In es iga ion in o p opulsi e cha ac e is ics o an inland essel in con ined
wa e way
Kel in Eloho*, Vladimi K asilniko *, and Benjamin F iedho †
*SINTEF Ocean AS, T ondheim, No way, †De elopmen Cen e o Ship Technology and T anspo
Sys ems, Duisbu g, Ge many
Kel in.Eloho@sin e .no
1 In oduc ion
Small o medium inland na iga ion essels (CEMT Classes I o IV) a e conside ed as a iable
al e na i e ca go anspo a ion mode o elie e loads on some o he mos conges ed Eu opean
mo o ways. In he Ho izon Eu ope p ojec AUTOFLEX (h ps://au o lex- essel.eu/), a no el ype o
au onomous inland ca go essel is being de eloped, which can ca y ou anspo se ices in p e iously
unde used con ined wa e ways. Con ined wa e ways, cha ac e ized by limi ed dep h, wid h, o bo h,
signi ican ly a ec essel hyd odynamics. In such condi ions, essels expe ience inc eased esis ance,
along wi h no able changes in sinkage and im compa ed o ope a ion in unbounded deep wa e .
Fu he mo e, in e ac ion wi h wa e way bounda ies a ec s conside ably he in low expe ienced by he
p opulso .
The model‐scale expe imen s emain he mos common app oach o p edic ing ship’s esis ance and
p opulsi e cha ac e is ics; and he ex apola ion p ocedu e based on he ITTC 1978 pe o mance
p edic ion me hod is commonly employed. Howe e , he alidi y o his app oach in applica ion o
inland essels in shallow wa e condi ions is subjec o c i icism (Mucha e al., 2017). The Lackenby
(1963) me hod, also desc ibed in ITTC (2014), shows limi ed applicabili y ac oss di e se hull o ms
due o i s eliance on limi ed expe imen al da a and hus exhibi s cons ained applicabili y ac oss di e se
hull o ms and ope a ing condi ions. The o m ac o concep o iginally p oposed by Hughes (1954),
and e ined by P ohaska’s me hod (ITTC, 2002) sepa a es he wa e esis ance componen (which
depends only on F oude numbe , 𝐹𝑟) and iscous esis ance (which depends only on Reynolds numbe ,
𝑅𝑒). The o m ac o , which is assumed independen on bo h 𝐹𝑟 and 𝑅𝑒 accoun s o he addi ional
iscous esis ance a ibu able o hull shape beyond la ‐pla e ic ion. This e y assump ion has been
subjec o c i icism in many s udies, nume ical, as well as expe imen al, wi h i s sys ema ic esul s
opposing he main o m- ac o hypo hesis p esen ed in ITTC (2008). Mo e ecen s udies (Zeng e al.,
2020) ha e also demons a ed ha , o dep h‐F oude numbe s 𝐹𝑟ℎ> 0.5422 and non‐slende hulls, he
wa e esis ance dependence on 𝐹𝑟 alone may no hold. Fu he mo e, he assumed linea dependency o
wa e esis ance coe icien on 𝐹𝑟4 may no be obse ed o a ious hull geome ies (Ko kmaz e al.,
2021). In gene al, scale e ec s in shallow wa e a e expec ed o be become mo e p onounced wi h
dec easing wa e dep h, since a lowe dep hs, bounda y laye s on he hull and channel loo expe ience
s onge in e ac ion as illus a ed by CFD analyses p esen ed in K asilniko e al. (2025). A e y low
dep hs, he said in e ac ion has app eciable in luence on wa e sys ems gene a ed by he ship due o
changes in p essu e dis ibu ion o e he hull. Wi h hese conside a ions in mind, i is easy o unde s and
he esul s p esen ed by Ra en (2019) which demons a ed ha adi ional model‐ o‐ship ex apola ion
me hods can o e es ima e wa e ‐dep h e ec s unless a dep h‐dependen o m- ac o is employed. A
e ised p ocedu e o co ec ing ull‐scale speed ials o accoun o wa e ‐dep h e ec s has been
p oposed, and i is now included in he ITTC guidelines (ITTC, 2017).
The p ima y pu pose o he p esen s udy is o in es iga e by means o CFD simula ions, he in luence
o limi ed wa e dep h on ship’s owing esis ance in ull‐scale, and o illus a e di e ences om he
equi alen es condi ions in model scale. The nume ical se up is based on he me hodology p esen ed
in K asilniko e al. (2025). The ul ima e objec i e is o es ablish a alida ed amewo k ha aids u he
in es iga ion o essel p opulsi e pe o mance in inland wa e ways.
