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Conceptual Question about One Dimensional Inviscid Burgers Equation

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Old   May 20, 2015, 05:22
Question Conceptual Question about One Dimensional Inviscid Burgers Equation
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Tanmay Agrawal
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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.
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Old   May 20, 2015, 06:52
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Filippo Maria Denaro
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Quote:
Originally Posted by tanmayagrawal7 View Post
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.
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Old   May 20, 2015, 10:22
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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.
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Old   May 20, 2015, 10:50
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Quote:
Originally Posted by FMDenaro View Post
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.
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