Combined fluid and structure mesh adaptivity with fluid-structure interaction in EUROPLEXUS.
Date: 2015-08-13
Institutions: Institute for the Protection and Security of the Citizen
Subjects: computer system, data collection, data transmission, research report, simulation, software

Combined Fluid and Structure Mesh 
Adaptivity with Fluid-Structure 
Interaction in EUROPLEXUS 

Folco Casadei 
Georgios Valsamos 
Martin Larcher 
Vincent Faucher  

2 0 1 5

Report EUR 27276 EN

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                     
European Commission 

Joint Research Centre 

Institute for the Protection and Security of the Citizen 

Contact information 

Georgios Valsamos 

Address: Joint Research Centre, Via Enrico Fermi 2749, TP 480, 21027 Ispra (VA), Italy 

E-mail: georgios.valsamos@jrc.ec.europa.eu 

Tel.: +39 0332 78 9004 

Fax: +39 0332 78 9049 

http://ipsc.jrc.ec.europa.eu/ 

http://www.jrc.ec.europa.eu/ 

This publication is a Technical Report by the Joint Research Centre of the European Commission. 

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JRC96043 

EUR 27276 EN 

ISBN 978-92-79-48420-9 (PDF) 

ISSN 1831-9424 (online) 

doi:10.2788/519724 

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© European Union, 2015 

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Technical Note

2015

Combined Fluid and Structure
Mesh Adaptivity
with Fluid-Structure Interaction
in EUROPLEXUS

F. Casadei, G. Valsamos, M. Larcher
 European Commission,
Institute for the Protection and Security of the Citizen
Joint Research Centre, 21020 Ispra, Italy

V. Faucher
CEA - Saclay (F)

17 May 2015

 
Contents

1 Introduction .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1

2 Formulation and implementation  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  4

2.1 Mesh adaptation sequence   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  4

2.2 Implementation notes .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  6

2.2.1 ALE adaptive calculations  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  7

2.2.2 Variable number of dofs  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  8

3 Numerical examples.  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  9

3.1 Combined Threshold / FLSW adaptivity .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  9

3.2 Combined Threshold / FLSR adaptivity  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   14

4 References.  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   21

i

List of Figures

1 - Flowchart of FLSW model with adaptivity  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  5

2 - Flowchart of FLSR model with adaptivity   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  6

3 - Fluid box with internal diaphragm   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  9

4 - Results of case COAD01   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   10

5 - Results of case COAD02   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   13

6 - Results of case COAD03   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   14

7 - Results of case COAD04   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   15

8 - Results of case COAD07   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   17

9 - Some results of case COAD05   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   18

10 - Further results of case COAD05 .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   18

11 - Some results of case COAD06 .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   19

12 - Further results of case COAD06 .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   19

13 - Comparison of tip structural displacements  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   20

14 - Comparison of fluid pressures  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   20

ii

List of Tables

1  - Box simulations with VFCCs and FLSW.  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  9

2  - Box simulations with FE and FLSR   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   14

iii

1.  Introduction

This report is a sequel to reports and publications [1-15] on mesh adaptivity in fast transient dynam-

ics  and  presents  the  formulation  and  implementation  of  mesh  adaptivity  in  both  the  fluid  and  the

structure domain in combination with Fluid-Structure Interaction (FSI) algorithms in fast transient

dynamics. The algorithms are implemented in the EUROPLEXUS code.

EUROPLEXUS [21] is a computer code for fast explicit transient dynamic analysis of fluid-structure

systems jointly developed by the French Commissariat à l’Energie Atomique et aux Energies Alter-

natives (CEA Saclay) and by the Joint Research Centre of the European Commission (JRC Ispra).

Reference [1] presented the first implementation in EUROPLEXUS of an adaptive mesh refinement

and un-refinement procedure, in two space dimensions (element shape QUA4) for solid mechanics.

The procedure was extended to fluid mechanics (FE formulation) in 2D in reference [2]. Then, refer-

ence [3] applied a similar refinement and un-refinement procedure in three space dimensions to the

CUB8 element shape, both in solids mechanics and in fluid mechanics (FE formulation).

All numerical examples presented in references [1-3] with a variable mesh used a so-called “man-

ual”  mesh  adaptation  directive,  the  WAVE  directive  (see  the  code  manual  in  reference  [21]),  first

introduced in reference [1]. This directive refines the mesh along “wavefronts” that are specified by

the user, e.g. according to a known analytical solution to the problem considered. This technique was

used with success to simulate a bar problem (in solid mechanics) and a shock tube problem (in fluid

mechanics) both in 2D and in 3D [1-3].

However, those solutions cannot be qualified as “true” adaptive solutions, because in (true) adaptiv-

ity mesh refinement and un-refinement should be completely automatic, based upon suitable error

estimators or error indicators. The formulation of error estimators in fast transient dynamics is chal-

lenging and is still a subject of research. The use of so-called error indicators, however, is much sim-

pler. For this reason, subsequent work in EUROPLEXUS focused on error indicators. References [4]

and  [5]  document  a  first  prototype  implementation  of  adaptivity  based  upon  error  indicators  in

EUROPLEXUS,  limited  to  2D  problems  in  continuum  and  fluid  mechanics.  An  extension  of  the

indicator technique to 3D is under development but has not been completed and documented yet.

Publications [6-7]  focus on  the natural quantities of  interest in goal-oriented  error assessment  and

adaptivity, but limited to the case of linear elasto-dynamics.

The adaptive technique was then applied to Cell-Centred Finite Volumes (CCFV) for the description

of the fluid domain, first in 2D (see [8]) and then also in 3D [9]. More recently, the technique has

also been extended for use with the CDEM combustion model which makes use of the CCFV formu-

1

lation [10]. A complete description of the element refinement and un-refinement techniques used in

mesh adaptation has been published in a paper [11].

A first contribution towards combination of mesh adaptivity with Fluid-Structure Interaction (FSI)

was given in reference [12], in which a model is described that automatically refines the fluid mesh

in the vicinity of an embedded structure which can move and deform until and beyond rupture (but

without being itself subjected to adaptivity).

In  [13]  adaptivity  was  activated  for  simplex  elements  (triangles  in  2D  and  tetrahedra  in  3D).  The

report  [14]  extends  adaptivity  to  CEA’s  family  of  fluid  elements.  Finally,  reference  [15]  extends

adaptivity  to  shell,  beam  and  bar  structural  elements.  It  becomes  therefore  possible  to  have  mesh

adaptivity both in a fluid and at the same time in a structure (typically made of shells) embedded in

the fluid.

The present work extends the automatic fluid mesh adaptation of reference [12] to the case where

adaptation of the structure according to the techniques described in [15] occurs simultaneously. This

technique  is  particularly  useful  in  conjunction  with  FSI  algorithms  of  the  embedded  or  immersed

type, such as the FLSR or FLSW algorithms available in EUROPLEXUS.

With these algorithms, the interacting fluid and structure are discretized in a completely independent

way at the topological level. Typically, the fluid is represented by a uniform and regular (even struc-

tured)  mesh  fixed  in  space  (Eulerian  description)  used  as  a  “background”  mesh.  The  structure  is

meshed independently and then it is “embedded” or “immersed” in the fluid mesh. The two meshes

are therefore simply superposed.

A description of the FLSR and FLSW algorithms can be found in references [16-20].

Clearly, the precision of Fluid-Structure coupling depends very much on the use of a sufficiently fine

fluid mesh, at least in the vicinity of the structure, and this is precisely the scope of adaptivity: to

refine the fluid mesh only where it is needed, in this case close to the structure. However, if the struc-

ture undergoes large deformations and may locally fail, it becomes important to activate adaptivity

also in the structure, by using some dedicated criteria, in order to better follow the damage and fail-

ure mechanism of the structure itself. Then, the FSI algorithm must be able to deal simultaneously

with adaptivity both in the structure and in the fluid sub-domains.

This document is organized as follows:

• Section 2 presents the formulation of FSI in conjunction with adaptivity in the structure. The strat-

egy for refining and un-refining the fluid mesh in the vicinity of the structure had been already 

described in [12].

2

• Section 3 presents some numerical examples for the verification of the proposed algorithms.

The Appendix contains a listing of all the input files mentioned in the present report.

3

2.  Formulation and implementation

We consider a general FSI problem in which the structural mesh is automatically adapted [15] by

some algorithm which  tries to catch  the structural damage and  failure, while at  the same time the

fluid mesh is automatically adapted close to the embedded structure [12].

We assume a FSI algorithm of the embedded (or immersed) type: FLSR if the fluid sub-domain is

discretized via Finite Elements (FE), or FLSW if the fluid sub-domain is discretized via Cell-Centred

Finite Volumes (VFCC).

Embedded FSI algorithms make use of the notion of “influence domain” of the structure. The influ-

ence domain is formed by the union of geometrical “entities”: spheres (in 3D, or circles in 2D) cen-

tred  at  the  structural  nodes,  and  other  more  complex  shapes  built  starting  from  the  spheres  (or

circles):  quadrilaterals  in  2D  and  cones/prisms/hexahedra  in  3D.  See  references  [16-20]  for  a

detailed description.

In the adaptive FSI models available prior to the present work the structure was not adapted and con-

sequently  the  structural  influence  domain  was  built  only  once,  at  the  beginning  of  the  calculation

(routine BUILD_FLSW in module M_LINK_FLSW). Of course, some geometrical quantities in the

structural  domain  entities  had  to  be  updated  at  every  step  (routine  UPDATE_FLSW  in  module

M_LINK_FLSW) due to structure motion. Also, due to possible failure and erosion of the structural

elements, some parts of the structure, and the corresponding influence domain entities, could became

inactive. However, the influence domain data structure was a relatively “static” one. For example,

the number and the nature of the entities forming the influence domain were constant during the cal-

culation.

With adaptivity (also) in the structure, it is clear that the structural influence domain becomes much

more “dynamic”. The number and nature of the influence domain entities may vary during the calcu-

lation. Therefore, the corresponding part of the data structure must be re-built each time there are

adaptive refinements or un-refinements of the structure during the calculation.

