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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. CACCIA∗AND 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 s−2. 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 s−1. 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 m−1)

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 10−4for 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 m−1] lift [N m−1]

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 m−1] f [Hz] lift [N m−1] 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 m−1] f [Hz] lift [N m−1] 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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