PISO Corrections

Mateja · April 9, 2021, 21:21

Hello,

I am using PISO pressure correction algorithm to simulate compressible flow in a CD nozzle in Fortran. My queries are

1. PISO solves the equations both implicitly and explicitly, shall I care about the CFL condition in the case i.e. CFL<1?

2. In the first correction of PISO, convective and diffusive terms are omitted from the pressure and velocity equations, as we subtract the implicit predictor momentum equation from the explicit momentum corrector equation (and convective and diffusive terms are same in both these equations), but what happens in the 2nd correction? We subtract the 1st corrector explicit momentum equation from the 2nd corrector explicit momentum equation. Now, the convective and diffusive terms are not omitted completely (as they are not same anymore) but we get them in the difference form. For example the laplcian term will be in the form laplacian(v**-v*) and similarly for the gradient of divergence term and convective term.

Please let me know if I am doing the PISO nd correction right?

Thank you in advance.

PenPencil · April 17, 2021, 19:53

For 1: you do not have to impose CFL<1, but you do have to care about the accuracy of your solution. The freedrom do explore CFL>= 1 must be accompanied by other considerations with respect to your flow, mesh and time step size.

For 2: I cannot answer this right now, but I would suggest Versteeg and Malalasekera's book. It is quite well explained there or Ferziger's.

April 9, 2021, 21:21	PISO Corrections	#1
Mateja New Member Mateja Join Date: Jan 2020 Posts: 20 Rep Power: 6	Hello, I am using PISO pressure correction algorithm to simulate compressible flow in a CD nozzle in Fortran. My queries are 1. PISO solves the equations both implicitly and explicitly, shall I care about the CFL condition in the case i.e. CFL<1? 2. In the first correction of PISO, convective and diffusive terms are omitted from the pressure and velocity equations, as we subtract the implicit predictor momentum equation from the explicit momentum corrector equation (and convective and diffusive terms are same in both these equations), but what happens in the 2nd correction? We subtract the 1st corrector explicit momentum equation from the 2nd corrector explicit momentum equation. Now, the convective and diffusive terms are not omitted completely (as they are not same anymore) but we get them in the difference form. For example the laplcian term will be in the form laplacian(v*-v) and similarly for the gradient of divergence term and convective term. Please let me know if I am doing the PISO nd correction right? Thank you in advance.

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April 17, 2021, 19:53		#2
PenPencil New Member Icaro Amorim de Carvalho Join Date: Dec 2020 Posts: 24 Rep Power: 5	For 1: you do not have to impose CFL<1, but you do have to care about the accuracy of your solution. The freedrom do explore CFL>= 1 must be accompanied by other considerations with respect to your flow, mesh and time step size. For 2: I cannot answer this right now, but I would suggest Versteeg and Malalasekera's book. It is quite well explained there or Ferziger's.