2.1  Mesh adaptation sequence

Since both the structure and the fluid mesh have to be potentially adapted at each time step of the cal-

culation, it is necessary to decide the order in which mesh adaptation should occur. In typical FSI-

driven fluid mesh adaptation strategies the refinement and un-refinement of the fluid mesh depends

upon the current position (and shape) of the structure. The opposite case, in which structure refine-

ment and un-refinement would depend upon the fluid (in particular, upon the local size of the fluid

mesh), although perhaps not impossible, looks much less interesting.

4

For these reasons, it seems preferable to always perform the adaptation of the structural mesh first, at

each time step, and then, immediately after, to perform adaptation of the fluid mesh. The adopted

logical sequence of operations is as follows:

I

Perform adaptation of the structure mesh according to criteria related only to the structure 
itself (damage, failure or other conditions).

II Then, if the structure mesh has changed with respect to the previous step (i.e., if any struc-
tural element has been either refined or un-refined), re-build the structural influence 
domain. This is not a simple update like in reference [15], since the number of structural 
influence entities may change. If no structural element has been adapted during the first 
part of the algorithm, then perform a simple update of the structural influence domain like 
in [15].

III Finally, perform adaptation of the fluid mesh according to the (possibly new) structural 

mesh’s influence domain according to the algorithm of reference [15].

Figure 1 shows a (simplified) flowchart of the calls related to the FLSW model for FSI in conjunc-

tion with adaptivity. Figure 2 shows the same flowchart for the FLSR model.

CALCUL

MESH_ADAPTIVITY

ADAP_THRESHOLD

(threshold)

(rebuild FSI candidate
fluid elements/nodes)

BUILD_FLSW

(rebuild structure FSI influence domain)

TRACK_WAVEFRONTS

(wave)

UPDATE_ADAP_FLSW

UPDATE_FLSW_F_ADAP

(indicators)

ERROR_INDICATOR

ADAPT_THE_MESH

(FSI-driven
fluid adaptation)
(point clouds)

ADAPT_FLSW

FIND_FLSW_ADAP

ADAPT_POINT_CLOUD

(update candidate
fluid elements/nodes)

BUILD_FLSW_FFACES

(rebuild VFCC interfaces)

UPDATE_FLSW

LINK_FLSW_SRC

Figure 1 - Flowchart of FLSW model with adaptivity

In the case of FLSW (Figure 1) the MESH_ADAPTIVITY routine is called at the beginning of each

step, in order to perform any required adaptations of the mesh (both in the structure and in the fluid,

in general). The various possible types of adaptation are then called (see Figure and short description

below).  Then, 

if 

the  fluid  mesh  (made  of  VFCCs)  has  been  adapted, 

the  call 

to

BUILD_FLSW_FFACES  (in  module  M_LINK_FLSW)  re-builds  the  VFCC  interfaces  in  order  to

compute  the  fluxes  in  the  fluid  sub-domain.  Finally,  the  call  to  LINK_FLSW_SRC  (in  module

5

M_LINK_FLSW) searches the fluid entities (volume centroids or directly the interfaces, depending

upon an input option) which are located “within” the influence domain of the structure.

In the MESH_ADAPTIVITY routine, several possible types of mesh adaptation are possible: thresh-

old-based  adaptation  (most  commonly  in  the  structure,  but  thresholds  for  the  fluid  are  also  under

implementation),  wavefront-tracking  adaptation,  error  indicator  based  adaptation,  and  FSI-based

adaptation. The indicator-based adaptation may be used via the classical indicators or by means of a

point-cloud based formulation. The wavefront-based, indicator-based (either in the classical or in the

point-cloud  form)  and  FSI-based  adaptations  may  not  be  combined  at  the  moment.  However,  the

threshold-based adaptation (typically in  the structure)  may indeed be  combined, say,  with  an FSI-

driven adaptation in the fluid, by means of the model described in this report.

The FLSR case (Figure 2) is quite similar to the FLSW case and needs no further comments.

CALCUL

MESH_ADAPTIVITY

ADAP_THRESHOLD

(threshold)

(rebuild FSI candidate
fluid elements/nodes)

BUILD_FLSR

(rebuild structure FSI influence domain)

TRACK_WAVEFRONTS

(wave)

UPDATE_ADAP_FLSR

UPDATE_FLSR_F_ADAP

(indicators)

ERROR_INDICATOR

ADAPT_THE_MESH

(FSI-driven
fluid adaptation)
(point clouds)

ADAPT_FLSR

FIND_FLSR_ADAP

ADAPT_POINT_CLOUD

(update candidate
fluid elements/nodes)

BUILD_FLSW_FFACES

(rebuild VFCC interfaces)

UPDATE_FLSR

LINK_FLSR

Figure 2 - Flowchart of FLSR model with adaptivity

2.2  Implementation notes

As  concerns  the  data  structure,  the  following  scalars  and  arrays  have  been  added  in  the  module

M_LINK_FLSW_DATA:

• N_FLSW_SELEMS_BASE : the number of base FLSW structural elements given in input

• FLSW_SELEMS_NBASE : the list of such elements given in input

In the input file of calculations with mesh adaptivity, the user deals only with base elements. Since,

due  to  adaptivity  in  the  structure,  the  structural  elements  forming  the  influence  domain  may  vary

6

during the transient, it is necessary to “remember” the list of such elements that was specified in the

input. Of course, these are all “base” elements in adaptivity.

Whenever the structure influence is re-built, the list of (current) FLSW structural elements is re-con-

structed  as  the  union  of  all  active  descendents  of  the  base  elements  in  the  list  given  in  input.  Of

course, if a base element has no descendents (it is active), it is also added to the list.

The  BUILD_FLSW  routine  in  module  M_LINK_FLSW  is  modified,  An  extra  input  parameter

(REBUILD, a logical variable) indicating whether this is the first build-up of the data structure (the

influence  domain  of  the  structural  mesh)  or  it  is  a  re-build  due  to  an  adaptation  of  the  structural

mesh. The BUILD_FLSW routine is still called at the initial time by READ_FLSW, in order to build

the  data  structure 

for 

the 

first 

time 

(REBUILD=.FALSE.). 

It 

is  also  called 

from

MESH_ADAPTIVITY  directly  after  the  CALL  ADAP_THRESHOLD,  whenever  any  changes

occur in the mesh due to the threshold-based adaptation model. In this case, REBUILD=.TRUE. so

that the routine first destroys the old data structure, and then builds it up again.

2.2.1  ALE adaptive calculations

Another set of changes has been performed due to the fact that this is the first time that adaptivity in

both the structure and the fluid is activated simultaneously in the same run. In such a case the calcu-

lation must be declared ALE, and in this case use is made of the MVGRIL array in order to move the

mesh (in particular, to compute the grid velocities in NVVGRIL).

Porting the MVGRIL data structure with related arrays and all the available mesh rezoning models to

the case with adaptivity would be a huge task. For the moment, a simplified (but partial) solution has

been adopted.

The proposed solution allows to use a mix of Eulerian (for the fluid) or Lagrangian (for the structure)

descendent  (adaptive)  nodes,  but  does  not  allow  the  use  of  ALE  descendent  nodes.  This  provides

already useful functionality and does not require too many changes nor a complete re-writing of the

rezoning-related data structure in the code.

The assumed rules are the following:

• All nodes I in the memory extension zone are initially considered as Eulerian (MVGRIL(I,1)=0). 

They are therefore all counted in the MSHEUL global counter, and listed in the MVGRIL(I,2) 

part of the table in the corresponding order.

• As one of this nodes becomes used, it automatically inherits the status from its “parent” nodes, if 

such nodes have all the same status. For example, the child of 4 Lagrangian nodes becomes 

Lagrangian. Otherwise, the child node remains (tentatively) Eulerian.

7

• When a descendent node gets unused again, it returns Eulerian.

• An extra loop is added in the NVVGRIL routine. Initially, the routine treats all nodes in the exten-

sion zone as Eulerian because it does not examine their MVGRIL(I,1) value, but uses instead the 

MSHEUL counter and the MVGRIL(I,2) table (for efficiency reasons). Rebuilding the 

MVGRIL(I,2) table as the nature of extension nodes changes would be very expensive. We just 

add an extra loop (in the adaptive case) which passes over all extension nodes and treats them 

appropriately in case they are Lagrangian.

2.2.2  Variable number of dofs

Another  new  aspect  that  has  emerged  during  this  implementation  is  the  fact  that  the  number  of

(effective) degrees of freedom (dofs) of extension nodes can vary in time. In fact, if adaptivity affects

both the fluid and the structure, a descendent node might at some time belong to the fluid, and at

another time belong to the structure. In the fluid, only continuum elements are used, so that the num-

ber of degrees of freedom per node equals the space dimension IDIM (2 or 3). In the structure, if

shells or other “structural” elements are used, the nodes also have rotational degrees of freedom in

addition to translational ones.

For  simplicity,  when  adaptive  nodes  dimensioning  is  declared  in  the  input,  the  code  assumes  the

same number of dofs for each of these nodes, which is the maximum needed: IDIM if there is no

adaptivity in the structure, otherwise one takes the maximum number of dofs per node needed by any

structural element for which adaptivity is possible.

Some memory is wasted in general, but this organization is much simpler than having to rebuild all

nodal tables each time the mesh is adapted.

The  routines  SET_NEW_NODE  and  UNUSE_NODE  in  module  M_ADAPTIVITY_UTIL  have

been generalized so that now they accept nodes with a variable number of degrees of freedom.

8

3.  Numerical examples

We now present some numerical examples in order to check the model that has been described in the 

previous Section.

3.1  Combined Threshold / FLSW adaptivity

We first consider an extremely simplified fluid-structure problem, a 2D box with rigid walls contain-

ing an internal deformable diaphragm, see Figure 3. An explosion takes place in a corner of the box 

and  the  generated  pressure  waves  load  the  internal  structure.  The  base  discretization  is  extremely 

crude:  only 

8

4×

  quadrilateral  (Q4VF)  elements  in  the  fluid  and  2  shell  elements  (ED01)  in  the 

structure. In this case we use VFCCs for the fluid and the FLSW algorithm to treat FSI.

The simulations performed are summarized in Table 1.

