Stabilized implicit co-simulation methods: solver coupling based on constitutive laws

Schweizer, Bernhard; Li, Pu; Lu, Daixing; Meyer, Tobias

doi:10.1007/s00419-015-0999-2

Cited by 12 publications

(11 citation statements)

References 27 publications

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“…by physical force/torque laws). Then, applied forces/torques are used to define the subsystem interaction . Solver or simulator coupling has been used in a large number of applications.…”

Section: Introductionmentioning

confidence: 99%

Implicit co‐simulation methods: Stability and convergence analysis for solver coupling approaches with algebraic constraints

Schweizer¹,

Li²,

Lu³

2015

Z Angew Math Mech

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The analysis of the numerical stability of co‐simulation methods with algebraic constraints is subject of this manuscript. Three different implicit coupling schemes are investigated. The first method is based on the well‐known Baumgarte stabilization technique. Basis of the second coupling method is a weighted multiplier approach. Within the third method, a classical projection technique is applied. The three methods are discussed for different approximation orders. Concerning the decomposition of the overall system into subsystems, we consider all three possible approaches, i.e. force/force‐, force/displacement‐ and displacement/displacement‐decomposition. The stability analysis of co‐simulation methods with algebraic constraints is inherently related to the definition of a test model. Bearing in mind the stability definition for numerical time integration schemes, i.e. Dahlquist's stability theory based on the linear single‐mass oscillator, a linear two‐mass oscillator is used here for analyzing the stability of co‐simulation methods. The two‐mass co‐simulation test model may be regarded as two Dahlquist equations, coupled by an algebraic constraint equation. By discretizing the co‐simulation test model with a linear co‐simulation approach, a linear system of recurrence equations is obtained. The stability of the recurrence system, which reflects the stability of the underlying coupling method, can simply be determined by an eigenvalue analysis.

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“…by physical force/torque laws). Then, applied forces/torques are used to define the subsystem interaction . Solver or simulator coupling has been used in a large number of applications.…”

Section: Introductionmentioning

confidence: 99%

Implicit co‐simulation methods: Stability and convergence analysis for solver coupling approaches with algebraic constraints

Schweizer¹,

Li²,

Lu³

2015

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

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“…Semi-implicit coupling : these techniques, 25,62–65 are similar to the ones above, except they perform two iterations only.…”

Section: Discussionmentioning

confidence: 99%

“…Algebraic constraint couplings: this coupling technique, 24,25,30,61 can be implemented by a fixed-point iteration (recall adaptation loop_sa) and extra algebraic computations on the units' inputs and outputs. Semi-implicit coupling: these techniques, 25,[62][63][64][65] are similar to the ones above, except they perform two iterations only. Error control: Richard extrapolation 9,47,66 can be implemented by creating a semantic adaptation that runs a whole scenario at twice the rate of the original one; multi-order input extrapolation 59,67 amounts to implementing two approximation schemes (see item above) run in parallel; the embedded method 68 requires that a semantic adaptation is implemented to perform a discretized numerical integration of some of the signals in the internal scenario; energy-based techniques 69 can be implementing by coding semantic adaptations which monitor for energy dissipativity in some of the signals in the internal FMUs.…”

Section: Expressivitymentioning

confidence: 99%

Semantic adaptation for FMI co-simulation with hierarchical simulators

et al. 2018

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Model-based design can shorten the development time of complex systems by the use of simulation techniques. However, it can be hard to simulate the system as a whole if it is developed in a concurrent fashion by multiple and specialized teams. Co-simulation, with the support of the Functional Mockup Interface (FMI) Standard, is proposed as a way to promote tool interoperability while protecting the intellectual property of subsystems. The standard allows uniform communication between subsystem simulators, but does not state how the inputs and outputs should be interpreted, nor how the subsystems should interact correctly. Semantic adaptations can be quickly made to correct the interactions with subsystem simulators that were produced with different assumptions, and avoid changing those subsystems, their simulators, or the orchestration algorithm that computes the co-simulation. In this work, we explore how to describe common adaptations and what their meaning is in the context of FMI co-simulation. The result is a sound language that enables the implementation of adaptations with minimal effort. A distinct feature is that it describes adaptations for groups of interconnected subsystem simulators in the same way as for a single simulator, and the implementation is itself a simulator, thanks to a sound definition of hierarchical co-simulation. This work paves the way for research into the correct combination and interfacing of different adaptations.

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“…The behaviour of the two sub-systems is affected reciprocally by each other. A particular aspect of the co-simulation procedure proposed concerns the synchronisation of the integration algorithms that run with independent time steps, being the numerical stability and accuracy of the dynamic analysis of the coupled systems a fundamental aspect to account for [50].…”

Section: Vehicle-track Co-simulationmentioning

confidence: 99%

A co-simulation approach to the wheel–rail contact with flexible railway track

et al. 2018

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The standard approach to railway vehicle dynamic analysis includes running the vehicle multibody models in rigid railway tracks. The wheel-rail contact, independently of the rolling contact model used, is either handled online or via lookup tables. This traditional approach disregards the coupling effects between the railway vehicle dynamics and the railway track flexibility. In this work the assumption of rigidity of the railway track is released and a finite element model of the complete track, i.e., rails, pads, sleepers, ballast and infrastructure, is used to represent the track geometry and flexibility. A rail-wheel contact model that evaluates the contact conditions and forces is used online. The dynamics of the railway vehicle is described using a multibody methodology while the track structure is described using a finite element approach. Due to the fact that not only the multibody and the finite element dynamic analysis use different integration algorithms but also because the vehicle and track models are simulated in different codes a co-simulation procedure is proposed and demonstrated to address the coupled dynamics of the system. This approach allows to analyse the vehicle dynamics in a flexible track with a general geometry modelled with finite elements, i.e., including curvature, cant, vertical slopes and irregularities, which is another novel contribution. The methodology proposed in this work is demonstrated in an application in which the railway vehicle-track interaction shows the influence of the vehicle dynamics on the track dynamics and vice-versa.

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Stabilized implicit co-simulation methods: solver coupling based on constitutive laws

Cited by 12 publications

References 27 publications

Implicit co‐simulation methods: Stability and convergence analysis for solver coupling approaches with algebraic constraints

Implicit co‐simulation methods: Stability and convergence analysis for solver coupling approaches with algebraic constraints

Semantic adaptation for FMI co-simulation with hierarchical simulators

A co-simulation approach to the wheel–rail contact with flexible railway track

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