Vijay, thanks a lot. 
I have figured it out. I solve the oscillator equation in physical space and  replace the newmark-beta scheme with the one we have in the old Nektar. now the displacement looks correct, please see the attached.



On Thu, Feb 27, 2020 at 12:04 AM VIJAY KUSHWAHA <bijay8833@sjtu.edu.cn> wrote:
Hi Zhicheng,
1. The structural stiffness parameter(StructStiff) is not defined in your .xml file. Instead you have defined that term in cable tension.
2. StructRho(m/rho*D^2) is the non-dimensional mass. For mass ratio to be defined as 2.0, you need to define it accordingly.
Try with these parameters.
Cheers,
Vijay Kushwaha

----- Original Message -----
From: "Wang, Zhicheng" <zhicheng_wang@brown.edu>
To: "ybao" <ybao@sjtu.edu.cn>
Cc: "Sherwin, Spencer J" <s.sherwin@imperial.ac.uk>, "nektar-users" <nektar-users@imperial.ac.uk>, "Lahooti, Mohsen" <m.lahooti@imperial.ac.uk>, "VIJAY KUSHWAHA" <bijay8833@sjtu.edu.cn>
Sent: Wednesday, February 26, 2020 11:16:52 PM
Subject: Re: [Nektar-users] VIV flow past a cylinder

Hi Mohsen and Yan, thanks for your reply. Please find the amplitude and
lift coefficient are attached below. The lift coef looks reasonable.
Personally, I have done tons of  similar simulations using the predecessor
SEM code Nektar, usually,  VIV simulation is not sensitive to quadrature
points, aliasing  error.... I will look at the code. Please let me know if
you get a chance  to find out the mistakes in my parameter file.


On Wed, Feb 26, 2020 at 7:31 AM ybao <ybao@sjtu.edu.cn> wrote:

> Hi Zhicheng,
>
> May you show me the time history of the cylinder vibration and lift
> coefficient for us?  in NEKTAR++, the Euler beam model was employed to
> describe the vibration of the structure, so you need to check whether or
> not the values of tension, structure stiffness and bending stiffness  are
> correct. recently  Vijay, a graduate student in my group, have run 2D
> simulations and got correct results.
>
> Hi Vijay, can you have a look on the xml from Zhicheng? many thanks!
>
> Cheers,
> Yan
>
> On 26 Feb 2020, at 05:09, Wang, Zhicheng <zhicheng_wang@brown.edu> wrote:
>
> Thank you Spencer.  I will wait for Yan Bao or Mohsen's response. There is
> no numerical instability issue for now, but thank you for the suggestion.
>
> On Tue, Feb 25, 2020 at 3:47 PM Sherwin, Spencer J <
> s.sherwin@imperial.ac.uk> wrote:
>
>> HI Zhicheng,
>>
>> I am forwarding your request to Yan Bao who is probably the most
>> experienced in this setup. Not sure if Yan is using the Nektar++ users list
>> however.
>>
>> I would be inclined to use the SpectralVanishingViscosity with DGKernel
>> and Dealisasing if you get any flow instability issues.
>>
>> Cheers,
>> Spencer
>>
>> PS Mohsen might be able to help too.
>>
>> On 25 Feb 2020, at 15:05, Wang, Zhicheng <zhicheng_wang@brown.edu> wrote:
>>
>> This email from zhicheng_wang@brown.edu originates from outside
>> Imperial. Do not click on links and attachments unless you recognise the
>> sender. If you trust the sender, add them to your safe senders list
>> <https://spam.ic.ac.uk/SpamConsole/Senders.aspx> to disable email
>> stamping for this address.
>>
>> Hi nektar++ users,
>> I wonder if there is anyone could check my simulation parameters for the
>> simulation of 2D vortex induced vibration (VIV) of flow past a cylinder
>> that is allowed to move in crossflow direction ?  Here  the cylinder is
>> rigidly mounted with a natural frequency f=0.17, mass per unit length =2.0,
>> Re=100.  For this particular case, the vibration amplitude is expected to
>> be around 0.5D, but the simulation gave me 0.05D. So I think I must have
>> made some mistakes somewhere in the parameter file. The parameter file I
>> used is posted below.
>>
>> ******************************************************************
>> <EXPANSIONS>
>>         <E COMPOSITE="C[0]" BASISTYPE="Modified_A, Modified_A"
>>            NUMMODES="3,3" POINTSTYPE="GaussLobattoLegendre,
>> GaussLobattoLegendre"
>>            NUMPOINTS="5,5"  FIELDS="u,v,w,p" />
>>     </EXPANSIONS>
>>
>>     <CONDITIONS>
>>         <SOLVERINFO>
>>             <I PROPERTY="SolverType" VALUE="VCSMapping" />
>>             <I PROPERTY="EQTYPE" VALUE="UnsteadyNavierStokes" />
>>             <I PROPERTY="AdvectionForm" VALUE="Convective" />
>>             <I PROPERTY="Projection" VALUE="Galerkin" />
>>             <I PROPERTY="HOMOGENEOUS" VALUE="1D"/>
>>             <I PROPERTY="USEFFT" VALUE="FFTW" />
>>             <I PROPERTY="TimeIntegrationMethod" VALUE="IMEXOrder2" />
>>             <I PROPERTY="GlobalSysSoln" VALUE="IterativeStaticCond" />
>>             <I PROPERTY="Preconditioner" VALUE="Block"/>
>>             <I PROPERTY="VibrationType" VALUE="Constrained"/>
>>             <I PROPERTY="SupportType" VALUE="Free-Free"/>
>>             <I PROPERTY="FictitiousMassMethod" VALUE="True"/>
>>         </SOLVERINFO>
>>
>>         <PARAMETERS>
>>             <P> TimeStep            = 0.005                        </P>
>>             <P> FinalTime           = 1000                         </P>
>>             <P> NumSteps            = FinalTime/TimeStep           </P>
>>             <P> IO_CheckSteps       = 2000                         </P>
>>             <P> IO_InfoSteps        = 25                           </P>
>>             <P> IO_CFLSteps         = 25                           </P>
>>             <P> Re                         = 100
>>  </P>
>>             <P> Kinvis                     = 1/Re
>> </P>
>>             <P> HomModesZ           = 2                            </P>
>>             <P> LZ                           = 0.01
>>   </P>
>>             <P> FreqY                     = 0.17
>> </P>
>>             <P> OmegaY                  = 2.0*PI*FreqY
>> </P>
>>             <P> StructStiff               = 0.0
>>  </P>
>>             <P> StructRho              = 2.0                          </P>
>>             <P> CableTension        = OmegaY*OmegaY*StructRho      </P>
>>             <P> BendingStiff           = 0.0                          </P>
