WENO 2D Euler

PicklER · July 29, 2014, 06:43

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:

$\frac{d\textbf{u}}{dt}$ + $\frac{d\textbf{F}}{dx}$ =0.

For the scalar case, my initial condition was $\textbf{u}$ (x,t=0) = sin( $\pi$ (x-t)) and u=F.
For the Euler conservation laws, my initial condition is:

$\textbf{u}=\left[\rho, \rho v, E\right]$ and

$\textbf{F}=\left[\rho v, P+\rho v^{2}, v(E+P)\right]$ ,

where $\rho$ 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

Catkun · August 19, 2014, 01:10

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.

PicklER · August 19, 2014, 04:40

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):

$u_{1}=u_{n}+\Delta tL(u_{n})$
$u_{2}=\frac{1}{4}(3u_{n} +u_{1}+\Delta t L(u_{1})$
$u_{n+1}=\frac{1}{3}(u_{n} +2(u_{2}+\Delta t L(u_{2}))$ ,

where

$L=\frac{1}{\Delta x}(F_{j+1/2}-F_{j-1/2})$ ,

where $F_{j+1/2}$ and $F_{j-1/2}$ are computed via the WENO reconstruction method.

ref: http://www.dam.brown.edu/scicomp/med...SC-2009-03.pdf

Catkun · August 19, 2014, 11:16

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.

PicklER · August 20, 2014, 01:56

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

Catkun · November 3, 2014, 21:13

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.

PicklER · November 9, 2014, 04:27

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

Answer=42 · July 11, 2016, 05:00

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.

crazyshock · October 16, 2017, 16:40

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.

July 29, 2014, 06:43	WENO 2D Euler	#1
PicklER 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: $\frac{d\textbf{u}}{dt}$ + $\frac{d\textbf{F}}{dx}$ =0. For the scalar case, my initial condition was $\textbf{u}$ (x,t=0) = sin( $\pi$ (x-t)) and u=F. For the Euler conservation laws, my initial condition is: $\textbf{u}=\left[\rho, \rho v, E\right]$ and $\textbf{F}=\left[\rho v, P+\rho v^{2}, v(E+P)\right]$ , where $\rho$ 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.

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August 19, 2014, 01:10		#2
Catkun 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
PicklER 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): $u_{1}=u_{n}+\Delta tL(u_{n})$ $u_{2}=\frac{1}{4}(3u_{n} +u_{1}+\Delta t L(u_{1})$ $u_{n+1}=\frac{1}{3}(u_{n} +2(u_{2}+\Delta t L(u_{2}))$ , where $L=\frac{1}{\Delta x}(F_{j+1/2}-F_{j-1/2})$ , where $F_{j+1/2}$ and $F_{j-1/2}$ 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
Catkun 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.

November 3, 2014, 21:13		#6
Catkun 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
PicklER 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

October 16, 2017, 16:40		#9
crazyshock 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.