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Coupling multi-body and fluid dynamics analisys with preCICE and MBDyn

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The software library preCICE allows to connect single physics solvers to perform mul-tiphysics cosimulations in a partitioned way. We interfaced preCICE with the multibody dynamics software MBDyn and assessed its performance with the set of well-known benchmarks proposed by Turek and Hron. The setup consists of a laminar incompressible flow around a slender elastic object, which is suitable to be simulated via MBDyn beam elements connected to a cloud of interface points. 1 MOTIVATION In this work, the Multibody Dynamics solver MBDyn 1 [10] has been interfaced with the multiphysics coupling library preCICE [3] to extend MBDyn capabilities to solve fluid structure interaction (FSI) problems. MBDyn is a free general-purpose Multibody Dynamics solver developed at the Department of Aerospace Science and Technology of Politecnico di Milano, which models the constrained nonlinear dynamics of rigid and flexible bodies formulated as sets of Differential-Algebraic Equations (DAEs) [10]. When FSI simulations involve slender and flexible structures, it is particularly interesting to use a reduced dimensionality finite element model (i.e. a set of beams or shells) along with a form of mapping between the interface (wet surface) and the structural model, especially when the two are topologically incompatible, in order to exchange the mutual kinematics and dynamics [12].
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IX International Conference on Computational Methods for Coupled Problems in Science and Engineering
COUPLED PROBLEMS 2021
E. O˜nate, M. Papadrakakis and B. Schrefler (Eds)
COUPLING MULTI-BODY AND FLUID DYNAMICS
ANALYSIS WITH PRECICE AND MBDYN
CLAUDIO G. CACCIAAND PIERANGELO MASARATI
Department of Aerospace Science and Technology, Politecnico di Milano
via La Masa 34, 20156, Milan, Italy
e-mail: claudiogiovanni.caccia@mail.polimi.it, web page: http://www.aero.polimi.it/
Department of Aerospace Science and Technology, Politecnico di Milano
via La Masa 34, 20156, Milan, Italy
e-mail: pierangelo.masarati@polimi.it, web page: http://www.aero.polimi.it/
Key words: Multibody System Dynamics, Cosimulation, Fluid-Structure Interaction
Abstract.
The software library preCICE allows to connect single physics solvers to perform mul-
tiphysics cosimulations in a partitioned way. We interfaced preCICE with the multibody
dynamics software MBDyn and assessed its performance with the set of well-known bench-
marks proposed by Turek and Hron. The set-up consists of a laminar incompressible flow
around a slender elastic object, which is suitable to be simulated via MBDyn beam ele-
ments connected to a cloud of interface points.
1 MOTIVATION
In this work, the Multibody Dynamics solver MBDyn1[10] has been interfaced with
the multiphysics coupling library preCICE [3] to extend MBDyn capabilities to solve fluid
structure interaction (FSI) problems.
MBDyn is a free general-purpose Multibody Dynamics solver developed at the De-
partment of Aerospace Science and Technology of Politecnico di Milano, which models
the constrained nonlinear dynamics of rigid and flexible bodies formulated as sets of
Differential-Algebraic Equations (DAEs) [10].
When FSI simulations involve slender and flexible structures, it is particularly inter-
esting to use a reduced dimensionality finite element model (i.e. a set of beams or shells )
along with a form of mapping between the interface (wet surface) and the structural
model, especially when the two are topologically incompatible, in order to exchange the
mutual kinematics and dynamics [12].
1https:/www.mbdyn.org/, last accessed May 2021.
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Claudio G. Caccia and Pierangelo Masarati
mbcnodal.h
libmbc.so
MBDyn
adapter
precice.h
libprecice.so
FSI
coupling
Figure 1: MBDyn adapter interface scheme
MBDyn models slender deformable components using an original, geometrically exact
finite volume formulation for beam elements with a high level of flexibility [8, 1]. MBDyn
is also able to exchange kinematics and load information with a cloud of external points
of arbitrary topology [12].
PreCICE is an increasingly popular open-source coupling library which provides the
components to connect traditional single-physics solvers to generate a partitioned multi-
physics simulation (e.g. fluid-structure interaction, conjugated heat transfer, solid-solid
interaction, etc.).
The implementation of an adapter connecting MBDyn and preCICE represents an
advantage and an extension of capabilities for both applications. On the one hand, various
preCICE adapters for fluid solvers have already been developed. MBDyn can connect in
a standardized way to a considerable number of codes, including many popular, well-
validated open source and commercial ones [18]2, thus extending its aeroservoelasticty
simulation capabilities (e.g. [4]).
