Hello
I created a new thread since the name is more suitable than the previous thread I started on ModelPDE.
I am trying to find out where the problem arises with my plasma physics equations.
So for all solvers I replaced
Linear System Solver = Iterative
by
Linear System Solver = Direct
and for all nonlinear equations, I replaced
Nonlinear System Relaxation Factor = 1
by
Nonlinear System Relaxation Factor = .3
But to no avail: The norm in the nonlinear iterations quickly become infinite within a microsecond.
Is that almost a mathematical proof that this is not a numerical problem but that the PDE's themselves have unstable coupling terms (for example like a term with a wrong sign which grows forever) ?
Wish you all a nice weekend
P.S.
the deltaT is 1.0e8 sec and the Mach number is .8 (272 m/sec around 1 atm and T = 300 Kelvin)
Unstable PDE's
Re: Unstable PDE's
Hello,
Can you post a minimum working example? Or at least a minimum almost working example?
Rich.
Can you post a minimum working example? Or at least a minimum almost working example?
Rich.
Re: Unstable PDE's
Actually I cannot ! I tried Elmer's original HeatSolver and FlowSolver both with Linear System Solver = Direct on a standard NACA0012 airfoil and the norm in the nonlinear iterations of the FlowSolver still becomes infinite within microseconds.
There are no other solvers called in the .sif (They are a lot of them but with Exec Solver = Never)
(the deltaT is 1.0e8 sec and the Mach number is .8 (272 m/sec around 1 atm and T = 300 Kelvin)
I use velocity = 0 Heat Flux = 0.0 boundary conditions on the airfoil itself. And I use
velocity = 272 m/sec, pressure = 1 atm and temperature = 300 Kelvin as boundary conditions everywhere in the farfield.
(These are also the initial conditions everywhere in the domain)
Either these conditions are unphysical or Elmer cannot handle highly compressible flows.
There are no other solvers called in the .sif (They are a lot of them but with Exec Solver = Never)
(the deltaT is 1.0e8 sec and the Mach number is .8 (272 m/sec around 1 atm and T = 300 Kelvin)
I use velocity = 0 Heat Flux = 0.0 boundary conditions on the airfoil itself. And I use
velocity = 272 m/sec, pressure = 1 atm and temperature = 300 Kelvin as boundary conditions everywhere in the farfield.
(These are also the initial conditions everywhere in the domain)
Either these conditions are unphysical or Elmer cannot handle highly compressible flows.

 Posts: 1210
 Joined: 25 Jan 2019, 01:28
 Antispam: Yes
Re: Unstable PDE's
FlowSolver by itself generally does not converge with high velocity flows. It can be coupled with kepsilon for imprvement
viewtopic.php?f=3&t=6995&hilit=turbulent
viewtopic.php?f=3&t=6995&hilit=turbulent
Re: Unstable PDE's
Turbulence models involve the energy equation but FlowSolver only handles continuity and momentum equations. Shouldn't HeatSolver also look at the turbulence keywords in the .sif ? Not according to its description under ElmerModelsManual. Moreover, I found keywords under ElmerTutorialFilesGUI that were different from those of ElmerModelsManual.
Best,
Marc
Best,
Marc

 Posts: 1210
 Joined: 25 Jan 2019, 01:28
 Antispam: Yes
Re: Unstable PDE's
In Elmer, I believe the heat only follows the flow (convection), except for conduction and radiation, and P=VRT. I believe since FlowSolver only handles continuity and momentum is the reason it can't converge on turbulent flow conditions. Therefore if the flow is turbulent other equations must be introduce. The software is developed and update daily, however the manuals, and tutorials are not, so the documentation lags significantly behind the development.
Re: Unstable PDE's
The theory of characteristics for compressional flows in 3D shows that to avoid instabilities and other problems for subsonic flow ( M <=.8 in my case) then,
we must prescribe at most 4 characteristic variables from the freestream values at the inflow boundary (the 5th variable being extrapolated from the interior domain) whereas at the outflow boundary it is the 5th variable which is prescribed from its freestream value and and all other 4 variables are extrapolated from the interior domain.
We can of course get the primitive variables on the boundaries from the characteristic variables.
The above is standard procedure in finitevolume CFD books but Elmer utilizes a finite element approach. (although finite volume is a special case of finite element methods)
Is this theory included in Elmer ?
we must prescribe at most 4 characteristic variables from the freestream values at the inflow boundary (the 5th variable being extrapolated from the interior domain) whereas at the outflow boundary it is the 5th variable which is prescribed from its freestream value and and all other 4 variables are extrapolated from the interior domain.
We can of course get the primitive variables on the boundaries from the characteristic variables.
The above is standard procedure in finitevolume CFD books but Elmer utilizes a finite element approach. (although finite volume is a special case of finite element methods)
Is this theory included in Elmer ?