2 Desc ip ion o CFD app oach
The CFD me hodology desc ibed in K asilniko e al. (2025) and used o in es iga ions in his pape
employs a ully pa ame e ized simula ion empla e de eloped in STAR-CCM+ ( 18.06.006),
speci ically con igu ed o essels ope a ing in con ined wa e ways. The compu a ional domain is
di ided in o he h ee egions:
• Backg ound Mesh (BM): a s a iona y block ep esen ing he wa e way, bounded by no-slip side
walls and loo , a eloci y inle 4 Lpp ups eam, and a p essu e ou le 4 Lpp downs eam o ship’s
a pe pendicula (AP). The inle /ou le bounda ies a e ollowed by 2 Lpp wa e-damping zones
en o ced o supp ess e lec ions.
• O e se Mesh (OM): a body- i ed, mo ing egion su ounding he ship ( ±1.05 Lpp ups eam o
–0.10 Lpp downs eam om AP, ±0.80 B la e ally om cen al plane (CP), –0.30 H o +1.35 H
e ically om base). He e and abo e, Lpp is he ship’s leng h be ween pe pendicula s, B is he
ship’s beam, and H is he ship’s heigh o uppe deck. To imp o e mass conse a ion ac oss he
o e se in e ace, we employ he leas -squa es scheme wi h mass- acking o mul i-phase low
models.
• Sliding Mesh (SM) Regions: cylind ical domains enclosing each p opulso (only in sel -p opulsion
uns), o a ing a p esc ibed RPM abou he sha axis and mo ing igidly wi h he OM.
Dynamic sinkage and im o he ship a e cap u ed using he Dynamic Fluid–Body In e ac ion (DFBI)
sol e wi h he Equilib ium body mo ion model. Du ing he simula ion, an ini ial ixed ship posi ion
pe iod (0.2 % o a ge simula ion ime) is ollowed by a 20 % elease pe iod wi h linea amping, a e
which sinkage and im angle a e adjus ed i e a i ely owa d ze o ne e ical o ce & pi ching momen .
A p edominan ly hexahed al g id is gene a ed by he T imme Cell Meshe , supplemen ed by six p ism
laye s ( wel e o ex eme shallow-wa e cases) o en o ce Y+ ≈ 50 using he k-ω SST u bulence
closu e model, which sol es he anspo equa ions wi h linea cons i u i e ela ion, wi h wall
unc ions. Howe e , in ull scale (FS), all dep hs and speeds u ilised 12 p ism laye s, wi h a a ge Y+
o a ound 121 (assumed o be a ound a s e ching ac o o 1.2 o 8km/h cases). Local e inemen boxes
and cylind ical con ols enhance esolu ion nea he ee su ace, in he wake, and a ound p opulso s.
De o ma ion o ee su ace is esol ed using a Volume-o -Fluid (VOF) sol e wi h a blended High-
Resolu ion In e ace Cap u ing (HRIC) scheme. The de aul uppe and lowe Cou an numbe limi s in
he HRIC scheme a e inc eased o he alues Coₗₒ = 200 and Coᵤₚ = 250 o educe solu ion dependency
on ime s ep while main aining in e ace sha pness. P essu e– eloci y coupling employs a SIMPLE
algo i hm wi h an AMG p essu e sol e (max cycles = 100; con e gence ole ance = 1e⁻³) and educed
unde - elaxa ion ac o s o acili a e solu ion s abili y in shallow wa e condi ions. The de ini ion o
ime s ep ollows a gene al o mula Δ = 0.005·(Lpp/V). Wi h his de ini ion o ime s ep, he Cou an
numbe on he ee su ace no mally a ies be ween 2 and 5 a ound he ship, and i eaches 7-8 in he
a eas whe e he bow and s e n wa e sys ems a e o med. Fo he gi en ship speed, a he cons an ime
s ep, Cou an numbe le els in he simula ions inc ease wi h he educ ion o wa e dep h, which is
explained by he inc ease o induced eloci ies. In ull scale, main aining he Cou an numbe le el
appea s mo e impo an o he o e all quali y o he nume ical solu ion.