>>             <P> FictDamp               = 1.0                          </P>
>>             <P> FictMass                = 1.5
>>  </P>
>>         </PARAMETERS>
>>
>>         <VARIABLES>
>>             <V ID="0"> u </V>
>>             <V ID="1"> v </V>
>>             <V ID="2"> w </V>
>>             <V ID="3"> p </V>
>>         </VARIABLES>
>>
>>         <BOUNDARYREGIONS>
>>             <B ID="0"> C[5] </B>    <!-- Wall -->
>>             <B ID="1"> C[3] </B>    <!-- y_min -->
>>             <B ID="2"> C[4] </B>    <!-- y_max -->
>>             <B ID="3"> C[2] </B>    <!-- Outlet -->
>>             <B ID="4"> C[1] </B>    <!-- Inflow -->
>>         </BOUNDARYREGIONS>
>>
>>         <BOUNDARYCONDITIONS>
>>             <REGION REF="0">
>>                 <D VAR="u" USERDEFINEDTYPE="MovingBody" VALUE="0" />
>>                 <D VAR="v" USERDEFINEDTYPE="MovingBody" VALUE="0" />
>>                 <D VAR="w" VALUE="0" />
>>                 <N VAR="p" USERDEFINEDTYPE="H" VALUE="0" />
>>             </REGION>
>>             <REGION REF="1">
>>                 <P VAR="u" VALUE="[2]" />
>>                 <P VAR="v" VALUE="[2]" />
>>                 <P VAR="w" VALUE="[2]" />
>>                 <P VAR="p" VALUE="[2]" />
>>            </REGION>
>>            <REGION REF="2">
>>                 <P VAR="u" VALUE="[1]" />
>>                 <P VAR="v" VALUE="[1]" />
>>                 <P VAR="w" VALUE="[1]" />
>>                 <P VAR="p" VALUE="[1]" />
>>            </REGION>
>>             <REGION REF="3">
>>                 <N VAR="u" VALUE="0" />
>>                 <N VAR="v" VALUE="0" />
>>                 <N VAR="w" VALUE="0" />
>>                 <D VAR="p" VALUE="0" />
>>             </REGION>
>>             <REGION REF="4">
>>                 <D VAR="u" VALUE="1" />
>>                 <D VAR="v" VALUE="0" />
>>                 <D VAR="w" VALUE="0" />
>>                 <N VAR="p" USERDEFINEDTYPE="H" VALUE="0" />
>>             </REGION>
>>         </BOUNDARYCONDITIONS>
>>
>>         <FUNCTION NAME="InitialConditions">
>>             <E VAR="u" VALUE="0" />
>>             <E VAR="v" VALUE="0" />
>>             <E VAR="w" VALUE="0" />
>>             <E VAR="p" VALUE="0" />
>>         </FUNCTION>
>>
>>
>>         <FUNCTION NAME="displacements">
>>             <E VAR="x" VALUE="0.0" />
>>             <E VAR="y" VALUE="A*cos(omega*t)*cos(2*PI*z/LZ)" />
>>         </FUNCTION>
>>         <FUNCTION NAME="velocities">
>>             <E VAR="x" VALUE="0.0" />
>>             <E VAR="y" VALUE="-1.0*omega*A*sin(omega*t)*cos(2*PI*z/LZ)" />
>>         </FUNCTION>
>>         <FUNCTION NAME="Mapping">
>>             <E VAR="x" VALUE="x" />
>>             <E VAR="y" VALUE="y+A*cos(omega*t)*cos(2*PI*z/LZ)" />
>>         </FUNCTION>
>>         <FUNCTION NAME="MappingVel">
>>             <E VAR="vx" VALUE="0.0" />
>>             <E VAR="vy" VALUE="-1.0*omega*A*sin(omega*t)*cos(2*PI*z/LZ)"
>> />
>>         </FUNCTION>
>>         <FUNCTION NAME="accelerations">
>>             <E VAR="x" VALUE="0.0" />
>>             <E VAR="y"
>> VALUE="-1.0*omega*omega*A*cos(omega*t)*cos(2*PI*z/LZ)" />
>>         </FUNCTION>
>>
>>     </CONDITIONS>
>>
>>     <MAPPING TYPE="XYofZ">
>>         <COORDS>Mapping</COORDS>
>>         <VEL>MappingVel</VEL>
>>         <TIMEDEPENDENT>True</TIMEDEPENDENT>
>>  </MAPPING>
>>
>>     <FORCING>
>>         <FORCE TYPE="MovingBody">
>>             <DISPLACEMENTS> displacements </DISPLACEMENTS>
>>             <VELOCITIES>    velocities    </VELOCITIES>
>>             <ACCELERATIONS> accelerations </ACCELERATIONS>
>>             <PARAM NAME="OutputFile">TensionedCable</PARAM>
>>             <PARAM NAME="OutputFrequency">25</PARAM>
>>             <PARAM NAME="Boundary"> B[0] </PARAM>
>>         </FORCE>
>>     </FORCING>
>>
>> ****************************************************************************************
>> Best Wishes,
>> Zhicheng Wang
>> _______________________________________________
>> Nektar-users mailing list
>> Nektar-users@imperial.ac.uk
>> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
>>
>>
>> Spencer Sherwin FREng, FRAeS
>> Head of Aerodynamics Section,
>> Director of Research Computing Service,
>> Professor of Computational Fluid Mechanics,
>> Department of Aeronautics,
>> s.sherwin@imperial.ac.uk                                   South
>> Kensington Campus,
>> Phone: +44 (0)20 7594 5052                              Imperial College
>> London,
>> Fax:   +44 (0)20 7594 1974                               London, SW7 2AZ,
>>  UK
>> http://www.imperial.ac.uk/people/s.sherwin/
>>
>>
>