On the other hand, with a fully integrated MBDyn adapter, the library preCICE gains
the opportunity to connect to a multibody dynamics software, which has not yet been
completely developed and tested in many contexts and applications.
2 ADAPTER DESCRIPTION
An adapter is the “glue-code” that allows the interface of an existing software compo-
nent to be used by another component without modifying its source code. In the present
case it is possible to exploit the APIs given by MBDyn and preCICE, so that the adapter
itself is independent from both codes (see Fig. 1).
2.1 MBDyn Features
MBDyn can simulate linear and non-linear dynamics of rigid and flexible bodies (inclu-
ding geometrically exact and composite-ready beam and shell finite elements, component
mode synthesis elements, lumped elements) subjected to kinematic constraints, external
forces and control subsystems [10]. Nodes are the basic blocks of an MBDyn model: they
instantiate kinematic degrees of freedom and the corresponding equilibrium equations.
Elements constitute the components of the multi-body model. With minor exceptions,
each of them connects one or more nodes. They write contributions to equations instanti-
2for an updated list see https://precice.org/adapters-overview.html
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Claudio G. Caccia and Pierangelo Masarati
(a) Model: nodes and beams (b) Interface geometry: shape
(c) Interface mesh: MLS mapping (d) Coupling to CFD solver
Figure 2: steps to perform FSI with MBDyn
ated by nodes and thus represent the connectivity and constitutive properties of a model.
The beam element is defined by its nodes, a reference line (Fig. 2a), and the orientation of
the beam section. The Finite Volume approach described in [8] is used to model the beam
element. The user defines a section constitutive law that is independent from the shape
of the beam itself (Fig. 2b), thus the aerodynamic aspects and the structural aspects are
handled by two distinct elements of the model.
In MBDyn, it is possible to exchange kinematic and dynamic information and to steer
the multi-body simulation from an external software (left side of Fig. 1). This information
can be exchanged directly on the nodes or on a cloud of external points, used for example
to define an interface geometry in FSI problems (e.g. the mesh in Fig. 2c). The mapping
consists in a constant matrix that computes the movement of the external points as
functions of those of the nodes, based on the Moving Least Squares (MLS) technique
[12]. This feature takes care of the topological inconsistency between the nodes and the
interface, thus simplifying the mapping at the wet surface, as the interface mesh can be
the same on both sides (Fig. 2d).
2.2 preCICE Features
The Open Source library preCICE aims at coupling existing solvers in a partitioned
black-box manner [6]: only minimal information about each solver is required; the con-
nection only involves the interface nodes.
In a nutshell, preCICE simply affects the input and observes the output of the solvers
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Claudio G. Caccia and Pierangelo Masarati
(called participants). The required data and control elements are accessed using an
adapter (right side of Fig. 1).
The actions required to perform a coupled simulation involve: the set up of the com-
munication between the participants, the computation of the mapping of data between
meshes, the implementation of the coupling strategy, the verification of convergence, and
the steering of the simulation.
2.3 Adapter Configuration
The adapter has been implemented in C++ and is currently available from GitLab3.
The code is conceptually divided in two classes. The main class implements the func-
tions given by the preCICE interface and has access to the other class, which takes care
of all the aspects regarding MBDyn.
Some data are needed in order to perform a simulation. Such data are stored in a
JSON file given as input. This information concerns:
setup: communication with preCICE and MBDyn, mesh location for coupling and
mapping
run: type of data to pass, parameters to progressively load the structure at the
beginning of simulation
output: forces, displacements and velocities at interface nodes (Fig. 3), resultant
force and resultant moment.
(a) Forces (b) Displacements
Figure 3: Simulation output
3https://public.gitlab.polimi.it/DAER/mbdyn/-/wikis/preCICE-MBDyn-adapter
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Claudio G. Caccia and Pierangelo Masarati
3 VALIDATION OF THE COMPONENTS
In order to validate the coupling adapter developed, we simulated some test cases to
confirm the correctness of the implementation.
The three Turek-Hron FSI test cases described in [14] are a set of well-known bench-
marks in FSI literature. They are characterized by the same domain (a circular cylinder
with a trailing flap) and the same fluid properties. Differences are only related to fluid
velocity and structural properties (in particular the density, ρ, and Young’s modulus, E).