Case

Fluid

Structure

FSI

Notes

COAD01

Adaptive

Not adaptive

FLSW Base calculation (adaptive fluid)

COAD02

Adaptive

Adaptive

FLSW

Add adaptivity in structure

COAD03

Not adaptive

Adaptive

FLSW

Remove adaptivity in fluid

Table 1 - Box simulations with VFCCs and FLSW

Fluid contour and internal structure

Initial mesh adapted in the fluid

Figure 3 - Fluid box with internal diaphragm

9

COAD01

The first simulation uses adaptivity only in the fluid sub-domain, according to the model presented in 

reference [12], and is considered as a reference solution. The adaptation of the fluid domain is done 

by specifying some dimensioning at the beginning of the input file:

DIME
  ADAP NPOI 81 Q4VF 88 NVFI 206 ENDA
  NALE 1 NBLE 1
TERM

and by adding the ADAP optional keyword to the FLSW directive:

LINK DECO
     FLSW STRU LECT stru TERM
          FLUI LECT flui TERM
          R 0.71    ! flui mesh size 1.0 : 1.0*0.71 = 0.71
          HGRI 1.6  ! stru mesh size 1.5
          DGRI
          FACE
          BFLU 2 FSCP 1
          ADAP LMAX 3

The RCON option is also added in order to keep the fluid mesh transition smooth:

OPTI PAS AUTO NOTE LOG 1
     CSTA 0.5
     ADAP RCON

Some results of this calculation are shown in Figure 4. The initial influence domain of the structure is 

shown in the left picture. The right picture presents the final influence domain, which follows the 

motion  and  deformation  of  the  structure,  and  the fluid velocities  around the  diaphragm. Note that 

also  the  fluid mesh  refinement  follows  the  structure.  Although  failure  of  the  structural  material is 

specified and erosion is activated (EROS 1.0), no structural element is eroded until the final time.

Initial influence domain

Final influence domain and
fluid velocities

Figure 4 - Results of case COAD01

10

COAD02

The next simulation adds adaptivity in the structure by means of the THRS (threshold) directive: The 

mesh adaptivity dimensioning must be updated:

DIME
  ADAP NPOI 81 Q4VF 88 ED01 8 NVFI 206 ENDA
  NALE 1 NBLE 1
TERM

A VM23 material is used in the structure with a failure criterion on von Mises equivalent stress:

MATE VM23 RO 8000. YOUN 1.D11 NU 0.3 ELAS 2.D8
          FAIL VMIS LIMI 7.5E7
          TRAC 3 2.D8 2.D-3 3.D8 1. 3.1D8 2.
          LECT stru _ed01 TERM

The  ECR(6)  value  for  this  material  (see  User’s  Manual  [21])  is  a  failure  flag,  which  assumes  the 

value 0 for a virgin Gauss point and the value 1 for a failed Gauss point. Since a shell element has 

several Gauss points (10 points by default in the case of ED01) the “average” global failure flag for 

the whole element may assume values between 0.0 and 1.0, depending on how many Gauss points 

have  failed.  When  the  global  failure  flag  reaches  the  limit  set  in  the  input  for  erosion  (1.0  in  this 

case), the element is eroded and it is no longer considered in the calculation.

The threshold directive for adaptivity in the structure is specified as follows:

ADAP THRS ECRO 6 TMIN 0.1 TMAX 0.5 MAXL 3
          LECT stru TERM

That is, the ECR(6) value is monitored in the structure (stru object) and structure mesh refinement 

from level 1 (base level, no refinement) up to level 3 (two successive refinements) is performed as 

the value passes from 0.1 to 0.5. Of course, the structure mesh must be refined when some damage 

(incomplete failure) takes place, i.e. well before the element has reached complete failure (according 

to the EROS parameter value) and is eroded. Only in this way can structure mesh adaptivity help to 

better capture the structural failure mechanism.

In order to precisely follow on the listing the mesh adaptation (in particular in the structure) in this 

calculation, we add the option:

OPTI ... ADAP dump stat RCON

The calculation takes 121 time steps to reach the final time of 20 ms. In the listing, we find the fol-

lowing messages concerning the splitting of structural elements:

SPLIT ELEMENT    33 AT STEP    75 AT TIME  1.50472D-02
SPLIT ELEMENT    35 AT STEP    75 AT TIME  1.50472D-02
SPLIT ELEMENT    36 AT STEP    75 AT TIME  1.50472D-02
SPLIT ELEMENT    34 AT STEP    75 AT TIME  1.50472D-02

Element number 33 is the lower base shell element, while element 34 is the upper one. Elements 35 

and 36 result from the splitting of element 33, and are further split.

11

We also learn from a message on the listing that element 40 (a descendent structural element) com-

pletely fails and is eroded at step 137:

** ATTENTION 3 IN PUT_FAILED_ELEM : STEP 137 T = 1.84387E-02 
   ELEMENT 37 BECOMES ERODED (MATERIAL)

This is the only eroded element in the whole calculation up to the final time. The fact that no element 

completely failed and was eroded in the “reference” solution (case COAD01) should not be surpris-

ing since of course the solution may depend slightly upon whether the structural mesh is adapted or 

not.

Interpretation of results

It is important to note the following detail: the step number and the time printed in the listing at each 

element  splitting  (with  OPTI  ADAP  DUMP  active)  are  the  values  at  the  beginning  of  the  step  at 

which the splitting occurs. In fact, MESH_ADAPTIVITY is called by CALCUL just before incre-

menting the step number and the time (see e.g. Figure 1) so that the step number and the time appear-

ing in the message are in reality those pertaining to the previous (just completed) time step. Thus, in 

the present example, if we would visualize the structural mesh at step 75, we would still see element 

33 in place (and not his children elements 35 and 36).

This (apparent) discrepancy of 1 time step is not critical in an explicit code such as EPX where the 

time increment is very small anyway due to stability constraints. However, it is important that the 

user be aware of such details.

In the light of these considerations, some results of this calculation are presented below in Figure 5.

At step 75 we still see 2 face domains, but they become 6 at step 76 as the structure is refined. At step 

136 all domains are still visible but starting from step 137 the failed element (eroded at step 137) and 

the corresponding face domain have disappeared. The final result (step 153) is also shown.

12

Figure 5 - Results of case COAD02

13

COAD03

The  next  and  final  simulation  is  similar  to  case  COAD02  but  adaptivity  in  the  fluid  is  removed. 

There is adaptivity only in the structure. As a consequence, the structural influence domain must be 

rebuilt like in case 02. Of course, this type of model is not recommended since, as the structure mesh 

is refined, it becomes even finer than the fluid mesh (which is not adapted in this case). However, we 

want to make sure that the code works even in an extreme (and ill-posed) situation like the present 

one.

This is indeed the case and some results of this (weird) simulation are presented in Figure 6. Element 

44 is eroded at step 130 and the calculation terminates normally at step 149.

Initial influence domain

Final influence domain and
fluid velocities

Figure 6 - Results of case COAD03

3.2  Combined Threshold / FLSR adaptivity

We now consider the same problem  as before  but  we discretize  the fluid domain by means of FE 

instead of VFCC and we use the FLSR model instead of FLSW for FSI.

The simulations performed are summarized in Table 2.

Case

Fluid

Structure

FSI

Notes

COAD04

Adaptive

Not adaptive

FLSR Base calculation (adaptive fluid)

COAD07

Adaptive

Not adaptive

FLSR

Twice finer meshes

COAD05

Adaptive

Adaptive

FLSR

Add adaptivity in structure

Table 2 - Box simulations with FE and FLSR

14

Case

Fluid

Structure

FSI

Notes

COAD06

Not adaptive

Adaptive

FLSR

Remove adaptivity in fluid

Table 2 - Box simulations with FE and FLSR

COAD04

This is similar to case COAD01 (adaptivity only in the fluid domain). With FE now to model the 

fluid domain, it becomes necessary to block the whole contour of the fluid domain along the appro-

priate direction(s) in order to simulate rigid walls (this was automatic with FLSW in the previous 

examples). Therefore the boundary conditions become:

LINK COUP SPLT NONE
     BLOQ 1 LECT 1 PAS 9 37 9 PAS 9 45 TERM
     BLOQ 2 LECT 1 PAS 1 9 37 PAS 1 45 TERM
     BLOQ 123 LECT base TERM
     FLSR STRU LECT stru TERM
          FLUI LECT flui TERM
          R 0.71    ! flui mesh size 1.0 : 1.0*0.71 = 0.71
          HGRI 1.6  ! stru mesh size 1.5
          DGRI
          BFLU 2 FSCP 1
          ADAP LMAX 3

The solution reaches normally the final time after 143 time steps. However, by visualizing the results 

an apparently strange phenomenon is observed. At a certain point of the calculation (step 93, time 

13.77 ms) the structure gets completely blocked (structural “locking”), see for example the plot in 

Figure 7 which shows the horizontal displacement of the structure tip.

Structure
“locking”

Figure 7 - Results of case COAD04

15

This phenomenon occurs since in this problem the mesh is very coarse and the number of constraints 

which arise at a certain moment of the solution is too large with respect to the number of degrees of 

freedom (dofs) of the problem.

Recall that in this case we have three different types of constraints:

• Blockages along the fluid boundary and at the base of the structure.

• FSI conditions (which are also imposed strongly in a coupled manner in this case)

• Further constraints at hanging nodes due to adaptivity (these are not needed with VFCCs).

To confirm this analysis, the same calculation is repeated by using a different solver for the links sys-

tem, the SPLIB solver. This is activated by adding the keywords SOLV SPLI to the LINK COUP 

directive. In this case, the code stops with an error message saying that “NO CONVERGENCE IS 

REACHED in 1000 ITERATIONS”.

This  is  a  clear  indication  that  the  system  of  constraints  to  be  solved  is  singular  (too  many  con-

straints). The fact that the standard solver (Cholesky) is able to continue the calculation is due to the 

special implementation of this solver in EPX, which is able to get rid of (a limited number of) redun-

dant constraints. However, in this case the solution obtained is unphysical.

The FLSW model combined with VFCCs of the previous simulations did not suffer of this problem. 

