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 February 15, 2015, 23:03 Steady-State solution by time-stepping? #1 New Member   John Join Date: Jan 2015 Posts: 18 Rep Power: 2 This might be a silly question, but I wrote a CFD code (compressible, unstructured mixed element in 2D and 3D) that I am having trouble converging in 3D for relatively low Mach numbers (~0.1). I am aware that the N-S and Euler equations become stiff at low Mach numbers. How are these cases typically dealt with? Are solutions to complex 3D problems typically time stepped to a steady-state solution? This will certainly make the linear system easier to solve, but seems rather inefficient. Is seems that straight-up Newton-Krylov would be better. I'm using GMRES to solve the linear system and have put in a lot of work to get a good preconditioner, to the point that I don't think I can do any better on the preconditioning side of things. Any advice would be great! Last edited by mavguy; February 16, 2015 at 01:25.

February 16, 2015, 08:14
#2
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,662
Rep Power: 23
Quote:
 Originally Posted by mavguy This might be a silly question, but I wrote a CFD code (compressible, unstructured mixed element in 2D and 3D) that I am having trouble converging in 3D for relatively low Mach numbers (~0.1). I am aware that the N-S and Euler equations become stiff at low Mach numbers. How are these cases typically dealt with? Are solutions to complex 3D problems typically time stepped to a steady-state solution? This will certainly make the linear system easier to solve, but seems rather inefficient. Is seems that straight-up Newton-Krylov would be better. I'm using GMRES to solve the linear system and have put in a lot of work to get a good preconditioner, to the point that I don't think I can do any better on the preconditioning side of things. Any advice would be great!
at low Mach you can use pre-conditioning techniques or, if accettaple, using the incompressible model. If the steady state really exists, you can reach it by using a time-integration method untile the time derivatives become smaller (in some norm) than some tolerance

February 16, 2015, 10:44
#3
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John
Join Date: Jan 2015
Posts: 18
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Quote:
 Originally Posted by FMDenaro If the steady state really exists, you can reach it by using a time-integration method untile the time derivatives become smaller (in some norm) than some tolerance
Shouldn't steady-state be reachable without time-stepping? In 2D, I use Newton's method and reach steady-state just fine. Is the initial guess for Newton typically just too far away from the solution in 3D for Newton to converge?

 February 16, 2015, 12:09 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 1,662 Rep Power: 23 Again, you can directly solve the steady-state solution. Sometimes, there is not a numerical solution to the discrete system and that can be a signal that the flow is unsteady. I suppose that for converging, the Newton method require you start from an initial guess not very far from the solution