ENO schemes in the vicinity of solid walls

jcsandov · April 6, 2020, 10:31

Hi everyone!,
I'm trying to solve the level-set equation using a 3rd order ENO scheme for a flow facing an obstacle in a channel. I'm having some problems in the vicinity of the solid wall because I don't know how to implement a stencil that preserves the accuracy and consistency of the fluxes and let me compute the variables in the second node from the wall. I'm using a non-staggered grid to compute the flow variables.
(this is a code developed by my advisor and my research group)
Thank you!

t.teschner · April 6, 2020, 10:42

I assume it is a structured grid? If so, you could use ghost cells and extrapolate information from the interior to the ghost cells using the boundary conditions, in which case your stencil would not change. Of course, depending on your extrapolation, you may not preserve third order accuracy at the wall. Alternatively you could switch to a one-sided stencil scheme (3rd order upwind) which may preserve the order.

For unstructured grids the second approach would work equally I suppose, ghost cells would be a bit more tricky to implement.

jcsandov · April 6, 2020, 10:46

Thank you very much. Yes, it is a structured grid. Do you have some reference where can I find some guidelines to implement these ghost points?
Regards

t.teschner · April 10, 2020, 05:04

Yes, I did go into some detail in my PhD thesis on that topic, which you can find here: https://dspace.lib.cranfield.ac.uk/handle/1826/14381 ... Have a look at Page 84 - 85 where I show how to to implement the ghost cell approach, hope this will help. Otherwise comment below and let me know if anything is unclear.

April 6, 2020, 10:31	ENO schemes in the vicinity of solid walls	#1
jcsandov New Member jcsandov@uc.cl Join Date: Nov 2015 Posts: 2 Rep Power: 0	Hi everyone!, I'm trying to solve the level-set equation using a 3rd order ENO scheme for a flow facing an obstacle in a channel. I'm having some problems in the vicinity of the solid wall because I don't know how to implement a stencil that preserves the accuracy and consistency of the fluxes and let me compute the variables in the second node from the wall. I'm using a non-staggered grid to compute the flow variables. (this is a code developed by my advisor and my research group) Thank you!

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April 6, 2020, 10:42		#2
t.teschner Senior Member Tom-Robin Teschner Join Date: Dec 2011 Location: Cranfield, UK Posts: 204 Rep Power: 16	I assume it is a structured grid? If so, you could use ghost cells and extrapolate information from the interior to the ghost cells using the boundary conditions, in which case your stencil would not change. Of course, depending on your extrapolation, you may not preserve third order accuracy at the wall. Alternatively you could switch to a one-sided stencil scheme (3rd order upwind) which may preserve the order. For unstructured grids the second approach would work equally I suppose, ghost cells would be a bit more tricky to implement.

April 6, 2020, 10:46		#3
jcsandov New Member jcsandov@uc.cl Join Date: Nov 2015 Posts: 2 Rep Power: 0	Thank you very much. Yes, it is a structured grid. Do you have some reference where can I find some guidelines to implement these ghost points? Regards

April 10, 2020, 05:04		#4
t.teschner Senior Member Tom-Robin Teschner Join Date: Dec 2011 Location: Cranfield, UK Posts: 204 Rep Power: 16	Yes, I did go into some detail in my PhD thesis on that topic, which you can find here: https://dspace.lib.cranfield.ac.uk/handle/1826/14381 ... Have a look at Page 84 - 85 where I show how to to implement the ghost cell approach, hope this will help. Otherwise comment below and let me know if anything is unclear.