In that case in fact, the only “strong” constraint imposed were the blockages at the base of the struc-

ture. No blockages on the contour of the fluid are necessary in that case. The FSI model uses a weak 

formulation  (direct  pressure  application),  which  again  introduces  no  constraints.  Finally,  even  the 

adaptive hanging nodes introduce no additional constraints with the VFCC model (because veloci-

ties are expressed at the cell centers and not at the nodes).

COAD07

This  simulation  is  similar  to  COAD04  but  uses  twice  finer  meshes,  both  for  the  fluid  and  for  the 

structure domain. The hope is that the balance between constraints and dofs becomes more favorable 

so that a (meaningful) solution to the problem can be found.

The locking occurs later than in case 04, but it is still visible as can be seen in Figure 8.

16

Structure
“locking”

Figure 8 - Results of case COAD07

COAD05

This simulation is similar to COAD04 for the initial meshes (fluid and structure) but adaptivity in the 

structure is added (like in case COAD02). Two elements fail completely and are eroded in this calcu-

lation: element 38 at step 151 (17.14 ms) and element 37 at step 185 (18.97 ms).

Perhaps due to this, no locking is observed, see Figure 9.

The new combined adaptivity model seems to work correctly, as can be seen in Figure 10.

COAD06

This  simulation  is  similar  to  05  but  we  remove  the  adaptivity  in  the  fluid  (although  as  already 

explained this is not good practice). The model works and there is no locking. Some results are pre-

sented in Figures 11 and 12. 

Two elements fail in this case: element 40 at step 102 (16.88 ms) and element 39 at step 112 (17.90 

ms).

Figures 13 and 14 compare the horizontal displacements at the structure tip and the fluid pressures in 

the “explosive” element, respectively, in solutions 01 to 06.

17

Figure 9 - Some results of case COAD05

Figure 10 - Further results of case COAD05

18

Figure 11 - Some results of case COAD06

Figure 12 - Further results of case COAD06

19

Figure 13 - Comparison of tip structural displacements

Figure 14 - Comparison of fluid pressures

20

4.  References
[1] F. CASADEI, P. DÍEZ, F. VERDUGO: “A Data Structure for Adaptivity in EUROPLEXUS”, JRC

Technical Note PUBSY N. JRC60795, September 2010.

[2] F. CASADEI, P. DÍEZ, F. VERDUGO: “Adaptivity in FE Models for Fluids in EUROPLEXUS”,

JRC Technical Note PUBSY N. JRC61622, November 2010.

[3] F.  CASADEI,  P.  DÍEZ,  F.  VERDUGO:  “Adaptive  3D  Refinement  and  Un-refinement  of  8-node

Solid  and  Fluid  Hexahedra  in  EUROPLEXUS”,  JRC  Technical  Note  PUBSY  N.  JRC63833,

March 2011.

[4] F. CASADEI, P. DÍEZ, F. VERDUGO: “Implementation of a 2D Adaptivity Indicator for Fast Tran-

sient Dynamics in EUROPLEXUS”, JRC Technical Note PUBSY N. JRC64506, April 2011.

[5] F. CASADEI, P. DÍEZ, F. VERDUGO: “Further Development of 2D Adaptivity Error Indicators in

EUROPLEXUS”, JRC Technical Note, PUBSY No. JRC66337, September 2011.

[6] F. VERDUGO, P. DÍEZ, F. CASADEI: “Natural quantities of interest in linear elastodynamics for

goal oriented error estimation and adaptivity”, Proceedings of the V International Conference

on  Adaptive  Modeling  and  Simulation  (ADMOS  2011),  D.  Aubry  and  P.  Díez  (Eds),  Paris,

France, 6-8 June 2011.

[7] F. VERDUGO, P. DÍEZ, F. CASADEI: “General form of the natural quantities of interest for goal

oriented error assessment and adaptivity in linear elastodynamics”, Submitted for publication in

the International Journal for Numerical Methods in Engineering, DOI: 10.1002/nme, PUBSY

No. JRC65788, July 2011.

[8] F.  CASADEI, G. VALSAMOS, P.  DÍEZ,  F. VERDUGO:  “Implementation of  Adaptivity  in  2D  Cell

Centred Finite Volumes in EUROPLEXUS”, Technical Note, PUBSY No. JRC67859, Decem-

ber 2011.

[9] F.  CASADEI,  P.  DÍEZ,  F.  VERDUGO:  “Implementation  of  Adaptivity  in  3D  Cell  Centred  Finite

Volumes in EUROPLEXUS”, Technical Note, PUBSY No. JRC68168, December 2011.

[10] F. CASADEI, P. DÍEZ, F. VERDUGO: “Testing Adaptivity in 2D Cell Centred Finite Volumes with

the CDEM Combustion Model in EUROPLEXUS”, Technical Note, PUBSY No. JRC68333,

December 2011.

[11] F.  CASADEI,  P.  DÍEZ,  F.  VERDUGO:  “An  algorithm  for  mesh  refinement  and  un-refinement  in

fast  transient  dynamics”,  International  Journal  of  Computational  Methods,  DOI  10.1142/

S0219876213500187, Vol. 10, No. 4, pp. 1350018-1 / 1350018-31, 2013.

[12] F. CASADEI, G. VALSAMOS, M. LARCHER, A. BECCANTINI: “Combination of Mesh Adaptivity

21

with Fluid-Structure Interaction in Europlexus”. Technical Note, PUBSY No. JRC89728, EUR

Report 26617 EN, 2014.

[13] F. CASADEI, M. LARCHER, G. VALSAMOS: “Adaptivity with Simplex Elements in Europlexus”.

Technical Note, PUBSY No. JRC89894, EUR Report 26630 EN, 2014.

[14] F. CASADEI, M. LARCHER, G. VALSAMOS: “Adaptivity in CEA’s Fluid Elements in Europlexus”.

Technical Note, PUBSY No. JRC89953, EUR Report 26632 EN, 2014.

[15] M.  LARCHER,  F.  CASADEI,  G.  VALSAMOS:  “Adaptivity  in  Shell/Beam/Bar  Elements  in  Euro-

plexus”. Technical Note, PUBSY No. JRC90456, EUR Report 26697 EN, 2014.

[16] F.  CASADEI:  “Fast  Transient  Fluid-Stucture  Interaction  with  Failure  and  Fragmentation”,

Extended  abstract  submitted  for  presentation  at  the  8th  World  Congress  on  Computational

Mechanics (WCCM8), Venice, Italy, June 30 - July 5, 2008.

[17] F. CASADEI, N. LECONTE: “Use of FLSR Fluid-Structure Interaction with Node-Centered Finite

Volumes in EUROPLEXUS. Technical Note, PUBSY No. JRC59686, August 2010.

[18] F.  CASADEI,  N.  LECONTE:  “FLSW  :  A  Weak,  Embedded-Type  Fluid-Structure  Interaction

Model with CCFV in EUROPLEXUS”, Technical Note, PUBSY No. JRC65826, July 2011.

[19] F. CASADEI, M. LARCHER, N. LECONTE: “Strong and weak forms of a fully non-conforming FSI

algorithm in fast transient dynamics for blast loading of structures”, PUBSY No. JRC60824.

COMPDYN 2011, III ECCOMAS Thematic Conference on Computational Methods in Struc-

tural Dynamics and Earthquake Engineering, Corfu, Greece, May 25{28, 2011.

[20] A. BECCANTINI, F. CASADEI, P. GALON: “Improvement of the FLSW model for Cell-Centered

Finite  Volumes  in  EUROPLEXUS.  Report  DEN/DANS/DM2S/STMF/LATF/NT/13-019/A,

April 2013.

[21] “EUROPLEXUS User’s Manual”, on-line version: http://europlexus.jrc.ec.europa.eu.

22

List of input files

coad01.epx  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   24
coad02.epx  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   24
coad03.epx  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   25
coad04.epx  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   25
coad05.epx  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   26
coad06.epx  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   27
coad07.dgibi   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   27
coad07.epx  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   28
resume.epx  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   28

23

coad01.epx

Appendix

Sample input files

This Section contains, in alphabetical file order, the
listings  of  all  input  files  related  to  the  examples
which were proposed in the previous Sections.

coad01.epx 

COAD01
ECHO
!CONV WIN
DPLA ALE
EROS 1.0
DIME

ADAP NPOI 81 Q4VF 88 NVFI 206 ENDA
NALE 1 NBLE 1

TERM
GEOM LIBR POIN 48 Q4VF 32 ED01 2 TERM
3 0
3 1
3 2
3 3
3 4

5 0
5 1
5 2
5 3
5 4

6 0
6 1
6 2
6 3
6 4

4 0
4 1
4 2
4 3
4 4

2 0
2 1
2 2
2 3
2 4

7 0
7 1
7 2
7 3
7 4

8 0
8 1
8 2
8 3
8 4

4 3

1 0
1 1
1 2
1 3
1 4
4 1.5

0 0
0 1
0 2
0 3
0 4
4 0
1 2 11 10
2 3 12 11
3 4 13 12
4 5 14 13
5 6 15 14
6 7 16 15
7 8 17 16
8 9 18 17
10 11 20 19
11 12 21 20
12 13 22 21
13 14 23 22
14 15 24 23
15 16 25 24
16 17 26 25
17 18 27 26
19 20 29 28
20 21 30 29
21 22 31 30
22 23 32 31
23 24 33 32
24 25 34 33
25 26 35 34
26 27 36 35
28 29 38 37
29 30 39 38
30 31 40 39
31 32 41 40
32 33 42 41
33 34 43 42
34 35 44 43
35 36 45 44
46 47
47 48

COMP GROU 4 'flui' LECT 1 PAS 1 32 TERM

'stru' LECT 33 34 TERM
'expl' LECT 1 TERM
'air'

LECT flui DIFF expl TERM

NGRO 2 'base' LECT 46 TERM
LECT 48 TERM

'p5s'

EPAI 1.E-2 LECT stru TERM
COUL ROUG LECT expl TERM
TURQ LECT air
TERM
VERT LECT stru TERM

GRIL LAGR LECT stru TERM
EULE LECT flui TERM

MATE VM23 RO 8000. YOUN 1.D11 NU 0.3 ELAS 2.D8

FAIL VMIS LIMI 7.5E7
TRAC 3 2.D8 2.D-3 3.D8 1. 3.1D8 2.
LECT stru TERM

GAZP RO 20.0 PINI 20.E5 GAMM 1.4 PREF 1.E5

LECT expl TERM

GAZP RO 1.0 PINI 1.E5 GAMM 1.4 PREF 1.E5

LECT air _q4vf TERM

LINK COUP SPLT NONE

BLOQ 123 LECT base TERM

LINK DECO

FLSW STRU LECT stru TERM
FLUI LECT flui TERM
R 0.71
HGRI 1.6
DGRI
FACE
BFLU 2 FSCP 1
ADAP LMAX 3

! flui mesh size 1.0 : 1.0*0.71 = 0.71
! stru mesh size 1.5

ECRI DEPL VITE ACCE FINT FEXT FLIA FDEC CONT ECRO VFCC TFRE 1.D0

FICH ALIC FREQ 1

OPTI PAS AUTO NOTE LOG 1

CSTA 0.5
ADAP RCON

CALC TINI 0. TEND 20.D-3
SUIT
*===============================================================================
COAD01A
ECHO

CONV WIN
OPTI PRIN
RESU ALIC GARD PSCR
SORT VISU NSTO 1
*-------------------------------------------------------------------------------
PLAY

8 May 2015 9:40 pm

CAME
!