Besides, they are all characterized by a high mass ratio M=ρF
ρSbetween the fluid and
structural density, which is known to lead to algorithmic instability of the coupled system
(e.g. [7, 11]).
All the presented results are compared to the “reference” data (i.e. defined as almost
grid-independent in [14]) obtained using a fully implicit monolithic ALE-FEM method
with a fully coupled multigrid solver.
3.1 Validation of the Structural Part
The tests named CSM in [14] are used to fit the structural part. The beam is loaded
only with gravitational force ~g = (0, g) = 2 m s2. Tests CSM1 and CSM2 are steady
state solutions at different Young’s modulus, while CSM3 is a time dependent solution
starting from the undeformed configuration.
An MBDyn cantilever beam model composed of three-node beam3 elements [8] has
been developed, as depicted in Fig. 4a. The beam section is uniform and rectangular
(w×h); the geometrical and physical properties (ρ,E,ν) are constant throughout the
length of the beam.
The inertia of the structure is provided by 2 rigid body elements attached to the
second and third node of each beam element. The center of gravity of each body is placed
at the corresponding node (see Fig. 4b). Special bodies are used for the first and last
element, with the correct mass, inertia moments, and center of mass location.
12345
L
l
x
y
z
(a) Cantilever made of 5 beam elements
l/2
hw
x
y
zCoG
n2
n1n3
(b) Body attached to node 2 of the beam
The main parameter considered in the analysis is the number of beam elements: tests
with 4 or 5 elements give results closest to the benchmark (see Table 1), while a higher
number of elements makes the structure more flexible.
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Claudio G. Caccia and Pierangelo Masarati
Table 1: Comparison of tip displacement (in mm)
CSM1 CSM2 CSM3
# el. uxuyuxuyuxuyf [Hz]
4 -7.28 -66.69 -0.47 -17.13 -14.46±14.46 -65.10±65.82 1.125
5 -7.73 -68.68 -0.51 -17.67 -15.29±15.29 -66.69±68.11 1.104
10 -8.74 -72.90 -0.58 -18.83 -17.57±17.57 -70.82±71.20 1.062
ref. -7.19 -66.10 -0.47 -16.97 -14.31±14.31 -63.61±65.16 1.099
3.2 Validation of the Fluid Part
The fluid part has been modeled with OpenFOAM, using a hexahedral mesh with
different levels of refinement (Fig. 5).
Figure 5: Fluid mesh used for CFD and FSI simulations
The tests named CFD in [14] have been used to understand the fitness of the fluid part.
All 3 cases share the same fluid properties, a parabolic inlet profile and a rigid domain.
They differ only in average fluid velocity, with values of 0.2, 1 and 2 m s1. The results
are shown in Table 2: at low fluid speed the impact of the fineness of the mesh is low or
negligible, whereas it becomes relevant for CFD3, characterized by alternating vortices
developing downstream of the structure.
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Claudio G. Caccia and Pierangelo Masarati
Table 2: Comparison of lift and drag (in N m1)
CFD1 CFD2 CFD3
size drag lift drag lift drag lift f [Hz]
25k 14.28 1.11 139.49 10.77 442.53±4.75 -17.39±384.22 4.38
49k 14.28 1.11 137.34 10.46 441.45±5.17 -15.51±412.03 4.41
ref. 14.29 1.12 136.7 10.53 439.45±5.62 -11.89±437.81 4.3956
4 TEST CASES
Once the solid and the fluid models have been assessed, we considered the FSI test
cases described in [14].
4.1 General Set-Up
For each simulation we used the staggered implicit coupling algorithm implemented in
preCICE, with the structural component as the first participant and the fluid component
as the second one. We considered the IQN-ILS algorithm ([2, 5]) and a filter in order to
drop nearly dependent columns [9]. The convergence criteria have been set to a relative
error of 104for both displacements and forces. This execution order proved to converge
much faster than the reciprocal, as interface displacements converge much faster than the
forces, which thus benefit of the acceleration algorithm. A parallel implicit coupling [11]
has yet to be assessed. All the simulations considered here use a ∆t= 1 ms.
4.2 FSI1
The first test case is characterized by a mass ratio M= 1 and an average Reynolds
number Re = 20. The position of the beam is not symmetric such that the lift is not zero
[17]. The final solution is steady (see Figure 6). It is nevertheless interesting because its
high mass ratio and low fluid velocity make the interaction stronger and the convergence
sometimes more difficult in partitioned algorithms. The results, in terms of tip displace-
ment and forces on the structure, are shown in Table 3 and compared with the reference
in [14].
