[aerosayan]

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

Does it matter which cells we select and solve first in an explicit solver? Or the order in which we solve them?

Say, a 2D structured grid is present (square domain), and we want to solve the compressible Euler equations in the cell volumes using an explicit solver.

We're not considering any performance penalties due to cache misses, and accessing any random index in the grid, is instantaneous.

So, if the flow is from right to left, will it matter if I iterate through the grid from left to right, or top to bottom, or in a random order ( in a worst case scenario )?

Thanks

[Eifoehn4]

It depends. If your explicit solver has to solve a large equation system (Poisson equation) in an iterative sense then the order might matter. Otherwise not, at least if you neglect roundofferrors.

[aerosayan]

Originally Posted by Eifoehn4

It depends. If your explicit solver has to solve a large equation system (Poisson equation) in an iterative sense then the order might matter. Otherwise not, at least if you neglect roundofferrors.

I do have a FDM based poisson solver for a structured grid.
How would the order matter there? Unfortunately, that is not clear to me.


Regarding the Euler solver : my intuition also says that the order won't matter in getting an accurate solution, since we don't care much about the order in which unstructured grids are accessed.


Thanks

[Eifoehn4]

For example if the solution of the Poisson equation is based on a Gauss-Seidel or SOR algorithm.
Here the solution depends on the current iteration values N and the next iteration values N+1 calculated in the same iteration step.
Such algorithms are non-linear meaning that a different ordering results in a different convergence.

[aerosayan]

Thanks for the explanation. Now it makes perfect sense.

[FMDenaro]

Originally Posted by aerosayan

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

Does it matter which cells we select and solve first in an explicit solver? Or the order in which we solve them?

Say, a 2D structured grid is present (square domain), and we want to solve the compressible Euler equations in the cell volumes using an explicit solver.

We're not considering any performance penalties due to cache misses, and accessing any random index in the grid, is instantaneous.

So, if the flow is from right to left, will it matter if I iterate through the grid from left to right, or top to bottom, or in a random order ( in a worst case scenario )?

Thanks

what kind of iterative solver are you using for compressible Euler flow and explicit time-marching method?

[aerosayan]

Originally Posted by FMDenaro

what kind of iterative solver are you using for compressible Euler flow and explicit time-marching method?

Cell centred FVM scheme for discretization, Van-Leer flux and Roe flux with entropy correction for flux calculation and solving the Riemann problem, and an m-stage time stepping scheme for the explicit time marching iterations.



The grid will be a block structured mesh which will be adaptively refined using more block structured grids. Similar to AMReX ( https://amrex-codes.github.io/amrex/gallery.html ), but the base structured grid will conform to the body's boundary so that I don't have to use Embedded Boundary Method for the boundaries.



Thanks

[duri]

Ordering doesn't matter. Both explicit and implicit equations doesn't have any spatial preference. Only the flux calculation depends on direction and that too doesn't have any spatial preference.