1 EYE
Q
VIEW
RIGH
UP
FOV

4.00000E+00
1.00000E+00
0.00000E+00
1.00000E+00
0.00000E+00
2.48819E+01

2.23607E+01
2.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00 -1.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
1.00000E+00

0.00000E+00

0.00000E+00

2.00000E+00

!NAVIGATION MODE: ROTATING CAMERA
4.00000E+00
!CENTER :
4.47214E+00
!RSPHERE:
2.23607E+01
!RADIUS :
1.00000E+00
!ASPECT :
1.74413E+01
:
!NEAR
!FAR
3.13050E+01
:
SCEN GEOM NAVI FREE
FACE HFRO
FLSW DOMA

VECT SCCO FIEL VCVI SCAL USER PROG 15 PAS 15 210 TERM

SUPP LECT flui TERM

TEXT VSCA
COLO PAPE
SLER CAM1 1 NFRA 1
TRAC OFFS FICH AVI NOCL NFTO 101 FPS 15 KFRE 10 COMP -1 NFAI REND
FREQ 1
GOTR LOOP 99 OFFS FICH AVI CONT NOCL NFAI REND
GO
TRAC OFFS FICH AVI CONT NFAI REND
ENDPLAY
*-------------------------------------------------------------------------------
SUIT
*===============================================================================
COAD01C
ECHO
OPTI PRIN
RESU ALIC GARD PSCR
SORT GRAP
PERF 'coad01.pun'
COUR 1 'dx_s'
TERM
COUR 2 'p_expl' ECRO COMP 1 ELEM LECT expl TERM
TRAC 1 AXES 1.0 'DEPL. [M]'
TRAC 2 AXES 1.0 'PRES. [PA]'
LIST 1 AXES 1.0 'DEPL. [M]'
LIST 2 AXES 1.0 'PRES. [PA]'
QUAL DEPL COMP 1 LECT p5s

DEPL COMP 1 NOEU LECT p5s

TERM REFE
ECRO COMP 1 LECT expl TERM REFE

2.40365E-01 TOLE 5.E-2
2.05255E+05 TOLE 1.E-2

*-------------------------------------------------------------------------------
FIN

coad02.epx 

COAD02
ECHO
!CONV WIN
DPLA ALE
EROS 1.0
DIME

ADAP NPOI 81 Q4VF 88 ED01 8 NVFI 206 ENDA
NALE 1 NBLE 1

TERM
GEOM LIBR POIN 48 Q4VF 32 ED01 2 TERM
3 0
3 1
3 2
3 3
3 4

6 0
6 1
6 2
6 3
6 4

4 0
4 1
4 2
4 3
4 4

2 0
2 1
2 2
2 3
2 4

5 0
5 1
5 2
5 3
5 4

7 0
7 1
7 2
7 3
7 4

8 0
8 1
8 2
8 3
8 4

4 3

1 0
1 1
1 2
1 3
1 4
4 1.5

0 0
0 1
0 2
0 3
0 4
4 0
1 2 11 10
2 3 12 11
3 4 13 12
4 5 14 13
5 6 15 14
6 7 16 15
7 8 17 16
8 9 18 17
10 11 20 19
11 12 21 20
12 13 22 21
13 14 23 22
14 15 24 23
15 16 25 24
16 17 26 25
17 18 27 26
19 20 29 28
20 21 30 29
21 22 31 30
22 23 32 31
23 24 33 32
24 25 34 33
25 26 35 34
26 27 36 35
28 29 38 37
29 30 39 38
30 31 40 39
31 32 41 40
32 33 42 41
33 34 43 42
34 35 44 43
35 36 45 44
46 47
47 48

COMP GROU 4 'flui' LECT 1 PAS 1 32 TERM

'stru' LECT 33 34 TERM
'expl' LECT 1 TERM
'air'

LECT flui DIFF expl TERM

NGRO 2 'base' LECT 46 TERM
LECT 48 TERM

'p5s'

EPAI 1.E-2 LECT stru _ed01 TERM
COUL ROUG LECT expl TERM
TURQ LECT air
TERM
VERT LECT stru TERM

GRIL LAGR LECT stru TERM
EULE LECT flui TERM

ADAP THRS ECRO 6 TMIN 0.1 TMAX 0.5 MAXL 3

LECT stru TERM

MATE VM23 RO 8000. YOUN 1.D11 NU 0.3 ELAS 2.D8

FAIL VMIS LIMI 7.5E7
TRAC 3 2.D8 2.D-3 3.D8 1. 3.1D8 2.

Page 24

coad03.epx

8 May 2015 9:40 pm

LECT stru _ed01 TERM

GAZP RO 20.0 PINI 20.E5 GAMM 1.4 PREF 1.E5

LECT expl TERM

GAZP RO 1.0 PINI 1.E5 GAMM 1.4 PREF 1.E5

LECT air _q4vf TERM

LINK COUP SPLT NONE

BLOQ 123 LECT base TERM

LINK DECO

FLSW STRU LECT stru TERM
FLUI LECT flui TERM
R 0.71
HGRI 1.6
DGRI
FACE
BFLU 2 FSCP 1
ADAP LMAX 3

! flui mesh size 1.0 : 1.0*0.71 = 0.71
! stru mesh size 1.5

ECRI DEPL VITE ACCE FINT FEXT FLIA FDEC CONT ECRO VFCC TFRE 1.D0

FICH ALIC FREQ 1

OPTI PAS AUTO NOTE LOG 1

CSTA 0.5
ADAP dump stat RCON
CALC TINI 0. TEND 20.D-3
SUIT
*===============================================================================
COAD02A
ECHO

CONV WIN
OPTI PRIN
RESU ALIC GARD PSCR
SORT VISU NSTO 1
*-------------------------------------------------------------------------------
PLAY
CAME
!

0.00000E+00

1 EYE
Q
VIEW
RIGH
UP
FOV

4.00000E+00
1.00000E+00
0.00000E+00
1.00000E+00
0.00000E+00
2.48819E+01

2.23607E+01
2.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00 -1.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
1.00000E+00

0.00000E+00

2.00000E+00

!NAVIGATION MODE: ROTATING CAMERA
4.00000E+00
!CENTER :
4.47214E+00
!RSPHERE:
2.23607E+01
!RADIUS :
1.00000E+00
!ASPECT :
1.74413E+01
:
!NEAR
!FAR
3.13050E+01
:
SCEN GEOM NAVI FREE
FACE HFRO
FLSW DOMA

VECT SCCO FIEL VCVI SCAL USER PROG 15 PAS 15 210 TERM

SUPP LECT flui TERM

TEXT VSCA
COLO PAPE
SLER CAM1 1 NFRA 1
TRAC OFFS FICH AVI NOCL NFTO 154 FPS 15 KFRE 10 COMP -1 NFAI REND
FREQ 1
GOTR LOOP 152 OFFS FICH AVI CONT NOCL NFAI REND
GO
TRAC OFFS FICH AVI CONT NFAI REND
ENDPLAY
*-------------------------------------------------------------------------------
SUIT
*===============================================================================
COAD02C
ECHO
OPTI PRIN
RESU ALIC GARD PSCR
SORT GRAP
PERF 'coad02.pun'
COUR 1 'dx_s'
TERM
COUR 2 'p_expl' ECRO COMP 1 ELEM LECT expl TERM
TRAC 1 AXES 1.0 'DEPL. [M]'
TRAC 2 AXES 1.0 'PRES. [PA]'
LIST 1 AXES 1.0 'DEPL. [M]'
LIST 2 AXES 1.0 'PRES. [PA]'
QUAL DEPL COMP 1 LECT p5s

DEPL COMP 1 NOEU LECT p5s

TERM REFE
ECRO COMP 1 LECT expl TERM REFE

2.43285E-01 TOLE 5.E-2
2.03872E+05 TOLE 1.E-2

*-------------------------------------------------------------------------------
FIN

coad03.epx 

COAD03
ECHO
!CONV WIN
DPLA ALE
EROS 1.0
DIME

ADAP NPOI 6 ED01 12 ENDA
NALE 1 NBLE 1

TERM
GEOM LIBR POIN 48 Q4VF 32 ED01 2 TERM
3 0
3 1
3 2
3 3
3 4

5 0
5 1
5 2
5 3
5 4

6 0
6 1
6 2
6 3
6 4

4 0
4 1
4 2
4 3
4 4

2 0
2 1
2 2
2 3
2 4

7 0
7 1
7 2
7 3
7 4

8 0
8 1
8 2
8 3
8 4

4 3

1 0
1 1
1 2
1 3
1 4
4 1.5

0 0
0 1
0 2
0 3
0 4
4 0
1 2 11 10
2 3 12 11
3 4 13 12
4 5 14 13
5 6 15 14
6 7 16 15
7 8 17 16
8 9 18 17
10 11 20 19
11 12 21 20
12 13 22 21
13 14 23 22
14 15 24 23
15 16 25 24
16 17 26 25
17 18 27 26
19 20 29 28
20 21 30 29
21 22 31 30