The coupled simulation converged with an average number of 2.8 iterations. There is
no significant difference with respect to the mesh size, and the results are close to the
reference.
4.3 FSI2
The second test case is characterized by a mass ratio M= 0.1 and an average Reynolds
number Re = 100. This test case is fully oscillating while the same problem, considering
the structure rigid (CFD2 in [14]) is steady: for this reason, it is considered an excellent
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Claudio G. Caccia and Pierangelo Masarati
(a) Forces (b) Tip displacements
Figure 6: FSI1 Simulation: 5 beams - 49k cells
Table 3: FSI1 results
size ux[mm] uy[mm] drag [N m1] lift [N m1]
25k 0.021 0.884 14.279 0.732
49k 0.021 0.887 14.283 0.733
ref. 0.023 0.821 14.295 0.764
check for interaction mechanisms [15]. Besides, it produces the largest deformation and
in some cases it is considered the most difficult of the three benchmarks [13].
(a) Forces (detail) (b) Tip displacements
Figure 7: FSI2 Simulation: 5 beams - 49k cells
The behavior of the structure in terms of tip displacement (mean value, amplitude and
frequency) is shown in Table 4, while drag and lift on the whole structure are shown in
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Claudio G. Caccia and Pierangelo Masarati
Table 5.
Table 4: FSI2 results (displacements)
size ux[mm] f [Hz] uy[mm] f [Hz]
25k -12.86±10.05 3.84 0.91±79.72 1.92
49k -10.66±7.72 3.79 1.67±74.19 1.90
ref. -14.58±12.44 3.86 1.23±80.6 1.93
Table 5: FSI2 results (forces)
size drag [N m1] f [Hz] lift [N m1] f [Hz]
25k 209.40±27.79 3.84 0.28±269.73 1.92
49k 212.51±22.85 3.79 -1.81±278.91 1.90
ref. 208.83±73.75 3.86 0.88±234.2 1.93
The coupled simulation converged with an average number of 3.8 iterations. The
agreement in terms of tip displacement is good, in particular with the coarser mesh and 5
beam elements (Figure 7 shows the results). Some differences are present in the oscillating
component of the forces.
4.4 FSI3
The last test case is characterized by a mass ratio M= 1 and an average Reynolds
number Re = 200. This case has been widely studied and a review of results obtained
with different approaches (monolithic or partitioned, with different solution strategies)
can be found in [16].
The behavior of the structure in terms of tip displacement (mean value, amplitude and
frequency) is shown in Table 6, while drag and lift on the whole structure are shown in
Table 7.
The coupled simulation converged with an average number of 3.5 iterations (Figure 8
shows the results). As pointed out in [16], different solution approaches lead to differences
of up to 50% for the drag and lift values, and up to 10% for the displacement values.
In our simulations, different discretizations lead to quite different solutions and the
trade-off between the efficiency of a coarser mesh and the accuracy of a finer one is
apparent. Besides, other simulation parameters have an impact on the results: e.g. the
structural damping of the elastic beam changes the amplitude of the ycomponent of the
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Claudio G. Caccia and Pierangelo Masarati
(a) Forces (detail) (b) Tip displacements
Figure 8: FSI3 Simulation: 4 beams - 49k cells
Table 6: FSI3 results (displacements)
size N ux[mm] f [Hz] uy[mm] f [Hz]
25k 5 -3.76±2.9 8.86 1.14±46.92 4.43
49k 5 -1.91±1.91 9.26 2.17±33.78 4.63
25k 4 -3.51±2.77 9.24 1.38±45.9 4.59
49k 4 -1.83±1.85 9.32 2.12±33.06 4.66
ref. -2.69±2.53 10.9 1.48±34.38 5.3
Table 7: FSI3 results (forces)
size N drag [N m1] f [Hz] lift [N m1] f [Hz]
25k 5 515.54±35.07 8.87 -1.28±78.65 4.43
49k 5 481.24±17.64 9.26 -0.48±164.52 4.63
25k 4 502.62±30.03 9.24 1.51±97.31 4.59
49k 4 481.12±19.07 9.32 -0.20±157.64 4.66
ref. 457.3±22.66 10.9 2.22±149.78 5.3
tip displacement and the oscillation frequency. This last result appears to be lower than
most of other studies in literature and might require a better tuning of the simulation of
parameters.
