Convergence criteria

Pilu · May 4, 2022, 18:28

Hello everybody, I'm a new dumb user of su2.
I'm working on the simulation of boundary layer on a flat plate in laminar regime.
I didn't catch how to state the convergence of the mesh.
I generated different meshes and I compute the residual between two consecutive Cd obtained with the mesh in this way:

res(cd)=abs(cd(i+1)-cd(i))/cd(i);

I also compute the exact skin friction coefficient for the Blausis solution cfe and I want to compute the norm of the error wrt the cf(i) of the different mesh.
It can be a good idea to state the convergence?

bigfootedrockmidget · May 5, 2022, 04:34

what would you like to show?

For instance, you can plot the drag coefficient as function of the number of grid points and use Richardson extrapolation to get estimates of the 'real' Cd.

You can also get an estimate of the error on any grid by assuming that Cd on your finest grid Cd(N) is the 'real' Cd and compute the error as Cd(i)-Cd(N). If you plot this in a log-log plot, you should retrieve the order of the numerical scheme as the slope in the error plot, although this works best if you have an analytical solution.

Pilu · May 9, 2022, 18:50

First of all, thank for the answer.
I want to prove in a quantitative way the mesh convergence, i.e.the fact that the simulation results doesn't change if i reduce the mesh sizes over a certain dimension.
For example, If i have the analytical relationship for the skin friction coefficient cf(x) and some different numerical solutions (computed on different meshes) defined only in some points on the wall, cf(k), how i can prove the convergence of my numerical cf(k) to exact one cf(x)?

bigfootedrockmidget · May 10, 2022, 18:41

So is this similar to the plots shown in this V&V section:
https://su2code.github.io/vandv/Flat_Plate/
In general the grid size is nonuniform so unless you have a structured uniform grid, you need to come up with some measure of the grid size. You could use h=1/sqrt(N) as in the Flat Plate validation study on the website.

You can then plot cf as function of the mean grid size h, together with the analytical value, or plot the error cf-cf_analytical.

May 4, 2022, 18:28	Convergence criteria	#1
Pilu New Member Pi Join Date: Oct 2021 Posts: 3 Rep Power: 5	Hello everybody, I'm a new dumb user of su2. I'm working on the simulation of boundary layer on a flat plate in laminar regime. I didn't catch how to state the convergence of the mesh. I generated different meshes and I compute the residual between two consecutive Cd obtained with the mesh in this way: res(cd)=abs(cd(i+1)-cd(i))/cd(i); I also compute the exact skin friction coefficient for the Blausis solution cfe and I want to compute the norm of the error wrt the cf(i) of the different mesh. It can be a good idea to state the convergence?

May 5, 2022, 04:34		#2
bigfootedrockmidget Senior Member bigfoot Join Date: Dec 2011 Location: Netherlands Posts: 679 Rep Power: 21	what would you like to show? For instance, you can plot the drag coefficient as function of the number of grid points and use Richardson extrapolation to get estimates of the 'real' Cd. You can also get an estimate of the error on any grid by assuming that Cd on your finest grid Cd(N) is the 'real' Cd and compute the error as Cd(i)-Cd(N). If you plot this in a log-log plot, you should retrieve the order of the numerical scheme as the slope in the error plot, although this works best if you have an analytical solution. PENGGEGE777 likes this.

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May 9, 2022, 18:50		#3
Pilu New Member Pi Join Date: Oct 2021 Posts: 3 Rep Power: 5	First of all, thank for the answer. I want to prove in a quantitative way the mesh convergence, i.e.the fact that the simulation results doesn't change if i reduce the mesh sizes over a certain dimension. For example, If i have the analytical relationship for the skin friction coefficient cf(x) and some different numerical solutions (computed on different meshes) defined only in some points on the wall, cf(k), how i can prove the convergence of my numerical cf(k) to exact one cf(x)?

May 10, 2022, 18:41		#4
bigfootedrockmidget Senior Member bigfoot Join Date: Dec 2011 Location: Netherlands Posts: 679 Rep Power: 21	So is this similar to the plots shown in this V&V section: https://su2code.github.io/vandv/Flat_Plate/ In general the grid size is nonuniform so unless you have a structured uniform grid, you need to come up with some measure of the grid size. You could use h=1/sqrt(N) as in the Flat Plate validation study on the website. You can then plot cf as function of the mean grid size h, together with the analytical value, or plot the error cf-cf_analytical.