22 23 32 31
23 24 33 32
24 25 34 33
25 26 35 34
26 27 36 35
28 29 38 37
29 30 39 38
30 31 40 39
31 32 41 40
32 33 42 41
33 34 43 42
34 35 44 43
35 36 45 44
46 47
47 48

COMP GROU 4 'flui' LECT 1 PAS 1 32 TERM

'stru' LECT 33 34 TERM
'expl' LECT 1 TERM
'air'

LECT flui DIFF expl TERM

NGRO 2 'base' LECT 46 TERM
LECT 48 TERM

'p5s'

EPAI 1.E-2 LECT stru _ed01 TERM
COUL ROUG LECT expl TERM
TURQ LECT air
TERM
VERT LECT stru TERM

GRIL LAGR LECT stru TERM
EULE LECT flui TERM

ADAP THRS ECRO 6 TMIN 0.1 TMAX 0.5 MAXL 3

LECT stru TERM

MATE VM23 RO 8000. YOUN 1.D11 NU 0.3 ELAS 2.D8

FAIL VMIS LIMI 7.5E7
TRAC 3 2.D8 2.D-3 3.D8 1. 3.1D8 2.
LECT stru _ed01 TERM

GAZP RO 20.0 PINI 20.E5 GAMM 1.4 PREF 1.E5

LECT expl TERM

GAZP RO 1.0 PINI 1.E5 GAMM 1.4 PREF 1.E5

LECT air _q4vf TERM

LINK COUP SPLT NONE

BLOQ 123 LECT base TERM

LINK DECO

FLSW STRU LECT stru TERM
FLUI LECT flui TERM
R 0.71
HGRI 1.6
DGRI
FACE
BFLU 2 FSCP 1

! flui mesh size 1.0 : 1.0*0.71 = 0.71
! stru mesh size 1.5

ECRI DEPL VITE ACCE FINT FEXT FLIA FDEC CONT ECRO VFCC TFRE 1.D0

FICH ALIC FREQ 1

OPTI PAS AUTO NOTE LOG 1

CSTA 0.5
ADAP RCON

CALC TINI 0. TEND 20.D-3
SUIT
*===============================================================================
COAD03A
ECHO

CONV WIN
OPTI PRIN
RESU ALIC GARD PSCR
SORT VISU NSTO 1
*-------------------------------------------------------------------------------
PLAY
CAME
!

0.00000E+00

1 EYE
Q
VIEW
RIGH
UP
FOV

4.00000E+00
1.00000E+00
0.00000E+00
1.00000E+00
0.00000E+00
2.48819E+01

2.23607E+01
2.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00 -1.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
1.00000E+00

0.00000E+00

2.00000E+00

!NAVIGATION MODE: ROTATING CAMERA
4.00000E+00
!CENTER :
4.47214E+00
!RSPHERE:
2.23607E+01
!RADIUS :
1.00000E+00
!ASPECT :
1.74413E+01
:
!NEAR
!FAR
3.13050E+01
:
SCEN GEOM NAVI FREE
FACE HFRO
FLSW DOMA

VECT SCCO FIEL VCVI SCAL USER PROG 15 PAS 15 210 TERM

SUPP LECT flui TERM

TEXT VSCA
COLO PAPE
SLER CAM1 1 NFRA 1
TRAC OFFS FICH AVI NOCL NFTO 150 FPS 15 KFRE 10 COMP -1 NFAI REND
FREQ 1
GOTR LOOP 148 OFFS FICH AVI CONT NOCL NFAI REND
GO
TRAC OFFS FICH AVI CONT NFAI REND
ENDPLAY
*-------------------------------------------------------------------------------
SUIT
*===============================================================================
COAD03C
ECHO
OPTI PRIN
RESU ALIC GARD PSCR
SORT GRAP
PERF 'coad03.pun'
COUR 1 'dx_s'
TERM
COUR 2 'p_expl' ECRO COMP 1 ELEM LECT expl TERM
TRAC 1 AXES 1.0 'DEPL. [M]'
TRAC 2 AXES 1.0 'PRES. [PA]'
LIST 1 AXES 1.0 'DEPL. [M]'
LIST 2 AXES 1.0 'PRES. [PA]'
QUAL DEPL COMP 1 LECT p5s

DEPL COMP 1 NOEU LECT p5s

TERM REFE
ECRO COMP 1 LECT expl TERM REFE

4.96136E-01 TOLE 5.E-2
2.28921E+05 TOLE 1.E-2

*-------------------------------------------------------------------------------
FIN

coad04.epx 

COAD04
ECHO
!CONV WIN
DPLA ALE

Page 25

8 0
8 1
8 2
8 3
8 4

8 May 2015 9:40 pm

TRAC OFFS FICH AVI NOCL NFTO 144 FPS 15 KFRE 10 COMP -1 NFAI REND
FREQ 1
GOTR LOOP 142 OFFS FICH AVI CONT NOCL NFAI REND
GO
TRAC OFFS FICH AVI CONT NFAI REND
ENDPLAY
*-------------------------------------------------------------------------------
SUIT
*===============================================================================
COAD04C
ECHO
OPTI PRIN
RESU ALIC GARD PSCR
SORT GRAP
PERF 'coad04.pun'
COUR 1 'dx_s'
TERM
COUR 2 'p_expl' ECRO COMP 1 ELEM LECT expl TERM
TRAC 1 AXES 1.0 'DEPL. [M]'
TRAC 2 AXES 1.0 'PRES. [PA]'
LIST 1 AXES 1.0 'DEPL. [M]'
LIST 2 AXES 1.0 'PRES. [PA]'
QUAL DEPL COMP 1 LECT p5s

DEPL COMP 1 NOEU LECT p5s

TERM REFE
ECRO COMP 1 LECT expl TERM REFE

1.20486E-01 TOLE 5.E-2
2.73005E+05 TOLE 1.E-2

*-------------------------------------------------------------------------------
FIN

coad05.epx 

COAD05
ECHO
!CONV WIN
DPLA ALE
EROS 1.0
DIME

ADAP NPOI 81 FL24 88 ED01 8 ENDA
NALE 1 NBLE 1

coad05.epx

EROS 1.0
DIME

ADAP NPOI 81 FL24 88 ENDA
NALE 1 NBLE 1

TERM
GEOM LIBR POIN 48 FL24 32 ED01 2 TERM
3 0
3 1
3 2
3 3
3 4

5 0
5 1
5 2
5 3
5 4

6 0
6 1
6 2
6 3
6 4

4 0
4 1
4 2
4 3
4 4

2 0
2 1
2 2
2 3
2 4

7 0
7 1
7 2
7 3
7 4

4 3

1 0
1 1
1 2
1 3
1 4
4 1.5

0 0
0 1
0 2
0 3
0 4
4 0
1 2 11 10
2 3 12 11
3 4 13 12
4 5 14 13
5 6 15 14
6 7 16 15
7 8 17 16
8 9 18 17
10 11 20 19
11 12 21 20
12 13 22 21
13 14 23 22
14 15 24 23
15 16 25 24
16 17 26 25
17 18 27 26
19 20 29 28
20 21 30 29
21 22 31 30
22 23 32 31
23 24 33 32
24 25 34 33
25 26 35 34
26 27 36 35
28 29 38 37
29 30 39 38
30 31 40 39
31 32 41 40
32 33 42 41
33 34 43 42
34 35 44 43
35 36 45 44
46 47
47 48

COMP GROU 4 'flui' LECT 1 PAS 1 32 TERM

'stru' LECT 33 34 TERM
'expl' LECT 1 TERM
'air'

LECT flui DIFF expl TERM

NGRO 2 'base' LECT 46 TERM
LECT 48 TERM

'p5s'

EPAI 1.E-2 LECT stru TERM
COUL ROUG LECT expl TERM
TURQ LECT air
TERM
VERT LECT stru TERM

GRIL LAGR LECT stru TERM
EULE LECT flui TERM

MATE VM23 RO 8000. YOUN 1.D11 NU 0.3 ELAS 2.D8

FAIL VMIS LIMI 7.5E7
TRAC 3 2.D8 2.D-3 3.D8 1. 3.1D8 2.
LECT stru TERM

FLUT RO 20.0 EINT 2.5E5 GAMM 1.4 PB 0 PREF 1.E5

ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5
CQ 2.56 PMIN 0 NUM 1
LECT expl TERM

FLUT RO 1.0 EINT 2.5E5 GAMM 1.4 PB 0 PREF 1.E5
ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5
CQ 2.56 PMIN 0 NUM 1
LECT air _fl24 TERM

LINK COUP SPLT NONE

BLOQ 1 LECT 1 PAS 9 37 9 PAS 9 45 TERM
BLOQ 2 LECT 1 PAS 1 9 37 PAS 1 45 TERM
BLOQ 123 LECT base TERM
FLSR STRU LECT stru TERM
FLUI LECT flui TERM
R 0.71
HGRI 1.6
DGRI
BFLU 2 FSCP 1
ADAP LMAX 3

! flui mesh size 1.0 : 1.0*0.71 = 0.71
! stru mesh size 1.5

ECRI DEPL VITE ACCE FINT FEXT FLIA FDEC CONT ECRO TFRE 1.D0

FICH ALIC FREQ 1

OPTI PAS AUTO NOTE LOG 1

CSTA 0.5
ADAP RCON

CALC TINI 0. TEND 20.D-3
SUIT
*===============================================================================
COAD04A
ECHO

CONV WIN
OPTI PRIN
RESU ALIC GARD PSCR
SORT VISU NSTO 1
*-------------------------------------------------------------------------------
PLAY
CAME
!