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Claudio G. Caccia and Pierangelo Masarati
5 CONCLUSIONS
The proposed adapter shows a good agreement with the considered benchmarks. De-
spite considering quite simple meshes, most results reported here look close to the refe-
rence values, showing that the current implementation proved to be robust with respect
to strong interaction (high mass ratio). Thorough assessment in compressible regime (e.g.
aeroelasticity) is underway.
Even though it must be thoroughly tested in realistic scenarios, the overall set-up
proved to be flexible, widely configurable and tunable. In particular the ability to pro-
gressively load the structure at the beginning of the simulation turned out to be a very
useful feature.
The adapter exploits the features provided by MBDyn for partitioned cosimulations
and, via the common interfacer preCICE, it can connect MBDyn to virtually any solver,
to perform FSI (fluid-solid interaction) and possibly hybrid multi-body full finite element
simulations. It still requires some minor improvements, e.g. to use nearest-projection
mappings in preCICE.
The code is independent of the MBDyn source code, which makes it easily extensible
and maintainable.
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In the emerging field of multi-physics simulations, we often face the challenge to establish new connections between physical fields, to add additional aspects to existing models, or to exchange a solver for one of the involved physical fields. If in such cases a fast prototyping of a coupled simulation environment is required, a partitioned setup using existing codes for each physical field is the optimal choice. As accurate models require also accurate numerics, multi-physics simulations typically use very high grid resolutions and, accordingly, are run on massively parallel computers. Here, we face the challenge to combine flexibility with parallel scalability and hardware efficiency. In this paper, we present the coupling tool preCICE which offers the complete coupling functionality required for a fast development of a multi-physics environment using existing, possibly black-box solvers. We hereby restrict ourselves to bidirectional surface coupling which is too expensive to be done via file communication, but in contrast to volume coupling still a candidate for distributed memory parallelism between the involved solvers. The paper gives an overview of the numerical functionalities implemented in preCICE as well as the user interfaces, i.e., the application programming interface and configuration options. Our numerical examples and the list of different open-source and commercial codes that have already been used with preCICE in coupled simulations show the high flexibility, the correctness, and the high performance and parallel scalability of coupled simulations with preCICE as the coupling unit.
Chapter
In this contribution, time discretizations of fluid-structure interactions are considered. We explore two specific complexities: first, the stiffness of the coupled system including different scales of the Navier-Stokes equations of parabolic type and the structure equation of hyperbolic type and second, the problem of moving domains that is inherent to fluid-structure interactions. Typical moving mesh approaches, such as the arbitrary Lagrangian-Eulerian framework, give rise to nonlinearities and time-derivatives with respect to the mesh-deformation. We derive different time-stepping techniques of Crank-Nicolson type and analyse their stability and approximation properties. Further, we closely look at the dominant time-scales that must be resolved to capture the global dynamics. Moreover, our discussion is supplemented with an analysis of the temporal discretization of Eulerian fixed-mesh approaches for fluid-structure interactions, where the interface between fluid and solid will change from time-step to time-step. Finally, a formulation of parallel multiple shooting methods for fluid-structure interaction is presented.
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As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed but this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the associated computational cost is overwhelming. Consequently, beam models, which are one-dimensional approximations of three-dimensional elasticity, have become the workhorse of many flexible multibody dynamics codes. Numerous beam formulations have been proposed, such as the geometrically exact beam formulation or the absolute nodal coordinate formulation, to name just two. New solution strategies have been investigated as well, including the intrinsic beam formulation or the DAE approach. This paper provides a systematic comparison of these various approaches, which will be assessed by comparing their predictions for four benchmark problems. The first problem is the Princeton beam experiment, a study of the static large displacement and rotation behavior of a simple cantilevered beam under a gravity tip load. The second problem, the four-bar mechanism , focuses on a flexible mechanism involving beams and revolute joints. The third problem investigates the behavior of a beam bent in its plane of greatest flexural rigidity , resulting in lateral buckling when a critical value of the transverse load is reached. The last problem investigates the dynamic stability of a rotating shaft. The predictions of eight independent codes are compared for these four benchmark problems and are found to be in close agreement with each other and with experimental measurements, when available. * Multibody System Dynamics, 37(1): pp 29-48, 2016.
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This paper presents a formulation for the efficient solution of general-purpose multibody/multiphysics problems. The core equations and details on structural dynamics and finite rotations handling are presented. The solution phases are illustrated. Highlights of the implementation are presented, and special features are discussed.