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February 15, 2015, 23:03 
SteadyState solution by timestepping?

#1 
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John
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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 NS 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 steadystate solution? This will certainly make the linear system easier to solve, but seems rather inefficient. Is seems that straightup NewtonKrylov 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
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Quote:


February 16, 2015, 10:44 

#3 
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John
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Shouldn't steadystate be reachable without timestepping? In 2D, I use Newton's method and reach steadystate 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 
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Filippo Maria Denaro
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Again, you can directly solve the steadystate 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 

Tags 
steadystate convergence, timestepping 
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