Simulating dense granular flow using the μ(<i>I</i>)‐rheology within a space‐time framework

Gesenhues, Linda; Behr, Marek

doi:10.1002/fld.5014

Cited by 5 publications

(3 citation statements)

References 32 publications

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“…Recent examples of simplex space-time simulations include the computation of complex fluid flows in production engineering applications 10,11 and the computation of dense granular flows. 12 Likewise, compressible flows have been successfully simulated on unstructured space-time meshes. [13][14][15] Note that the solution of transient three-dimensional problems with space-time finite elements requires four-dimensional meshes.…”

Section: Motivationmentioning

confidence: 99%

“…To benefit from these advantages, space‐time finite elements have been used to perform simulations in various fields of computational fluid dynamics (CFD). Recent examples of simplex space‐time simulations include the computation of complex fluid flows in production engineering applications 10,11 and the computation of dense granular flows 12 . Likewise, compressible flows have been successfully simulated on unstructured space‐time meshes 13‐15 .…”

Section: Introductionmentioning

confidence: 99%

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Time‐continuous and time‐discontinuous space‐time finite elements for advection‐diffusion problems

Danwitz

Voulis

Hosters

et al. 2023

Numerical Meth Engineering

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We construct four variants of space‐time finite element discretizations based on linear tensor‐product and simplex‐type finite elements. The resulting discretizations are continuous in space, and continuous or discontinuous in time. In a first test run, all four methods are applied to a linear scalar advection‐diffusion model problem. Then, the convergence properties of the time‐discontinuous space‐time finite element discretizations are studied in numerical experiments. Advection velocity and diffusion coefficient are varied, such that the parabolic case of pure diffusion (heat equation), as well as, the hyperbolic case of pure advection (transport equation) are included in the study. For each model parameter set, the L2$$ {L}_2 $$ error at the final time is computed for spatial and temporal element lengths ranging over several orders of magnitude to allow for an individual evaluation of the methods' spatial, temporal, and space‐time accuracy. In the parabolic case, particular attention is paid to the influence of time‐dependent boundary conditions. Key findings include a spatial accuracy of second order and a temporal accuracy between second and third order. The temporal accuracy tends toward third order depending on how advection‐dominated the test case is, on the choice of the specific discretization method, and on the time‐(in)dependence and treatment of the boundary conditions. Additionally, the potential of time‐continuous simplex space‐time finite elements for heat flux computations is demonstrated with a piston ring pack test case and a subtractive manufacturing test case.

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Section: Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time‐continuous and time‐discontinuous space‐time finite elements for advection‐diffusion problems

Danwitz

Voulis

Hosters

et al. 2023

Numerical Meth Engineering

Self Cite

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“…19 Further, recent application examples of four-dimensional SST meshes from the field of mathematics deal with parabolic evolution problems 20,21 or a broader class of transient PDEs recast as constrained first-order system. 22 In the field of computational engineering science, adaptive temporal refinement of pentatope meshes is used for two-phase flow simulations 23 -also combined with complex material laws such as the Carreau-Yasuda-WLF model 24 or the 𝜇(I)-rheology 25 -as well as gas flow simulations in the piston ring-pack of internal combustion engines. 9 In this work, we generate pentatope finite element meshes for spatial domains with time-variant topology.…”

Section: F I G U R Ementioning

confidence: 99%

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

Danwitz

Antony

Key

et al. 2021

Numerical Methods in Fluids

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Considering the flow through biological or engineered valves as an example, there is a variety of applications in which the topology of a fluid domain changes over time. This topology change is characteristic for the physical behavior, but poses a particular challenge in computer simulations. A way to overcome this challenge is to consider the application‐specific space‐time geometry as a contiguous computational domain. In this work, we obtain a boundary‐conforming discretization of the space‐time domain with four‐dimensional simplex elements (pentatopes). To facilitate the construction of pentatope meshes for complex geometries, the widely used elastic mesh update method is extended to four‐dimensional meshes. In the resulting workflow, the topology change is elegantly included in the pentatope mesh and does not require any additional treatment during the simulation. The potential of simplex space‐time meshes for domains with time‐variant topology is demonstrated in a valve simulation, and a flow simulation inspired by a clamped artery.

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Development of a non-local partial Peridynamic explicit mesh-free incompressible method and its validation for simulating dry dense granular flows

2022

Acta Geotech.

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Simulating dense granular flow using the μ(I)‐rheology within a space‐time framework

Cited by 5 publications

References 32 publications

Time‐continuous and time‐discontinuous space‐time finite elements for advection‐diffusion problems

Time‐continuous and time‐discontinuous space‐time finite elements for advection‐diffusion problems

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

Development of a non-local partial Peridynamic explicit mesh-free incompressible method and its validation for simulating dry dense granular flows

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