3 Ex apola ion o model es esul s o ull scale
As poin ed ou in he in oduc ion, adi ional ex apola ion me hods om model scale (MS) o ull scale
(FS) exhibi no able unce ain ies applied o shallow-wa e condi ions. The e o e, he p ocedu e
p oposed by Ra en (2019) is ollowed o es ima e hull owing esis ance in ull scale based on he esul s
o model-scale expe imen . Acco ding o his me hod, he e ised, dep h-dependen o m ac o
(1+𝑘∗) main ains consis en beha iou a bo h model and ull scale, p o ided ha 𝑇/ℎ ≤ 0.5, whe e
𝑇 is he ship’s d augh and ℎ is he wa e dep h. A s anda d decomposi ion o he o al esis ance in o
he wa e and iscous componen is hen ollowed: 𝐶𝑇(F , Re) = 𝐶𝑊(F ) + 𝐶𝑉(Re) wi h he
assump ion ha 𝐶𝑉(Re, ℎ) = (1+𝑘∗(ℎ)) 𝐶𝑓0(Re), whe e 𝐶𝑓0 ep esen s he con en ional la -pla e
ic ion coe icien acco ding o ITTC 1957 ex apola ion line.
I is shown ha , o mode a ely shallow wa e condi ions (𝑇/ℎ ≤ 0.5), he a io ep esen ing he
ela i e inc ease in 𝐶𝑉 due o limi ed dep h, 𝐶𝑉(ℎ)
𝐶𝑉
∞ , emains essen ially unchanged om model-scale o
ull-scale Reynolds numbe s. Consequen ly, a dep h-dependen o m ac o is de ined as ollows:
1+𝑘∗(𝑇/ℎ)=𝐶𝑉(ℎ)
𝐶𝑓0 =𝐶𝑉(ℎ)
𝐶𝑉
∞(1+𝑘∞)
whe e 1+𝑘∞ is he deep-wa e o m ac o . I is assumed ha , o men ioned ange o ela i e wa e
dep h (𝑇/ℎ ≤ 0.5), he dep h-dependen o m- ac o is independen on scale. Fo p ac ical applica ions,
Ra en (2019) p o ides he eg ession o mula ha app oxima es inc ease o iscous esis ance wi h
wa e dep h: 𝐶𝑉(ℎ)
𝐶𝑉
∞≈ 1+0.57(𝑇/ℎ)1.79
4 Calcula ion esul s in model scale and dep h-dependen o m- ac o
In he p esen wo k, o CFD s. EFD compa isons, we use he alida ion da ase o he M2052 model
de eloped a DST as a pa o he es campaign wi h he ou ships ha ing iden ical bow shapes and
di e en s e n and p opulsion sys em con igu a ions (F iedho e al., 2019). This model is
ep esen a i e o a CEMT Class Va single-sc ew inland na iga ion essel o he ollowing main
dimensions: 𝐿𝑝𝑝 =110 m; 𝐵=11.4 m; max d augh 𝑇𝑚𝑎𝑥 =2 m. The essel’s block coe icien is
𝐶𝐵=0.895 a he olume displacemen o 3150 𝑚3. In acco dance wi h model es s, CFD esis ance
simula ions we e pe o med a he scale o 1/16, wi hou udde s, duc and p opelle , a he d augh
T=2.8 m.
The compa isons be ween he model-scale CFD simula ions and expe imen al da a a e desc ibed in
de ail in K asilniko e al. (2025). A summa y compa ison o he compu ed and measu ed owing
esis ance is p esen ed in Fig.1 o di e en ela i e wa e dep hs, ℎ/𝑇, and ange o F oude numbe ,
𝐹𝑟. In he mos ele an speed ange be ween he F oude numbe s o 0.065 and 0.105 (speed 8 o 12
km/h in ull scale), he ag eemen be ween he CFD and EFD esul s is ound o be e y close.
Disc epancies become la ge a highe speeds. In his pape , he nume ical esul s we e u he examined
o he in luence o ank wall e ec s. While he CFD esul s p esen ed in Fig.1 we e ob ained in he
compu a ional domain co esponding exac ly o he wid h o he es ing acili y wi h side walls, selec ed
condi ions we e ep oduced in he domain wi hou he es ic ion o side bounda ies (symme y plane
bounda ies we e used ins ead), a he same wa e dep h. Fo he condi ion o he lowes wa e dep h,
ℎ/𝑇 =1.25, ela i e di e ence in mean axial eloci y on he ans e se (Y-Z) plane a he ee su ace
le el p oduced by he es ic ed domain and unbounded domain simula ions we e abou 0.2 %, while
he espec i e alues o o al hull esis ance di e ed by less han 0.5%. These numbe s a e indica i e
o mino in luence o ank walls, which is an impo an esul o subsequen compa isons wi h ull-
scale simula ions, which a e pe o med in a la e ally unbounded domain.
