# WENO 2D Euler

 Register Blogs Members List Search Today's Posts Mark Forums Read

 July 29, 2014, 06:43 WENO 2D Euler #1 Member   Join Date: Jul 2014 Posts: 39 Rep Power: 11 Hello New to forum, so here goes: I have successfully implemented the 5th order WENO reconstruction method for 1D scalar and Euler conservation laws of the form: +=0. For the scalar case, my initial condition was (x,t=0) = sin((x-t)) and u=F. For the Euler conservation laws, my initial condition is: and , where is density, P is pressure, v is velocity and E is energy. I used the 5th order WENO with Lax Friedrichs flux splitting and Runge-Kutta 3rd order to solve this. I even got it working for the 2D scalar case, but I cannot solve the 2D Euler conservation equations. I've read a wide wide variety of articles containing WENO, but need a simple template for the 2D case to use as comparison. So I'm asking for code of such an example (preferably in MATLAB). Any help will be greatly appreciated Last edited by PicklER; August 14, 2014 at 02:41.

 August 19, 2014, 01:10 #2 New Member   Cat Join Date: Aug 2014 Posts: 6 Rep Power: 11 Hi Pickler, I am working on 1D conservation law but have met difficulty for the time discretization. Could you share your code? Also, for the problem you met, are you using FD or FV? From what I read, FV is intensively harder when dimension increases while FD simply requires you to write another "do" loop.

 August 19, 2014, 04:40 #3 Member   Join Date: Jul 2014 Posts: 39 Rep Power: 11 Hey Catkun I'm using FD and yes, also read that to extend it a simple do-loop should be added but that only works for the scalar test case and not for the conservation laws. Do you only need the time discretization? As I've said, I only used the 3rd order Runge-Kutta which looks as follows (found in any article describing the WENO reconstruction method, ref below): , where , where and are computed via the WENO reconstruction method. ref: http://www.dam.brown.edu/scicomp/med...SC-2009-03.pdf

 August 19, 2014, 11:16 #4 New Member   Cat Join Date: Aug 2014 Posts: 6 Rep Power: 11 Hi Pickler, Thanks for your reply. I guess my problem is that I don't know how to compute . I am new to CFD and maybe misunderstand something in the paper. I also read the reference paper you mentioned but still don't quite know how to get the value of after the first time step. Could you share your matlab code for the 1D case so I can read through and get a better idea? Thanks.

August 20, 2014, 01:56
#5
Member

Join Date: Jul 2014
Posts: 39
Rep Power: 11
Hi Catkun

Here is an example of my WENO for the 1D shocktube case. The scalar case is simpler version of this with only one equation. Hope it helps!

Vrede
Attached Files
 test_WENO_1D_shock.tar.gz (1.9 KB, 146 views)

 November 3, 2014, 21:13 #6 New Member   Cat Join Date: Aug 2014 Posts: 6 Rep Power: 11 Hi Pickler, I wonder if you are still working on this problem. I have finished the 1D case and then started working on the 2D case. Actually I think there is some problem in your code for the 1D simulation, (or I may be wrong . If you are still working on the problem and would like to discuss, I'd be happy to do so. All the best.

 November 9, 2014, 04:27 #7 Member   Join Date: Jul 2014 Posts: 39 Rep Power: 11 Hey Catkun I paused on the WENO case and started on other things. What is the mistake in the 1D case? Will gladly have a look at it again if you have new info on it. Kind regards

July 11, 2016, 05:00
Revision
#8
New Member

Aranya Dan
Join Date: Jul 2016
Posts: 1
Rep Power: 0
Quote:
 Originally Posted by PicklER Hey Catkun I paused on the WENO case and started on other things. What is the mistake in the 1D case? Will gladly have a look at it again if you have new info on it. Kind regards
Hi,
If this thread is still active, I would like to draw your attention to a few corrections on your code. (Just a few small errors).

In the main file,
Line 22: Replace function name with 'initiali_1D_shock' and replace 'x' passed as parameter with 'n_x'.
Line 110: Replace 'x' as x-axis with 'x(1:length(x)-1)'. This will get the code up and running.

I am new to CFD myself and your code was a huge help. I am attempting 5th order WENO for shock formation on a 2d wedge.
Thank you.

P.S. If anybody has the 2d WENO figured out, a little help would be appreciated.

 October 16, 2017, 16:40 #9 New Member   Aranya Dan Join Date: Oct 2017 Posts: 19 Rep Power: 8 https://github.com/aranyadan/WENO52D_fortran 2D weno code I wrote and validated with Reimann test cases. Hit me for any other assistance you might need.

 Tags 2 dimensional, code, euler, matlab, weno