To investigate an efficient solution method for the stiff Stokes Flow system, we apply first (backward Euler (BE)) and second order (trapezoidal method (TR) and trapezoidal rule—backward difference formula (TR-BDF2)) accurate implicit methods for the MIC solution scheme. The introduction of implicit time integration schemes results in nonlinear systems of equations. We utilize a Jacobian free Newton Krylov (JFNK) based Newton framework to solve the resulting nonlinear equations. In this work we also investigate two efficient implicit solution strategies to reduce the computational cost when solving stiff nonlinear systems. The two methods differ in how the advective term in the material transport evolution equation is treated. We refer to the method that employs Lagrangian update as “fully implicit” (Imp), whilst the method that employs Eulerian update is referred to as “semi-implicit” (SImp). Using a finite difference (FD) method, we have performed a series of numerical experiments which clarify the accuracy of solutions and trade-off between the computational cost associated with the nonlinear solver and time step size. In comparison with the general explicit Euler method, the second order accurate Imp methods reduce total computational cost successfully through the utilization of a large time step without sacrificing accuracy and stability. Moreover, the proposed SImp method is effective in reducing the computational cost associated with evaluating the nonlinear residual while obtaining a solution similar to the Imp method.
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implicit solution of the material transport in Stokes Flow simulation toward thermal convection simulation surrounded by free surface
Computer Physics Communications, 2015Co-Authors: Mikito FuruichiAbstract:Abstract We present implicit time integration schemes suitable for modeling free surface Stokes Flow dynamics with marker in cell (MIC) based spatial discretization. Our target is for example thermal convection surrounded by deformable surface boundaries to simulate the long term planetary formation process. The numerical system becomes stiff when the dynamical balancing time scale for the increasing/decreasing load by surface deformation is very short compared with the time scale associated with thermal convection. Any explicit time integration scheme will require very small time steps; otherwise, serious numerical oscillation (spurious solutions) will occur. The implicit time integration scheme possesses a wider stability region than the explicit method; therefore, it is suitable for stiff problems. To investigate an efficient solution method for the stiff Stokes Flow system, we apply first (backward Euler (BE)) and second order (trapezoidal method (TR) and trapezoidal rule—backward difference formula (TR-BDF2)) accurate implicit methods for the MIC solution scheme. The introduction of implicit time integration schemes results in nonlinear systems of equations. We utilize a Jacobian free Newton Krylov (JFNK) based Newton framework to solve the resulting nonlinear equations. In this work we also investigate two efficient implicit solution strategies to reduce the computational cost when solving stiff nonlinear systems. The two methods differ in how the advective term in the material transport evolution equation is treated. We refer to the method that employs Lagrangian update as “fully implicit” (Imp), whilst the method that employs Eulerian update is referred to as “semi-implicit” (SImp). Using a finite difference (FD) method, we have performed a series of numerical experiments which clarify the accuracy of solutions and trade-off between the computational cost associated with the nonlinear solver and time step size. In comparison with the general explicit Euler method, the second order accurate Imp methods reduce total computational cost successfully through the utilization of a large time step without sacrificing accuracy and stability. Moreover, the proposed SImp method is effective in reducing the computational cost associated with evaluating the nonlinear residual while obtaining a solution similar to the Imp method.
Qing Li - One of the best experts on this subject based on the ideXlab platform.
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a variational level set method for the topology optimization of steady state navier Stokes Flow
Journal of Computational Physics, 2008Co-Authors: Shiwei Zhou, Qing LiAbstract:The smoothness of topological interfaces often largely affects the fluid optimization and sometimes makes the density-based approaches, though well established in structural designs, inadequate. This paper presents a level-set method for topology optimization of steady-state Navier-Stokes Flow subject to a specific fluid volume constraint. The solid-fluid interface is implicitly characterized by a zero-level contour of a higher-order scalar level set function and can be naturally transformed to other configurations as its host moves. A variational form of the cost function is constructed based upon the adjoint variable and Lagrangian multiplier techniques. To satisfy the volume constraint effectively, the Lagrangian multiplier derived from the first-order approximation of the cost function is amended by the bisection algorithm. The procedure allows evolving initial design to an optimal shape and/or topology by solving the Hamilton-Jacobi equation. Two classes of benchmarking examples are presented in this paper: (1) periodic microstructural material design for the maximum permeability; and (2) topology optimization of Flow channels for minimizing energy dissipation. A number of 2D and 3D examples well demonstrated the feasibility and advantage of the level-set method in solving fluid-solid shape and topology optimization problems.