Fig.1: Compa ison o hull owing esis ance
p edic ed by CFD wi h he esul s o model es s a
di e en wa e dep hs.
Fig.2: Compa ison o dep h-dependen o m ac o
de i ed om he CFD calcula ions in model and ull
scale wi h app oxima ion o mula by Ra en (2019)
Fo he nex s ep, he dep h-dependen o m ac o (1+𝑘∗) was compu ed in model scale and ull scale
a he lowes F oude numbe o 0.068 co esponding o ship speed o 8 km/h in ull scale. This exe cise
in ol ed de e mining he a io o o al compu ed iscous esis ance o ic ion esis ance de i ed om
he ITTC57 Model-Ship co ela ion line. Simula ions pe o med a ℎ/𝑇≥4 we e assumed ep esen a i e
o deep-wa e condi ions. The ob ained alues o o m- ac o a e compa ed wi h p edic ions using he
empi ical ela ionship om Ra en (2019) in Fig.2. In gene al, he dependencies o o m- ac o on wa e
dep h de i ed om CFD exhibi a end consis en wi h Ra en's p edic ions. Some di e ences in o m-
ac o es ima ions ob ained in model scale and ull scale a e also no iced, indica ing ha o m- ac o
may no be en i ely ee om scale e ec . Addi ionally, as illus a ed in Fig.3, e en in his low F oude
numbe case disc epancies a e ound be ween he o al esis ance and iscous esis ance componen ,
and hey inc ease wi h educ ion o wa e dep h as he in luence o wa e making esis ance becomes
mo e p onounced. Despi e he men ioned di e ences, he dep h-dependen a m- ac o de i ed om
0
0.5
1
1.5
2
2.5
3
3.5
0 1 2 3 4
1+k*
h/T
CFD(FS) CFD(MS) Ra en (2016)
CFD simula ions is ound adequa e o he use in ex apola ion o model es esul s o ull scale
condi ions o he compa ison wi h ull-scale CFD esul s.
Fig.3: Compa ison o he o al and iscous esis ance componen s compu ed a di e en wa e dep hs, o he
F oude numbe 𝐹𝑟 =0.068 (8km/h), ull scale
5 Calcula ion esul s in ull scale and scale e ec s
Fig.4 p esen s a compa ison o ship’s owing esis ance compu ed in ull scale wi h he esul s o
ex apola ion p ocedu e using he dep h-dependen o m- ac o es ima ed in Sec ion 4. The compa ison
is p esen ed o ship speed o 8 km/h and di e en wa e dep hs. The model es da a a e used in he
ex apola ion, and no addi ional co ec ions o co ela ion ac o s is applied in he p edic ion. Likewise,
ull-scale CFD simula ions a e pe o med on a ba e hull wi hou su ace oughness.
Fig.4: Compa ison o ull-scale CFD esis ance wi h
ex apola ions o model es s da a a 8 km/h (𝑭𝒓 =0.068)
Fig. 5: Va ia ion o he o al esis ance and i s ic ion and
p essu e componen s wi h wa e dep h in model and ull
scale. Ship speed 8 km/h (𝑭𝒓 =0.068).
The compu ed ship esis ance exhibi s a consis en o e p edic ion compa ed o he esul s o
ex apola ion using he dep h-dependen o m ac o , while main aining a simila end in he inc ease
o esis ance wi h educ ion o wa e dep h. A he same ime, he esul s o ex apola ion wi hou dep h-
dependen o m- ac o p edic a signi ican ly la ge inc ease o esis ance a lowe wa e dep hs.
To be e unde s and he mechanisms behind esis ance a ia ion, he compu ed ic ion and p essu e
esis ance componen s a e shown sepa a ely in Fig.5. As ela i e wa e dep h dec eases om deep wa e
( ep esen ed as h/T =4) condi ion o ℎ/𝑇≈ 1.25, ull-scale o al esis ance inc eases om ≈ 0.0027 o
≈ 0.0036 (+33 %), whe eas in model-scale i inc eases om ≈ 0.0043 o ≈ 0.0069 (+60 %). This
di e ence unde sco es he ampli ica ion o shallow-wa e e ec s in model-scale es s compa ed o ull-
scale condi ions, which may be misleading, i le unco ec ed du ing ex apola ion. E en la ge
de ia ions will be seen a highe ship speeds. The ull-scale ic ional esis ance, C , inc eases by ≈ 21 %
( om 0.0019 o 0.0023) om deep o shallow condi ions, while model-scale ic ion ises by ≈ 11 %
(0.0037 o 0.0041). Fo ℎ/𝑇 > 2.7, he pe cen age inc eases in C emains simila (≈ 5 %) be ween
scales. Howe e , o ℎ/𝑇 < 2.0, he ull-scale inc ease o C ou paces model-scale, e ealing ha
changes in shea s ess dis ibu ion o e he hull a e y shallow wa e condi ions a e scale dependen .