0.00000E+00

1 EYE
Q
VIEW
RIGH
UP
FOV

4.00000E+00
1.00000E+00
0.00000E+00
1.00000E+00
0.00000E+00
2.48819E+01

2.23607E+01
2.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00 -1.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
1.00000E+00

0.00000E+00

2.00000E+00

!NAVIGATION MODE: ROTATING CAMERA
4.00000E+00
!CENTER :
4.47214E+00
!RSPHERE:
2.23607E+01
!RADIUS :
1.00000E+00
!ASPECT :
1.74413E+01
:
!NEAR
!FAR
3.13050E+01
:
SCEN GEOM NAVI FREE
FACE HFRO
FLSR DOMA

VECT SCCO FIEL VITE SCAL USER PROG 15 PAS 15 210 TERM

SUPP LECT flui TERM

TEXT VSCA
COLO PAPE
SLER CAM1 1 NFRA 1

TERM
GEOM LIBR POIN 48 FL24 32 ED01 2 TERM
3 0
3 1
3 2
3 3
3 4

4 0
4 1
4 2
4 3
4 4

6 0
6 1
6 2
6 3
6 4

2 0
2 1
2 2
2 3
2 4

5 0
5 1
5 2
5 3
5 4

7 0
7 1
7 2
7 3
7 4

8 0
8 1
8 2
8 3
8 4

4 3

1 0
1 1
1 2
1 3
1 4
4 1.5

0 0
0 1
0 2
0 3
0 4
4 0
1 2 11 10
2 3 12 11
3 4 13 12
4 5 14 13
5 6 15 14
6 7 16 15
7 8 17 16
8 9 18 17
10 11 20 19
11 12 21 20
12 13 22 21
13 14 23 22
14 15 24 23
15 16 25 24
16 17 26 25
17 18 27 26
19 20 29 28
20 21 30 29
21 22 31 30
22 23 32 31
23 24 33 32
24 25 34 33
25 26 35 34
26 27 36 35
28 29 38 37
29 30 39 38
30 31 40 39
31 32 41 40
32 33 42 41
33 34 43 42
34 35 44 43
35 36 45 44
46 47
47 48

COMP GROU 4 'flui' LECT 1 PAS 1 32 TERM

'stru' LECT 33 34 TERM
'expl' LECT 1 TERM
'air'

LECT flui DIFF expl TERM

NGRO 2 'base' LECT 46 TERM
LECT 48 TERM

'p5s'

EPAI 1.E-2 LECT stru _ed01 TERM
COUL ROUG LECT expl TERM
TURQ LECT air
TERM
VERT LECT stru TERM

GRIL LAGR LECT stru TERM
EULE LECT flui TERM

ADAP THRS ECRO 6 TMIN 0.1 TMAX 0.5 MAXL 3

LECT stru TERM

MATE VM23 RO 8000. YOUN 1.D11 NU 0.3 ELAS 2.D8

FAIL VMIS LIMI 7.5E7
TRAC 3 2.D8 2.D-3 3.D8 1. 3.1D8 2.
LECT stru _ed01 TERM

FLUT RO 20.0 EINT 2.5E5 GAMM 1.4 PB 0 PREF 1.E5

ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5
CQ 2.56 PMIN 0 NUM 1
LECT expl TERM

FLUT RO 1.0 EINT 2.5E5 GAMM 1.4 PB 0 PREF 1.E5
ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5
CQ 2.56 PMIN 0 NUM 1
LECT air _fl24 TERM

LINK COUP SPLT NONE

BLOQ 1 LECT 1 PAS 9 37 9 PAS 9 45 TERM
BLOQ 2 LECT 1 PAS 1 9 37 PAS 1 45 TERM
BLOQ 123 LECT base TERM
FLSR STRU LECT stru TERM
FLUI LECT flui TERM
R 0.71
HGRI 1.6
DGRI
BFLU 2 FSCP 1
ADAP LMAX 3

! flui mesh size 1.0 : 1.0*0.71 = 0.71
! stru mesh size 1.5

ECRI DEPL VITE ACCE FINT FEXT FLIA FDEC CONT ECRO TFRE 1.D0

Page 26

coad06.epx

FICH ALIC FREQ 1

OPTI PAS AUTO NOTE LOG 1

CSTA 0.5
ADAP dump stat RCON
LNKS STAT DIAG
CALC TINI 0. TEND 20.D-3
SUIT
*===============================================================================
COAD05A
ECHO

CONV WIN
OPTI PRIN
RESU ALIC GARD PSCR
SORT VISU NSTO 1
*-------------------------------------------------------------------------------
PLAY
CAME
!

0.00000E+00

1 EYE
Q
VIEW
RIGH
UP
FOV

4.00000E+00
1.00000E+00
0.00000E+00
1.00000E+00
0.00000E+00
2.48819E+01

2.23607E+01
2.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00 -1.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
1.00000E+00

0.00000E+00

2.00000E+00

!NAVIGATION MODE: ROTATING CAMERA
4.00000E+00
!CENTER :
4.47214E+00
!RSPHERE:
2.23607E+01
!RADIUS :
1.00000E+00
!ASPECT :
1.74413E+01
:
!NEAR
!FAR
3.13050E+01
:
SCEN GEOM NAVI FREE
FACE HFRO
FLSR DOMA

VECT SCCO FIEL VITE SCAL USER PROG 15 PAS 15 210 TERM

SUPP LECT flui TERM

TEXT VSCA
COLO PAPE
SLER CAM1 1 NFRA 1
TRAC OFFS FICH AVI NOCL NFTO 186 FPS 15 KFRE 10 COMP -1 NFAI REND
FREQ 1
GOTR LOOP 184 OFFS FICH AVI CONT NOCL NFAI REND
GO
TRAC OFFS FICH AVI CONT NFAI REND
ENDPLAY
*-------------------------------------------------------------------------------
SUIT
*===============================================================================
COAD05C
ECHO
OPTI PRIN
RESU ALIC GARD PSCR
SORT GRAP
PERF 'coad05.pun'
COUR 1 'dx_s'
TERM
COUR 2 'p_expl' ECRO COMP 1 ELEM LECT expl TERM
TRAC 1 AXES 1.0 'DEPL. [M]'
TRAC 2 AXES 1.0 'PRES. [PA]'
LIST 1 AXES 1.0 'DEPL. [M]'
LIST 2 AXES 1.0 'PRES. [PA]'
QUAL DEPL COMP 1 LECT p5s

DEPL COMP 1 NOEU LECT p5s

TERM REFE
ECRO COMP 1 LECT expl TERM REFE

2.42487E-01 TOLE 5.E-2
2.72789E+05 TOLE 1.E-2

*-------------------------------------------------------------------------------
FIN

coad06.epx 

COAD06
ECHO
!CONV WIN
DPLA ALE
EROS 1.0
DIME

ADAP NPOI 4 ED01 8 ENDA
NALE 1 NBLE 1

TERM
GEOM LIBR POIN 48 FL24 32 ED01 2 TERM
3 0
3 1
3 2
3 3
3 4

5 0
5 1
5 2
5 3
5 4

6 0
6 1
6 2
6 3
6 4

4 0
4 1
4 2
4 3
4 4

2 0
2 1
2 2
2 3
2 4

7 0
7 1
7 2
7 3
7 4

8 0
8 1
8 2
8 3
8 4

4 3

1 0
1 1
1 2
1 3
1 4
4 1.5

0 0
0 1
0 2
0 3
0 4
4 0
1 2 11 10
2 3 12 11
3 4 13 12
4 5 14 13
5 6 15 14
6 7 16 15
7 8 17 16
8 9 18 17
10 11 20 19
11 12 21 20
12 13 22 21
13 14 23 22
14 15 24 23
15 16 25 24
16 17 26 25
17 18 27 26
19 20 29 28
20 21 30 29
21 22 31 30
22 23 32 31
23 24 33 32
24 25 34 33
25 26 35 34
26 27 36 35
28 29 38 37
29 30 39 38
30 31 40 39
31 32 41 40
32 33 42 41
33 34 43 42
34 35 44 43
35 36 45 44
46 47
47 48

COMP GROU 4 'flui' LECT 1 PAS 1 32 TERM

8 May 2015 9:40 pm

'stru' LECT 33 34 TERM
'expl' LECT 1 TERM
'air'

LECT flui DIFF expl TERM

NGRO 2 'base' LECT 46 TERM
LECT 48 TERM

'p5s'

EPAI 1.E-2 LECT stru _ed01 TERM
COUL ROUG LECT expl TERM
TURQ LECT air
TERM
VERT LECT stru TERM

GRIL LAGR LECT stru TERM
EULE LECT flui TERM

ADAP THRS ECRO 6 TMIN 0.1 TMAX 0.5 MAXL 3

LECT stru TERM

MATE VM23 RO 8000. YOUN 1.D11 NU 0.3 ELAS 2.D8

FAIL VMIS LIMI 7.5E7
TRAC 3 2.D8 2.D-3 3.D8 1. 3.1D8 2.
LECT stru _ed01 TERM

FLUT RO 20.0 EINT 2.5E5 GAMM 1.4 PB 0 PREF 1.E5

ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5
CQ 2.56 PMIN 0 NUM 1
LECT expl TERM

FLUT RO 1.0 EINT 2.5E5 GAMM 1.4 PB 0 PREF 1.E5
ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5
CQ 2.56 PMIN 0 NUM 1
LECT air _fl24 TERM

LINK COUP SPLT NONE

BLOQ 1 LECT 1 PAS 9 37 9 PAS 9 45 TERM
BLOQ 2 LECT 1 PAS 1 9 37 PAS 1 45 TERM
BLOQ 123 LECT base TERM
FLSR STRU LECT stru TERM
FLUI LECT flui TERM
R 0.71
HGRI 1.6
DGRI
BFLU 2 FSCP 1

! flui mesh size 1.0 : 1.0*0.71 = 0.71
! stru mesh size 1.5

ECRI DEPL VITE ACCE FINT FEXT FLIA FDEC CONT ECRO TFRE 1.D0

FICH ALIC FREQ 1

OPTI PAS AUTO NOTE LOG 1

CSTA 0.5
ADAP dump stat RCON
LNKS STAT DIAG
CALC TINI 0. TEND 20.D-3
SUIT
*===============================================================================
COAD06A
ECHO

CONV WIN
OPTI PRIN
RESU ALIC GARD PSCR
SORT VISU NSTO 1
*-------------------------------------------------------------------------------
PLAY
CAME
!

