# Conceptual Question about One Dimensional Inviscid Burgers Equation

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 May 20, 2015, 04:22 Conceptual Question about One Dimensional Inviscid Burgers Equation #1 New Member   Tanmay Agrawal Join Date: May 2015 Location: Taiwan Posts: 29 Rep Power: 10 Hello everyone! I am trying to use Adaptive mesh refinement and I was just going through the PhD thesis of Marsha Berger. She wrote inviscid Burgers equation as u_t = u*u_x While at almost every place, I have seen it as u_t + u*u_x = 0. Is there any significant difference between the solutions of these two equations? I am trying to write a code using Lax-Wendroff Scheme for the equation she has given. Can I expect good results? Thanks and looking forward for responses.

May 20, 2015, 05:52
#2
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by tanmayagrawal7 Hello everyone! I am trying to use Adaptive mesh refinement and I was just going through the PhD thesis of Marsha Berger. She wrote inviscid Burgers equation as u_t = u*u_x While at almost every place, I have seen it as u_t + u*u_x = 0. Is there any significant difference between the solutions of these two equations? I am trying to write a code using Lax-Wendroff Scheme for the equation she has given. Can I expect good results? Thanks and looking forward for responses.
In my opinion u_t = u*u_x is not the classic expression for Burgers equation... if you express the total variation du:

du =dt (du/dt + dx/dt * du/dx)

therefore, to have the classical fact that that u is conserved along path line, you need the condition for the characteristic curves

du = 0 -> dx/dt = -u

on the other hand, if you denote f=-u:

du/dt +f*du/dx=0

you can find the classical Burgers equation for the field f.

 May 20, 2015, 09:22 #3 New Member   Tanmay Agrawal Join Date: May 2015 Location: Taiwan Posts: 29 Rep Power: 10 Thanks a lot. Perhaps it could be mistakenly written in the thesis I was reading or it could be the second option as you mentioned. I will try them both to see which corresponds to the solution mentioned by her.

May 20, 2015, 09:50
#4
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Tanmay Agrawal
Join Date: May 2015
Location: Taiwan
Posts: 29
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Quote:
 Originally Posted by FMDenaro In my opinion u_t = u*u_x is not the classic expression for Burgers equation... if you express the total variation du: du =dt (du/dt + dx/dt * du/dx) therefore, to have the classical fact that that u is conserved along path line, you need the condition for the characteristic curves du = 0 -> dx/dt = -u on the other hand, if you denote f=-u: du/dt +f*du/dx=0 you can find the classical Burgers equation for the field f.
Yes, it was a typing error instead. If I use the classical inviscid Burgers equation, in fact I can get the same kind of results as in the thesis. Thanks a lot.

 Tags amr, burgers equation, cfd, inviscid, theory