The p essu e esis ance componen , Cp, exhibi s e en g ea e sensi i i y o dep h a ia ion. I in deep
wa e condi ion, he ull-scale Cp≈0.0006 and model scale Cp≈0.0011, hen a ℎ/𝑇=1.25, he ull-
scale Cp ≈ 0.0013 (+117 %) and model-scale Cp≈ 0.0029 (+164 %), espec i ely. Thus, changes in
he p essu e esis ance wi h a ia ion o wa e dep h also depend on Reynolds numbe . I is wo h no ing
ha he ic ion esis ance coe icien s p edic ed by CFD in deep wa e shows a good ma ch wi h he
ITTC57 ic ion line (0.0019 s. 0.00188 in ull scale, and 0.0037 s. 0.0037 in model scale).
The men ioned dependencies in he a ia ion o he ic ion and p essu e esis ance in shallow wa e
condi ions on scale (Reynolds numbe ) is explained by he in e ac ion be ween he bounda y laye o
ship hull wi h he channel loo .
0
0.001
0.002
0.003
0.004
1.25 1.79 2.68 Deep
h/T
C , To al (F =0.06765) C ,Viscous (F =0.06765)
0
5
10
15
20
25
1.25 1.79 2.68 4.00
R_T (kN)
h/T
CFD(FS) Ex ap. wi h compu ed o m ac o ini ial ex ap. om model es
0
0.002
0.004
0.006
0.008
1.25 1.79 2.68 4.00
h/T
C (FS) C (MS) C (FS)
C (MS) Cp(FS) Cp(MS)
Fig.6: Fields o o ici y magni ude a di e en wa e dep hs in model and ull scale. Ship speed 8
km/h (𝐹𝑟 =0.068). Le : Model scale. Righ : Full scale. Top: 5m dep h. Bo om: 7.5m dep h.
As illus a ed in Fig.6, in model scale he bounda y laye on ship hull is ela i ely hicke and mo e
di used han in ull scale. A hicke bounda y laye expe iences s onge in e ac ion (and hence
unde goes s onge changes) wi h dec ease o wa e dep h. A he ex eme shallow wa e condi ions,
he said in e ac ion also a ec s gene a ion o ship induces wa es, in pa icula downs eam o midship,
hus adding a iscous con ibu ion o he po en ial pa o wa e making caused by domain con inemen .
The changes in he dynamic sinkage and im o he ship wi h a ia ion o wa e dep h show gene ally
simila ends in model and ull scale (see Fig.7).
Fig.7: Changes in dynamic posi ion o he ship wi h a ia ion o wa e dep h in model and ull scale. Ship speed 8
km/h (𝐹𝑟 =0.068).
Excep o lowes wa e dep h, he alues compu ed by CFD a e ound o be in good ag eemen wi h
expe imen al measu emen s. A ℎ/𝑇=1.25, he alue o dynamic im angle compu ed in model scale
ag ees be e wi h he measu ed da a, a a e y close alue o he dynamic sinkage. I should howe e
be no ed ha , due o he in e ac ion be ween he hull bounda y laye and channel loo and low
sepa a ion ha de elops a he a ship, he low pa e n a ound ship hull in ex eme shallow wa e
condi ions becomes uns able. In such scena ios, one can he e o e ques ion alidi y o he Equilib ium
mo ion model employed in he DFBI solu ion, ha d i es he solu ion o a s eady s a e which may no
exis in he eali y.
As demons a ed expe imen ally in F iedho e al. (2019) and con i med nume ically in K asilniko e
al. (2025), limi a ion o wa e dep h has a p o ound e ec on he wake ield pas ship hull. Na u ally,
he said e ec also depends on scale, and in iew o he abo e discussion abou he bounda y laye
in e ac ion wi h domain loo , i is s onge in model-scale condi ions. As illus a ed in Fig.8, wi h
educ ion o wa e dep h om 7.5 m o 5.0 m, he axial wake ield in model scale becomes hea ie
(g ea e low e a da ion) on he whole p opelle disk a ea as well as on he sides o he ship. The
inc ease o low sepa a ion is e iden om la ge zones o swi led low ( o ici y o ma ion), which
also mo e close o he hull su ace and become wide due o low con inemen . In ull-scale, he inc ease
o wake eloci y de ici wi h dep h educ ion is smalle , and i is mos ly limi ed o p opelle disk,
pa icula ly a ound he loca ion o ship’s cen al plane.