0.00000E+00

1 EYE
Q
VIEW
RIGH
UP
FOV

4.00000E+00
1.00000E+00
0.00000E+00
1.00000E+00
0.00000E+00
2.48819E+01

2.23607E+01
2.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00 -1.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
1.00000E+00

0.00000E+00

2.00000E+00

!NAVIGATION MODE: ROTATING CAMERA
4.00000E+00
!CENTER :
4.47214E+00
!RSPHERE:
2.23607E+01
!RADIUS :
1.00000E+00
!ASPECT :
1.74413E+01
:
!NEAR
!FAR
3.13050E+01
:
SCEN GEOM NAVI FREE
FACE HFRO
FLSR DOMA

VECT SCCO FIEL VITE SCAL USER PROG 15 PAS 15 210 TERM

SUPP LECT flui TERM

TEXT VSCA
COLO PAPE
SLER CAM1 1 NFRA 1
TRAC OFFS FICH AVI NOCL NFTO 134 FPS 15 KFRE 10 COMP -1 NFAI REND
FREQ 1
GOTR LOOP 132 OFFS FICH AVI CONT NOCL NFAI REND
GO
TRAC OFFS FICH AVI CONT NFAI REND
ENDPLAY
*-------------------------------------------------------------------------------
SUIT
*===============================================================================
COAD06C
ECHO
OPTI PRIN
RESU ALIC GARD PSCR
SORT GRAP
PERF 'coad06.pun'
COUR 1 'dx_s'
TERM
COUR 2 'p_expl' ECRO COMP 1 ELEM LECT expl TERM
TRAC 1 AXES 1.0 'DEPL. [M]'
TRAC 2 AXES 1.0 'PRES. [PA]'
LIST 1 AXES 1.0 'DEPL. [M]'
LIST 2 AXES 1.0 'PRES. [PA]'
QUAL DEPL COMP 1 LECT p5s

DEPL COMP 1 NOEU LECT p5s

TERM REFE
ECRO COMP 1 LECT expl TERM REFE

2.35154E-01 TOLE 5.E-2
2.68996E+05 TOLE 1.E-2

*-------------------------------------------------------------------------------
FIN

coad07.dgibi 

opti echo 1;
opti dime 2 elem qua4;
opti trac psc ftra 'coad07_mesh.ps';
opti sauv form 'coad07.msh';
p0 = 0 0;
p1 = 8 0;
p2 = 8 4;
p3 = 0 4;
c1 = p0 d 16 p1;
c2 = p1 d
8 p2;
c3 = p2 d 16 p3;
c4 = p3 d
8 p0;
flui = dall c1 c2 c3 c4 plan;
fsrn = cont flui;
p4s = 4 0;

Page 27

8 May 2015 9:40 pm

resume.epx 

FICH 'coad01.pun' RENA 'dx_s_01'

FICH 'coad02.pun' RENA 'dx_s_02'

FICH 'coad03.pun' RENA 'dx_s_03'

RESUME
ECHO
OPTI PRIN
RESU ALIC 'coad06.ali' GARD PSCR
SORT GRAP
RCOU 11 'dx_s'
RCOU 12 'p_expl' FICH 'coad01.pun' RENA 'p_expl_01'
RCOU 21 'dx_s'
RCOU 22 'p_expl' FICH 'coad02.pun' RENA 'p_expl_02'
RCOU 31 'dx_s'
RCOU 32 'p_expl' FICH 'coad03.pun' RENA 'p_expl_03'
RCOU 41 'dx_s'
RCOU 42 'p_expl' FICH 'coad04.pun' RENA 'p_expl_04'
RCOU 51 'dx_s'
RCOU 52 'p_expl' FICH 'coad05.pun' RENA 'p_expl_05'
RCOU 61 'dx_s'
RCOU 62 'p_expl' FICH 'coad06.pun' RENA 'p_expl_06'
TRAC 11 21 31 41 51 61 AXES 1.0 'DEPL. [M]' YZER
COLO NOIR BLEU VERT TURQ ROSE ROUG
TRAC 12 22 32 42 52 62 AXES 1.0 'PRES. [PA]' YZER
COLO NOIR BLEU VERT TURQ ROSE ROUG
*-------------------------------------------------------------------------------
FIN

FICH 'coad04.pun' RENA 'dx_s_04'

FICH 'coad05.pun' RENA 'dx_s_05'

FICH 'coad06.pun' RENA 'dx_s_06'

coad07.epx

p5s = 4 3;
stru = p4s d 4 p5s;
mesh = flui et stru et fsrn;
tass mesh;
trac qual mesh;
sauv form mesh;
fin;

coad07.epx 

COAD07
ECHO
!CONV WIN
DPLA ALE
CAST mesh
EROS 1.0
DIME

ADAP NPOI 144 FL24 160 ENDA
NALE 1 NBLE 1

TERM
GEOM FL24 flui ED01 stru TERM
COMP GROU 2 'expl' LECT flui TERM COND NEAR NODE LECT p0 TERM
LECT flui DIFF expl TERM

'air'

NGRO 1 'base' LECT p4s TERM
EPAI 1.E-2 LECT stru TERM
COUL ROUG LECT expl TERM
TURQ LECT air
TERM
VERT LECT stru TERM

GRIL LAGR LECT stru TERM
EULE LECT flui TERM

MATE VM23 RO 8000. YOUN 1.D11 NU 0.3 ELAS 2.D8

FAIL VMIS LIMI 7.5E7
TRAC 3 2.D8 2.D-3 3.D8 1. 3.1D8 2.
LECT stru TERM

FLUT RO 20.0 EINT 2.5E5 GAMM 1.4 PB 0 PREF 1.E5

ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5
CQ 2.56 PMIN 0 NUM 1
LECT expl TERM

FLUT RO 1.0 EINT 2.5E5 GAMM 1.4 PB 0 PREF 1.E5
ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5
CQ 2.56 PMIN 0 NUM 1
LECT air _fl24 TERM

LINK COUP SPLT NONE

LECT fsrn TERM

FSR
BLOQ 123
LECT base TERM
FLSR STRU LECT stru TERM
FLUI LECT flui TERM
R 0.355
HGRI 0.8
DGRI
BFLU 2 FSCP 1
ADAP LMAX 3

! flui mesh size 0.5 : 0.5*0.71 = 0.355
! stru mesh size 0.75

ECRI DEPL VITE ACCE FINT FEXT FLIA FDEC CONT ECRO TFRE 1.D0

FICH ALIC FREQ 1

OPTI PAS AUTO NOTE LOG 1

CSTA 0.5
ADAP RCON

CALC TINI 0. TEND 20.D-3
SUIT
*===============================================================================
COAD07A
ECHO

CONV WIN
OPTI PRIN
RESU ALIC GARD PSCR
SORT VISU NSTO 1
*-------------------------------------------------------------------------------
PLAY
CAME
!

0.00000E+00

1 EYE
Q
VIEW
RIGH
UP
FOV

4.00000E+00
1.00000E+00
0.00000E+00
1.00000E+00
0.00000E+00
2.48819E+01

2.23607E+01
2.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00 -1.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
1.00000E+00

0.00000E+00

2.00000E+00

!NAVIGATION MODE: ROTATING CAMERA
4.00000E+00
!CENTER :
4.47214E+00
!RSPHERE:
2.23607E+01
!RADIUS :
1.00000E+00
!ASPECT :
1.74413E+01
:
!NEAR
!FAR
3.13050E+01
:
SCEN GEOM NAVI FREE
FACE HFRO
FLSR DOMA

VECT SCCO FIEL VITE SCAL USER PROG 15 PAS 15 210 TERM

SUPP LECT flui TERM

TEXT VSCA
COLO PAPE
SLER CAM1 1 NFRA 1
TRAC OFFS FICH AVI NOCL NFTO 206 FPS 15 KFRE 10 COMP -1 NFAI REND
FREQ 1
GOTR LOOP 204 OFFS FICH AVI CONT NOCL NFAI REND
GO
TRAC OFFS FICH AVI CONT NFAI REND
ENDPLAY
*-------------------------------------------------------------------------------
SUIT
*===============================================================================
COAD07C
ECHO
OPTI PRIN
RESU ALIC GARD PSCR
SORT GRAP
PERF 'coad07.pun'
COUR 1 'dx_s'
TERM
COUR 2 'p_expl' ECRO COMP 1 ELEM LECT expl TERM
TRAC 1 AXES 1.0 'DEPL. [M]'
TRAC 2 AXES 1.0 'PRES. [PA]'
LIST 1 AXES 1.0 'DEPL. [M]'
LIST 2 AXES 1.0 'PRES. [PA]'
QUAL DEPL COMP 1 LECT p5s

DEPL COMP 1 NOEU LECT p5s

TERM REFE
ECRO COMP 1 LECT expl TERM REFE

5.40360E-02 TOLE 5.E-2
1.84645E+05 TOLE 1.E-2

*-------------------------------------------------------------------------------
FIN

Page 28

Europe Direct is a service to help you find answers to your questions about the European Union 

Freephone number (*): 00 800 6 7 8 9 10 11 

(*) Certain mobile telephone operators do not allow access to 00 800 numbers or these calls may be billed. 

A great deal of additional information on the European Union is available on the Internet. 

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where you can place an order with the sales agent of your choice. 

The Publications Office has a worldwide network of sales agents. 

You can obtain their contact details by sending a fax to (352) 29 29-42758. 

European Commission 

EUR 27276 EN – Joint Research Centre – Institute for the Protection and Security of the Citizen 

Title: Combined Fluid and Structure Mesh Adaptivity with Fluid-Structure Interaction in EUROPLEXUS 

Author(s): Folco Casadei, Georgios Valsamos, Martin Larcher, Vincent Faucher 

Luxembourg: Publications Office of the European Union 

2015 – 32 pp. – 21.0 x 29.7 cm 

EUR – Scientific and Technical Research series – ISSN 1831-9424 (online) 

ISBN 978-92-79-48420-9 (PDF) 

doi:10.2788/519724 

Abstract 

The  present  work  extends  the  automatic  fluid  mesh  adaptation  to  the  case  where  adaptation  of  the  structure  occurs

simultaneously.  This technique is particularly  useful  in  conjunction with FSI algorithms of the embedded  or  immersed

type, such as the FLSR or FLSW algorithms available in EUROPLEXUS.    

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
L
B
-
N
A
-
2
7
2
7
6
-
E
N
-
N

ISBN 978-92-79-48420-9 

doi:10.2788/519724