A partitioned solution approach for electro-thermo-mechanical problems

Erbts, Patrick; Hartmann, Stefan; Düster, Alexander

doi:10.1007/s00419-014-0941-z

Cited by 26 publications

(20 citation statements)

References 51 publications

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“…A similar structure of the coupled equations is shared by other classical systems as the Biot equations in poroelasticity, or thermoelasticity-based problems, for which a much richer, numerically-oriented literature is available (see e.g. [3,8,13,19,20,29,31] and the references therein).…”

Section: Introductionmentioning

confidence: 98%

Partitioned coupling of advection–diffusion–reaction systems and Brinkman flows

Lenarda

Paggi

Ruiz–Baier

2017

Journal of Computational Physics

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We present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection-di↵usion-reaction systems and incompressible, viscous flow. The space discretization of the governing equations is based on mixed finite element methods defined on unstructured meshes, whereas the time integration hinges on an operator splitting strategy that exploits the di↵er-ences in scales between the reaction, advection, and di↵usion processes, considering the global system as a number of sequentially linked sets of partial di↵erential, and algebraic equations. The flow solver presents the advantage that all unknowns in the system (here vorticity, velocity, and pressure) can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective. The robustness of the proposed method is illustrated with a series of numerical tests in 2D and 3D, relevant in the modelling of bacterial bioconvection and Boussinesq systems.

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Section: Introductionmentioning

confidence: 98%

Partitioned coupling of advection–diffusion–reaction systems and Brinkman flows

Lenarda

Paggi

Ruiz–Baier

2017

Journal of Computational Physics

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“…The additional computational input remains acceptable for this method since the minimization problem leads to an equation system with unknowns k. Moreover, this scheme enables to reuse the data from previous time increments, so that the approximated Jacobian can be updated over several time-steps beyond. Further details and extensions regarding this technique can be found in [55,56,38]. …”

Section: Partitioned Approachmentioning

confidence: 98%

“…According to the proposal in [48,28,38], we perform a linear extrapolation of the last equilibrium states, in this case adapted to the requirements of thermo-mechanically coupled problems,…”

Section: Monolithic Approachmentioning

confidence: 99%

“…Here, we draw on the method of vertical lines, where the initial boundary-value problem is discretized in space first, see [34,29] for the case of thermo-viscoplasticity, for the general treatment [35], for thermo-elasticity [28,36] or for small-strain electro-thermo-elasticity in [37,38]. This leads to a system of differential-algebraic equations, which is solved using the Backward-Euler method yielding a system of coupled non-linear equations.…”

Section: Numerical Solution Of the Initial Boundary-value Problemmentioning

confidence: 99%

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Monolithic and partitioned coupling schemes for thermo-viscoplasticity

Rothe

Erbts

Düster

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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“…Additionally, this volumetric coupling problem is complicated by mechanical, thermal and electrical contact conditions (moving punch, thermal and electrical contact resistances between the tools and betweens the tools and the powder). We treat the spatial discretization by means of a finite element approach, where apart from the local balance of linear momentum (quasi-static formulation), the transient heat equation and the stationary charge equation are reformulated by a weak formulation, see, for example, [2,3] and the references cited therein. The displacements, temperature and electrical potential and their virtual counterpart are discretized with shape functions, which yield, together with the constitutive model, a system of differentialalgebraic equations (DAE-system).…”

Section: Introductionmentioning

confidence: 99%

Field Assisted Sintering Technology, Part II: Simulation

Rothe

Hartmann

2017

GAMM-Mitteilungen

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Field-assisted sintering technology (FAST) implies a multifield problem between electrical, thermal and mechanical fields. Based on a constitutive model proposed in [1], the numerical treatment of the three-field problem in a monolithic finite element framework is discussed. Apart from algorithmic considerations, numerical simulations are performed treating the complex contact problem, large deformations and the multifield issues themselves. This is combined with a PID-controller, which is required when the temperature process is given at specific positions in the graphite tool system and the electrical current is uncertain. The numerical simulations are validated by real experiments.

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A partitioned solution approach for electro-thermo-mechanical problems

Cited by 26 publications

References 51 publications

Partitioned coupling of advection–diffusion–reaction systems and Brinkman flows

Partitioned coupling of advection–diffusion–reaction systems and Brinkman flows

Monolithic and partitioned coupling schemes for thermo-viscoplasticity

Field Assisted Sintering Technology, Part II: Simulation

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