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
1.00 2.00 3.00 4.00
Sinkage/T
h/T
CFD(FS) CFD(MS) Exp
0
0.005
0.01
0.015
0.02
1.25 1.79 2.68 4.00
T im (deg.)
h/T
CFD(FS) CFD(MS) Exp
Model Scale
Full Scale
5m
7.5m
Fig.8: Changes in nominal wake ield wi h a ia ion o wa e dep h in model and ull
scale. Ship speed 8 km/h (F =0.068).
6 Conclusions
The CFD se up o simula ion o p opulsion pe o mance o inland essels de eloped and alida ed a
model scale in K asilniko e al. (2025) has been applied o in es iga e he in luence o shallow wa e
condi ions on ship esis ance in ull scale and analyse associa ed scale e ec s. Compa isons u ilize
esul s om esul s o model es s pe o med a DST on a CEMT Class Va single-sc ew inland essel.
The in es iga ion e eals di icul ies wi h ex apola ion o model es esul s o ull-scale using
con en ional scaling p ocedu es es ablished o deep-wa e condi ions. The key inding is ha he
in luence o limi ed wa e dep h a ec s bo h he ic ion and p essu e esis ance componen s, and
changes in hese componen s depend on bo h he F oude numbe and Reynolds numbe . The physical
mechanism unde lying he men ioned dependencies is he in e ac ion be ween he hull bounda y laye
and wa e way loo , causing inc ease and e-dis ibu ion o wall shea s ess on he hull, changes
p essu e dis ibu ion and al e s low sepa a ion pa e n a he a ship. A he ex eme shallow wa e
condi ions, he said in e ac ion also a ec s gene a ion o ship induces wa es, hus adding a iscous
con ibu ion o he po en ial pa o wa e making due o domain con inemen . Since he ela i e
hickness o hull bounda y laye a ies wi h Reynolds numbe , hese desc ibed changes become scale
dependen , ende ing he ex apola ion p ocedu e based on he con en ional deep-wa e o m- ac o
inadequa e. I is shown ha using a dep h-dependen o m ac o as sugges ed in Ra en (2019) allows
o an imp o emen be ween he CFD and EFD p ognoses in ull-scale, and i can be employed o
enginee ing p edic ions in absence o CFD esul s, a leas in he ange o d augh - o-dep h a io (𝑇/ℎ)
below 0.5. None heless, iscous CFD simula ions emain ecommended o he elabo a ion o dep h-
dependen o m- ac o and, mo e gene ally, o he p edic ion o esis ance and p opulsion pe o mance
o inland essels, since he desc ibed in e ac ion be ween he essel and wa e way is also ound o ha e
signi ican impac on he wake ield pas ship hull.
Fu he mo e, i was no iced ha o highly con ined condi ions (H/T ≤ 1.5), he ee-mo ion DFBI
me hod p o ides supe io pe o mance compa ed o he DFBI equilib ium app oach. Unde ex eme
con inemen , he equilib ium sol e a i icially en o ces a s eady sinkage and im, masking inhe en
uns eady squa dynamics and wake oscilla ions. Howe e , i is no ed ha he ee-mo ion me hod
signi ican ly inc eases compu a ional demands compa ed o he equilib ium app oach when combined
wi h he O e se Mesh echnique. This is because he o e se in e ace equi es upda ing a each inne
i e a ion o e e y ime s ep, esul ing in app oxima ely ou imes longe simula ion imes o iden ical
physical du a ions. The ac ual compu a ional o e head may u he inc ease depending on he numbe
o inne i e a ions used pe ime s ep. Con e sely, he ee-mo ion app oach p ese es hese uns eady
phenomena, yielding imp o ed con e gence o hyd odynamic o ces, as demons a ed in he case o
H/T = 1.25, whe e he ee-mo ion simula ion was success ully ini ialized ollowing a DFBI equilib ium
un.
Acknowledgemen s
The p esen esea ch is unded by he p ojec AUTOFLEX (AUTOnomous small and FLEXible essels)
unde he G an Ag eemen 101136257 o he Eu opean Union Ho izon Eu ope P og amme.
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