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Hello! I created two meshes using a model of renal artery stenosis. The small mesh size is 1.99million, and big one is 4.38million. The simulation of small mesh run for 8 cardiac cycles successfully. However, the nonlinear residual of simulation using big mesh failed to converge on the third cardiac cycle. All parameters and boundary conditions are set same in both simulation. Local size were used to increase mesh size of visceral arteries and regional refinement were used to increase mesh size of renal artery stenosis. The coordinate and radius of sphere of regional refinement were set same in both meshes. The only difference of these two meshes were the global max edge size, local size and the size of regional refinement.
What is the cause of converge failure of big mesh size? Figure of big mesh size is attached.

Hi Yun,

Thank you for your question! The problem you are encountering is indeed a common one in numerical flow simulation. In general, when you refine the resolution of the spatial domain, this requires you to also reduce the timestep in order to get stable and accurate solutions. There is an index called the CFL number which you can use to quickly check the timestep restrictions on your simulation. We refer you to this webpage for an in-depth discussion: https://www.simscale.com/blog/2017/08/cfl-condition/. But the summary of this is that the following relationship must hold:

CFL = v dt/dx <= 1

Where v is a characteristic velocity of your simulation, dt is the timestep size, and dx is the grid size (i.e. the length of an edge in a finite element simulation). This ratio should be less than 1 for a converged and accurate simulation. It can be a little inconvenient to compute a characteristic velocity in your simulation, but you have a unique case where you can apply the CFL condition. You have a working simulation with 1.99 million elements with a timestep that works. In your finer mesh, you probably reduced the edge size by a factor. You must then reduce your timestep by (at most) the same factor to get a similarly converged solution. In other words, if you make a finer mesh whose elements have half the edge length, you must also halve your timestep size to get a similarly converged solution.

Hope that helps!

Thank you, Justin! The highest velocity appears at renal artery stenosis. The mesh edge size of coarse mesh is 1.33 times of the fine mesh at renal stenosis. Thus, I will try to run simulation by reducing the timestep size of fine mesh to a half of the coarse mesh.