[Emily1412]

According to Tutorial 2, Multigrid is a convergence acceleration technique where the original mesh is simplified into a series of coarser meshes, and calculations are performed on all mesh levels with each solver iteration in order to provide a better residual update. Does it mean that for every simulation case when MGLEVEL= 3 and MGCYCLE= 1, SU2 runs fastest?
And about the CFL_REDUCTION, what's the meaning of this option? Does it mean that for every simulation case, bigger CFL_REDUCTION leads to faster run but lower stability?

[awendorff]

Multigrid helps to converge the solution in a reduced number of steps. Depending on the size of the mesh, more levels of multigrid might make sense so MGLEVEL = 3 is not necessarily the fastest, but instead is just faster than MGLEVEL = 0, 1, or 2.
Since the CFL number is based on the time step (or virtual time step) and the mesh size, when coarsening the grid in the case of multigrid, the stability is impacted. Having a CFL_REDUCTION closer to 1 will lead to less stability and a quicker run.

Hope this helps.

[Emily1412]

Originally Posted by awendorff

Multigrid helps to converge the solution in a reduced number of steps. Depending on the size of the mesh, more levels of multigrid might make sense so MGLEVEL = 3 is not necessarily the fastest, but instead is just faster than MGLEVEL = 0, 1, or 2.
Since the CFL number is based on the time step (or virtual time step) and the mesh size, when coarsening the grid in the case of multigrid, the stability is impacted. Having a CFL_REDUCTION closer to 1 will lead to less stability and a quicker run.

Hope this helps.

Thank you for your reply. But I still can't understand that if MGLEVEL=3 is faster than 0,1 and 2, what is the meaning of "not necessarily the fastest"?
And what's the result of unstability?
Hope for your reply. Thank you!

[awendorff]

So you could have higher multigrid number then it will be faster, but I am not sure if MGLEVEL three is the maximum. It could be that you could use a higher MGLEVEL so you have to be careful when saying the fastest. The result of instability is the solution will blow up and yield a meaningless result instead of converge.

[pdp.aero]

Originally Posted by Emily1412

Thank you for your reply. But I still can't understand that if MGLEVEL=3 is faster than 0,1 and 2, what is the meaning of "not necessarily the fastest"?
And what's the result of unstability?
Hope for your reply. Thank you!

Multigrid is one of the popular convergence acceleration method. Let me explain it in this way. Typically, when you are iterating a computational fluid dynamics based problem, you need to throw off errors from your simulation to reach the solution. Imagine a house full of trash, if you are transferring trash faster to the outside, you will find the solution faster or you will converge faster.

On the other hand, high frequency error will have been dumping faster in fine grid, and low frequency error will have been dumping faster in coarse grid. In Mutigrid you are displacing the solution between fine and coarse grid to make it faster to converge. You may use W cycle that is more accurate but it will take longer or V cycle that is less accurate but it will work faster for displacing the solution between fine and coarse grid. In the algebraic method you may using Gauss-Seidlel or ILU or other way to merge cells and coarse your initial fine grid because you need to level your grid into fine and coarse.

MGLEVEL=3 means that you have three grid levels from fine to coarse for displacing the solution and accelerating the convergence. If you are displacing the solution between too much level you are just wasting your time because the solution will not change any more. Besides, you may confront instability and hinder your solution from the convergence.

CFL_REDUCTION changes the CFL number for the coarse level in order for providing stability.

[Emily1412]

Originally Posted by pdp.aero

Multigrid is one of the popular convergence acceleration method. Let me explain it in this way. Typically, when you are iterating a computational fluid dynamics based problem, you need to throw off errors from your simulation to reach the solution. Imagine a house full of trash, if you are transferring trash faster to the outside, you will find the solution faster or you will converge faster.

On the other hand, high frequency error will have been dumping faster in fine grid, and low frequency error will have been dumping faster in coarse grid. In Mutigrid you are displacing the solution between fine and coarse grid to make it faster to converge. You may use W cycle that is more accurate but it will take longer or V cycle that is less accurate but it will work faster for displacing the solution between fine and coarse grid. In the algebraic method you may using Gauss-Seidlel or ILU or other way to merge cells and coarse your initial fine grid because you need to level your grid into fine and coarse.

MGLEVEL=3 means that you have three grid levels from fine to coarse for displacing the solution and accelerating the convergence. If you are displacing the solution between too much level you are just wasting your time because the solution will not change any more. Besides, you may confront instability and hinder your solution from the convergence.

CFL_REDUCTION changes the CFL number for the coarse level in order for providing stability.

Thank you for your reply! This helps me a lot!