Problem with second order upwind

kalanpi4 · October 25, 2016, 16:02

Hi,

I am writing a code to implement SIMPLE algorithm. It runs satisfactorily for First Order Upwind. I am trying to implement Second Order Upwind for the convective terms. However, when I wrote the discretized equation, some coefficients are negative and they can't be as mentioned in the four basic rules in Patankar's book.

Can somebody help me with a solution?

Thanks.

FMDenaro · October 25, 2016, 16:06

According to the Godunov theorem, no linear schemes greater than first order of accuracy can have all coefficients positive.

j_02 · October 25, 2016, 22:29

Have you attempted the deferred correction procedure?

I am working to implement this approach with a central difference scheme. I am following this approach after seeing it referenced in the work of Ferzig & Peric and in the CFD-Online Wiki on this very website.

kalanpi4 · November 1, 2016, 09:06

I tried the van Leer scheme but could not implement it successfully. Does anybody have any papers for BOUNDED SECOND ORDER UPWIND implementation?

FMDenaro · November 1, 2016, 11:31

A simple second order central space with a second order time integration must work in simulating the shedding

kalanpi4 · November 4, 2016, 15:49

Can any of the Flux limiter schemes used explicitly?

October 25, 2016, 16:02	Problem with second order upwind	#1
kalanpi4 New Member Kalyan Join Date: Jun 2016 Posts: 5 Rep Power: 9	Hi, I am writing a code to implement SIMPLE algorithm. It runs satisfactorily for First Order Upwind. I am trying to implement Second Order Upwind for the convective terms. However, when I wrote the discretized equation, some coefficients are negative and they can't be as mentioned in the four basic rules in Patankar's book. Can somebody help me with a solution? Thanks.

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October 25, 2016, 16:06		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	According to the Godunov theorem, no linear schemes greater than first order of accuracy can have all coefficients positive.

October 25, 2016, 22:29		#3
j_02 New Member Join Date: Mar 2014 Posts: 14 Rep Power: 12	Have you attempted the deferred correction procedure? I am working to implement this approach with a central difference scheme. I am following this approach after seeing it referenced in the work of Ferzig & Peric and in the CFD-Online Wiki on this very website.

November 1, 2016, 09:06		#4
kalanpi4 New Member Kalyan Join Date: Jun 2016 Posts: 5 Rep Power: 9	I tried the van Leer scheme but could not implement it successfully. Does anybody have any papers for BOUNDED SECOND ORDER UPWIND implementation?

November 1, 2016, 11:31		#5
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	A simple second order central space with a second order time integration must work in simulating the shedding

November 4, 2016, 15:49		#6
kalanpi4 New Member Kalyan Join Date: Jun 2016 Posts: 5 Rep Power: 9	Can any of the Flux limiter schemes used explicitly?