Why Fluent does not have 2-order Runge-Kutta scheme?

aerosjc · October 16, 2013, 00:57

Sometimes we only need a 2-order Runge-Kutta scheme. A 4-order Runge-Kutta maybe give a strange solution.
Anyone knows?

sbaffini · October 16, 2013, 03:45

Not all numerical schemes are created equal. The 2nd order Runge-Kutta scheme has very different stability properties with respect to the 4th order one. More specifically, its stability region does not cut the imaginary axis, hence it is not well suited for convection dominated problems.

aerosjc · October 23, 2013, 21:32

But whydoes it have Explicit 2-order Runge-Kutta Time Integration Scheme in the commerical sofaware GASPex, produced by AeroSoft. Inc? Please enlighten me. Thanks

sbaffini · October 24, 2013, 04:12

Well, i didn't say the 2nd order RK scheme is impossible to use, just that it is not well suited for convection dominated flows. If you look at the code page:

http://www.aerosoftinc.com/gasp/features_main.php

you can notice that all the convection schemes are dissipative, hence you can't actually use the code in a way such that the eigenvalues are purely imaginary, which should be enough for the 2nd order scheme to work. I'm just guessing...

aerosjc · October 24, 2013, 12:18

ok, many thanks! I will read some textbooks to get better understanding.

October 16, 2013, 00:57	Why Fluent does not have 2-order Runge-Kutta scheme?	#1
aerosjc Member Jingchang.Shi Join Date: Aug 2012 Location: Hang Zhou, China Posts: 78 Rep Power: 14	Sometimes we only need a 2-order Runge-Kutta scheme. A 4-order Runge-Kutta maybe give a strange solution. Anyone knows?

October 16, 2013, 03:45		#2
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,195 Blog Entries: 29 Rep Power: 39	Not all numerical schemes are created equal. The 2nd order Runge-Kutta scheme has very different stability properties with respect to the 4th order one. More specifically, its stability region does not cut the imaginary axis, hence it is not well suited for convection dominated problems. ghost82 and RodriguezFatz like this.

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October 23, 2013, 21:32		#3
aerosjc Member Jingchang.Shi Join Date: Aug 2012 Location: Hang Zhou, China Posts: 78 Rep Power: 14	But whydoes it have Explicit 2-order Runge-Kutta Time Integration Scheme in the commerical sofaware GASPex, produced by AeroSoft. Inc? Please enlighten me. Thanks

October 24, 2013, 04:12		#4
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,195 Blog Entries: 29 Rep Power: 39	Well, i didn't say the 2nd order RK scheme is impossible to use, just that it is not well suited for convection dominated flows. If you look at the code page: http://www.aerosoftinc.com/gasp/features_main.php you can notice that all the convection schemes are dissipative, hence you can't actually use the code in a way such that the eigenvalues are purely imaginary, which should be enough for the 2nd order scheme to work. I'm just guessing...

October 24, 2013, 12:18		#5
aerosjc Member Jingchang.Shi Join Date: Aug 2012 Location: Hang Zhou, China Posts: 78 Rep Power: 14	ok, many thanks! I will read some textbooks to get better understanding.