A fictitious domain method for the simulation of thermoelastic deformations in NC‐milling processes

Byfut, A.; Schröder, Jörg

doi:10.1002/nme.5609

Cited by 8 publications

(5 citation statements)

References 45 publications

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“…3a shows an example of such a geometry: a large mountain region with a complex and fine-structured surface (the Lauterbrunnen Valley in Switzerland). For instance, in [6] the varying boundary in an NC-milling process is resolved by using the marching volume polytopes algorithm in order to simulate thermoelastic deformations. The application of the marching volume polytopes algorithm as introduced in [7] gives a piecewise linear approximation of the surface, see Fig.…”

Section: Finite Cell Methodsmentioning

confidence: 99%

“…The FCM approach can also be applied to geometries with varying boundaries (in time). For instance, in [6] the varying boundary in an NC-milling process is resolved by using the marching volume polytopes algorithm in order to simulate thermoelastic deformations. We emphasize that using FCM drastically reduce the engineering effort for pre-processing (almost no cost for meshing) and one benefits from the high robustness of the method with respect to imprecise or even flawed CAD models [8].…”

Section: Finite Cell Methodsmentioning

confidence: 99%

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A posteriori error control for the finite cell method

Stolfo

Düster

Kollmannsberger

et al. 2019

Proc Appl Math and Mech

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The paper presents some concepts of the finite cell method and discusses a posteriori error control for this approach. The focus is on the application of the dual weighted residual approach (DWR), which enables the control of the error with respect to a user-defined quantity of interest. Since both the discretization error and the quadrature error are estimated, the application of the DWR approach provides an adaptive strategy which equilibrates the error contributions resulting from discretization and quadrature. The strategy consists in refining either the finite cell mesh or its associated quadrature mesh. Numerical experiments confirm the performance of the error control and the adaptive scheme for a non-linear problem in 2D.

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Section: Finite Cell Methodsmentioning

confidence: 99%

Section: Finite Cell Methodsmentioning

confidence: 99%

A posteriori error control for the finite cell method

Stolfo

Düster

Kollmannsberger

et al. 2019

Proc Appl Math and Mech

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“…For a more detailed discussion of the described variant of the fictitious domain method, see the work of Byfut and Schröder. 38…”

Section: Figure 11mentioning

confidence: 99%

“…For a more detailed discussion of the material parameters, the boundary data, and the temporal and spatial discretizations of (30), see the work of Byfut and Schröder. 38 For the mesh generation with respect to the time-dependent domains (29), the initial domainΩ is meshed with paraxial hexahedrons to yield some initial set of hexahedrons. As described in Section 5.3, an octree-like refinement is used for every considered time step of the temporal discretization to obtain a set of hexahedrons that is refined toward the interface Γ t .…”

Section: Simulation Of An Nc Milling Processmentioning

confidence: 99%

Marching volume polytopes algorithm

Byfut

Hellwig

Schröder

2018

Numerical Meth Engineering

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This paper presents an algorithm for the refinement of two-or threedimensional meshes with respect to an implicitly given domain, so that its surface is approximated by facets of the resulting polytopes. Using a Cartesian grid, the proposed algorithm may be used as a mesh generator. Initial meshes may consist of polytopes such as quadrilaterals and triangles, as well as hexahedrons, pyramids, and tetrahedrons. Given the ability to compute edge intersections with the surface of an implicitly given domain, the proposed marching volume polytopes algorithm uses predefined refinement patterns applied to individual polytopes depending on the intersection pattern of their edges. The refinement patterns take advantage of rotational symmetry. Since these patterns are applied independently to individual polytopes, the resulting mesh may encompass the so-called orientation problem, where two adjacent polytopes are rotated against one another. To allow for a repeated application of the marching volume polytopes algorithm, the proposed data structures and algorithms account for this ambiguity. A simple example illustrates the advantage of the repeated application of the proposed algorithm to approximate domains with sharp corners. Furthermore, finite element simulations for two challenging real-world problems, which require highly accurate approximations of the considered domains, demonstrate its applicability. For these simulations, a variant of the fictitious domain method is used. KEYWORDSfictitious domain method, finite element method, marching cubes, marching tetrahedrons, mesh generation, volume mesh Delaunay, quadtree/octree, and advancing-front methods for mesh generation. Using quadtree or octree techniques, 2-6 Cartesian grids covering a given domain are repeatedly refined via isotropic bisections of quadrilaterals into four similar sub-quadrilaterals or of hexahedrons into eight similar sub-hexahedrons for

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“…The feature that no complicated mesh topological operation is needed makes the fixed mesh method more and more popular for moving boundary problems in recent years. [18][19][20][21][22][23][24][25] FDM has received considerable interest and is widely used so far. This kind of method is generally a body-force-based method since the particle's effect on the fluid is modeled by introducing a body force in the momentum equation.…”

Section: Introductionmentioning

confidence: 99%

A consistent sharp interface fictitious domain method for moving boundary problems with arbitrarily polyhedral mesh

Chai

Wang

et al. 2021

Numerical Methods in Fluids

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A consistent, sharp interface fully Eulerian fictitious domain method is proposed in this article for moving boundary problems. In this method, a collocated finite volume method is used for the continuous phase; a geometry intersection method is employed for numerical integrals over the solid domain and transport of the body force; the pseudo body force defined at "solid centers" ensures the algorithm consists of the body force between the continuous form and its discretization counterpart; an explicit flux correction on cell faces and resulting mass source is introduced into the continuity equation to lower noncontinuity errors in the velocity correction step. This method is valid for stationary and moving boundary problems with arbitrarily polyhedral mesh.Several numerical tests are carried out to validate the proposed method. A second-order spatial accuracy is found in the flow around a cylinder case, and the spurious force oscillation is well suppressed for the in-line oscillation of a circular cylinder case. The performances on different meshes are tested, and structured mesh yields the best result, polyhedral next, and tetrahedral worst. A serial of tests is further performed on structured mesh to verify the effect of three different features (i.e., storing the body force at the solid centers, flux correction, and whether including the body force in the momentum equation) on the numerical predictions. Numerical results show that, in the in-line oscillation of a circular cylinder, "flux correction" can eliminate the large spikes in the drag coefficient, and "including the body force in the momentum equation" helps suppress the small oscillations. For other tests, "storing the body force at the solid centers" has enormous impacts on the final results of moving boundary problems, "flux correction" has little effects and the necessity of "including the body force in the momentum equation" is case dependent.

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A fictitious domain method for the simulation of thermoelastic deformations in NC‐milling processes

Cited by 8 publications

References 45 publications

A posteriori error control for the finite cell method

A posteriori error control for the finite cell method

Marching volume polytopes algorithm

A consistent sharp interface fictitious domain method for moving boundary problems with arbitrarily polyhedral mesh

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