Level set topology optimization of scalar transport problems

Makhija, David; Maute, Kurt

doi:10.1007/s00158-014-1142-7

Cited by 23 publications

(18 citation statements)

References 73 publications

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“…In this example, we apply our CutFEM framework to the modeling and optimizing of a micromixer at a low Reynolds number and steady-state conditions. The example is the 3D analog to the 2D problem found in [35], and is similar to the micromixer studies with flow topology optimization found in [69], [70] and [71]. The problem setup is shown in Figure 15.…”

Section: Design Of a Micromixermentioning

confidence: 77%

“…where r φ is the filter radius. The linear filter was used previously in the studies of [34,35] to widen the zone of influence of the optimization variables, and to improve the convergence rate. Furthermore, the filter may promote (but does not guarantee) smooth shapes of the phase boundaries; however, in contrast to density or sensitivity filters used in density methods, the filter above does not guarantee control of the minimum feature size [43].…”

Section: Topology Optimizationmentioning

confidence: 99%

“…For a general overview of the XFEM, the reader is referred to [33]. In the context of topology optimization of fluid flow problems, the enforcement of no-slip boundary conditions along the phase boundaries via the XFEM and a stabilized Lagrange multiplier method was adopted by [34] for a Navier-Stokes fluid model; a hydrodynamic Boltzmann model was employed in combination with a level set-based interface representation for generalized topology optimization of fluids by [35].…”

Section: Introductionmentioning

confidence: 99%

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CutFEM topology optimization of 3D laminar incompressible flow problems

Villanueva

Maute

2017

Computer Methods in Applied Mechanics and Engineering

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This paper studies the characteristics and applicability of the CutFEM approach [1] as the core of a robust topology optimization framework for 3D laminar incompressible flow and species transport problems at low Reynolds number (Re < 200). CutFEM is a methodology for discretizing partial differential equations on complex geometries by immersed boundary techniques. In this study, the geometry of the fluid domain is described by an explicit level set method, where the parameters of a level set function are defined as functions of the optimization variables. The fluid behavior is modeled by the incompressible Navier-Stokes equations. Species transport is modeled by an advection-diffusion equation. The governing equations are discretized in space by a generalized extended finite element method. Face-oriented ghost-penalty terms are added for stability reasons and to improve the conditioning of the system. The boundary conditions are enforced weakly via Nitsche's method. The emergence of isolated volumes of fluid surrounded by solid during the optimization process leads to a singular analysis problem. An auxiliary indicator field is modeled to identify these volumes and to impose a constraint on the average pressure. Numerical results for 3D, steady-state and transient problems demonstrate that the CutFEM analyses are sufficiently accurate, and the optimized designs agree well with results from prior studies solved in 2D or by density approaches.

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Section: Design Of a Micromixermentioning

confidence: 77%

Section: Topology Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CutFEM topology optimization of 3D laminar incompressible flow problems

Villanueva

Maute

2017

Computer Methods in Applied Mechanics and Engineering

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“…Topology optimisation for fluid systems began with the treatment of Stokes flow by Borrvall and Petersson [11] and has since been applied to Navier-Stokes flow [12], as well as passive transport problems [13,14], reactive flows [15], transient flows [16,17,18], fluid-structure interaction [19,20], amongst many others. The extension of topology optimisation to turbulent fluid flow is still in its infancy [21,22].…”

Section: Introductionmentioning

confidence: 99%

Design of passive coolers for light-emitting diode lamps using topology optimisation

Alexandersen

Sigmund

Meyer

et al. 2018

International Journal of Heat and Mass Transfer

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Topology optimised designs for passive cooling of light-emitting diode (LED) lamps are investigated through extensive numerical parameter studies. The designs are optimised for either horizontal or vertical orientations and are compared to a lattice-fin design. The different orientations result in significant differences in topologies. The optimisation favors placing material at outer boundaries of the design domain, leaving a hollow core that allows the buoyancy forces to accelerate the air to higher speeds. Investigations show that increasing design symmetry yields performance with less sensitivity to orientation with a minor loss in mean performance. The topology-optimised designs of heat sinks for natural convection yield a 26% lower package temperature using around 12% less material compared to the lattice-fin design, while maintaining low sensitivity to orientation. Furthermore, they exhibit several defining features and provide insight and general guidelines for the design of passive coolers for LED lamps.

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“…An extension of the fluid nozzle problem studied by Refs. [56][57][58], to 3D is studied here. The design domain with boundary conditions and the initial design are shown in Fig.…”

Section: Beam In 3dmentioning

confidence: 99%

A regularization scheme for explicit level-set XFEM topology optimization

et al. 2019

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Regularization of the level-set (LS) field is a critical part of LS-based topology optimization (TO) approaches. Traditionally this is achieved by advancing the LS field through the solution of a Hamilton-Jacobi equation combined with a reinitialization scheme. This approach, however, may limit the maximum step size and introduces discontinuities in the design process. Alternatively, energy functionals and intermediate LS value penalizations have been proposed. This paper introduces a novel LS regularization approach based on a signed distance field (SDF) which is applicable to explicit LSbased TO. The SDF is obtained using the heat method (HM) and is reconstructed for every design in the optimization process. The governing equations of the HM, as well as the ones describing the physical response of the system of interest, are discretized by the extended finite element method (XFEM). Numerical examples for problems modeled by linear elasticity, nonlinear hyperelasticity and the incompressible Navier-Stokes equations in two and three dimensions are presented to show the applicability of the proposed scheme to a broad range of design optimization problems.

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Level set topology optimization of scalar transport problems

Cited by 23 publications

References 73 publications

CutFEM topology optimization of 3D laminar incompressible flow problems

CutFEM topology optimization of 3D laminar incompressible flow problems

Design of passive coolers for light-emitting diode lamps using topology optimisation

A regularization scheme for explicit level-set XFEM topology optimization

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