Spectral interpolations

drudox · January 28, 2019, 07:03

Hi everybody ,
I'm developing a CFD in-house code (Fortran) , The code is develop to simulate a polymer chain (macro-molecule) interacting with turbulent flow, using a coupling between DNS for the Navier Stokes equation and Langevin equation for polymer chain dynamic.

the polymer chain is smaller than one cell , so we need to interpolate the velocity field in order to taking into account the hydro dynamic interaction between polymer and liquid

from the letterature I've found that other researchers compute a spectral interpolation to the polymer trajectory... in the paper there is nothing other report (about this interpolation) but I have to implement into the code this kind of interpolation!
Does some body said me where I can found some information about this interpolation ? and maybe some application to the CFD ... I didn't find nothing about !

thanks in advance

FMDenaro · January 28, 2019, 07:13

Standard references for spectral methods:

https://www.springer.com/gp/book/
https://www.springer.com/la/book/9783540522058

drudox · January 28, 2019, 09:12

there is nothing free ? that book is readable over payment otherwise no

sbaffini · January 28, 2019, 09:26

First of all, is your DNS code spectral? Are the codes of the researchers you are referring to spectral as well?

Otherwise there might be no point in going spectral for the polymer interpolation

drudox · January 28, 2019, 09:35

the code of the researchers is not mentioned in the paper ... is very poor of information .. they doesn't say the nature of the polymer (which polymer is used for the simulation)

Our code is no spectral .. but I have to try this interpolation. is it possible ?

FMDenaro · January 28, 2019, 09:58

Free material is here https://people.maths.ox.ac.uk/trefethen/books.html

you can see that the spectral interpolation (it is nothing but a construction of a Fourier series) requires some constraints in the grid arrangement...on the other hand you could find useful to search for spectral elements.

drudox · January 28, 2019, 10:15

oh thank you so much !

sbaffini · January 28, 2019, 15:28

Very generally speaking, It has no sense in using a spectral interpolation for something that is not spectrally accurate. You get garbage for everything below your grid step (or even more).

In practical terms, doing a spectral interpolation will require you to actually make a sort of spectral code

drudox · January 29, 2019, 02:37

which other accurate interpolation I may use ? now I'm just implement the triliear interpolation .. but it is so rough

FMDenaro · January 29, 2019, 02:56

Quote:

Originally Posted by drudox

which other accurate interpolation I may use ? now I'm just implement the triliear interpolation .. but it is so rough

The accuracy of the interpolation can be of the same order of accuracy of the computed velocity field

January 28, 2019, 07:03	Spectral interpolations	#1
drudox Member Marco Ghiani Join Date: Jan 2011 Posts: 35 Rep Power: 15	Hi everybody , I'm developing a CFD in-house code (Fortran) , The code is develop to simulate a polymer chain (macro-molecule) interacting with turbulent flow, using a coupling between DNS for the Navier Stokes equation and Langevin equation for polymer chain dynamic. the polymer chain is smaller than one cell , so we need to interpolate the velocity field in order to taking into account the hydro dynamic interaction between polymer and liquid from the letterature I've found that other researchers compute a spectral interpolation to the polymer trajectory... in the paper there is nothing other report (about this interpolation) but I have to implement into the code this kind of interpolation! Does some body said me where I can found some information about this interpolation ? and maybe some application to the CFD ... I didn't find nothing about ! thanks in advance

January 28, 2019, 15:28		#8
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,190 Blog Entries: 29 Rep Power: 39	Very generally speaking, It has no sense in using a spectral interpolation for something that is not spectrally accurate. You get garbage for everything below your grid step (or even more). In practical terms, doing a spectral interpolation will require you to actually make a sort of spectral code AliE likes this.

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January 28, 2019, 07:13		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,849 Rep Power: 73	Standard references for spectral methods: https://www.springer.com/gp/book/ https://www.springer.com/la/book/9783540522058

January 28, 2019, 09:12		#3
drudox Member Marco Ghiani Join Date: Jan 2011 Posts: 35 Rep Power: 15	there is nothing free ? that book is readable over payment otherwise no

January 28, 2019, 09:26		#4
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,190 Blog Entries: 29 Rep Power: 39	First of all, is your DNS code spectral? Are the codes of the researchers you are referring to spectral as well? Otherwise there might be no point in going spectral for the polymer interpolation

January 28, 2019, 09:35		#5
drudox Member Marco Ghiani Join Date: Jan 2011 Posts: 35 Rep Power: 15	the code of the researchers is not mentioned in the paper ... is very poor of information .. they doesn't say the nature of the polymer (which polymer is used for the simulation) Our code is no spectral .. but I have to try this interpolation. is it possible ?

January 28, 2019, 09:58		#6
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,849 Rep Power: 73	Free material is here https://people.maths.ox.ac.uk/trefethen/books.html you can see that the spectral interpolation (it is nothing but a construction of a Fourier series) requires some constraints in the grid arrangement...on the other hand you could find useful to search for spectral elements.

January 28, 2019, 10:15		#7
drudox Member Marco Ghiani Join Date: Jan 2011 Posts: 35 Rep Power: 15	oh thank you so much !

January 29, 2019, 02:37		#9
drudox Member Marco Ghiani Join Date: Jan 2011 Posts: 35 Rep Power: 15	which other accurate interpolation I may use ? now I'm just implement the triliear interpolation .. but it is so rough