[aerosayan]

This maybe a basic question, but I don't know the answer to it.


I was reading a code that does local timestepping in each cell to allegedly accelerate the solution convergence of a steady compressible Euler solver.


As shown in the picture attached, we can see the logic being used to calculate the minimum timestep possible for a cell, then updating the cell values with an m-stage process.


I don't understand how this actually works, and how the solution make any physical sense.



Based on the code, we can see that each cell will be advanced to different points in time, since every cell will have a different timestep calculated for it.


How does the simulation work when each cell is at a different point in time?



Thanks

[flotus1]

steady compressible Euler solver

The solution is only correct once the steady state is reached. I.e. the solution is fully converged.

[aerosayan]

Originally Posted by flotus1

The solution is only correct once the steady state is reached. I.e. the solution is fully converged.

Okay, that seems correct. The simulations do work, and I've validated them before.


Thanks.

[FMDenaro]

Originally Posted by aerosayan

This maybe a basic question, but I don't know the answer to it.


I was reading a code that does local timestepping in each cell to allegedly accelerate the solution convergence of a steady compressible Euler solver.


As shown in the picture attached, we can see the logic being used to calculate the minimum timestep possible for a cell, then updating the cell values with an m-stage process.


I don't understand how this actually works, and how the solution make any physical sense.



Based on the code, we can see that each cell will be advanced to different points in time, since every cell will have a different timestep calculated for it.


How does the simulation work when each cell is at a different point in time?



Thanks

The key to understand the issue is to forget about a physical meaning of the time step and considering only that the equations have a residual that is driven to zero by using local parameters for accelerating the convergence.