Alternatives to SIMPLE for solving Navier-stokes equations in a fully coupled way

jpanchog · November 19, 2022, 10:22

Hello.

I am just wondering, which alternatives to the is the SIMPLE-algorithm exist for the solution of NS equations.

I am aware of fractional steps such as the projection method exists, or also other approaches such as PISO.

What i really don't quite understand is why is just not possible to use a more "overall" scheme, where a large nonlinear system is assembled and solved? I can imagine only that it is not done mainly due to performance issues?

Thank you

FMDenaro · November 19, 2022, 12:27

Quote:

Originally Posted by jpanchog

Hello.

I am just wondering, which alternatives to the is the SIMPLE-algorithm exist for the solution of NS equations.

I am aware of fractional steps such as the projection method exists, or also other approaches such as PISO.

What i really don't quite understand is why is just not possible to use a more "overall" scheme, where a large nonlinear system is assembled and solved? I can imagine only that it is not done mainly due to performance issues?

Thank you

Actually, the topic of the solution of the fully coupled system is an old discussion in literature, e.g., see:

https://www.researchgate.net/publica...al_Step_Method

https://www.researchgate.net/publica...okes_Equations

sbaffini · November 19, 2022, 13:59

There are coupled pressure and density based methods.

Density based methods are probably more like what you might intend as overall. Pressure based ones are more like assembling together previously segregated equations.

Historically, robust and flexible coupled methods have been developed later. And, I guess, one of the reasons is the same that eventually also slowed down their acceptance: higher memory consumption. As in coupled methods previous scalar matrix coefficients become nxn matrices, so you get an nxn memory increase. Let me also say that this is not always compensated by any benefit in convergence rate.

Today, however, they are both very common and, if properly coded, can also give a higher arithmetic intensity to the code, which most of the times means higher performances.

November 19, 2022, 10:22	Alternatives to SIMPLE for solving Navier-stokes equations in a fully coupled way	#1
jpanchog New Member Join Date: Nov 2013 Posts: 5 Rep Power: 13	Hello. I am just wondering, which alternatives to the is the SIMPLE-algorithm exist for the solution of NS equations. I am aware of fractional steps such as the projection method exists, or also other approaches such as PISO. What i really don't quite understand is why is just not possible to use a more "overall" scheme, where a large nonlinear system is assembled and solved? I can imagine only that it is not done mainly due to performance issues? Thank you aerosayan likes this.

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November 19, 2022, 13:59		#3
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,195 Blog Entries: 29 Rep Power: 39	There are coupled pressure and density based methods. Density based methods are probably more like what you might intend as overall. Pressure based ones are more like assembling together previously segregated equations. Historically, robust and flexible coupled methods have been developed later. And, I guess, one of the reasons is the same that eventually also slowed down their acceptance: higher memory consumption. As in coupled methods previous scalar matrix coefficients become nxn matrices, so you get an nxn memory increase. Let me also say that this is not always compensated by any benefit in convergence rate. Today, however, they are both very common and, if properly coded, can also give a higher arithmetic intensity to the code, which most of the times means higher performances.