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On the solution of Burgers equation

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Old   February 12, 2021, 09:19
Default On the solution of Burgers equation
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Balakrishna
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I have modelled a Riemann solver using the first order and TVD methods for solving the Inviscid 1D burgers equation. As far as the solution is concerned, they are consistent. But I want to evaluate their accuracy and identify the first order and second-order accurate natures of the solutions.
Are there ways to identify the differences in the solution nature of 1st order and 2nd order accuracy without actually knowing the analytical solutions?
Thanks in advance
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Old   February 12, 2021, 09:25
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Originally Posted by balkiii View Post
I have modelled a Riemann solver using the first order and TVD methods for solving the Inviscid 1D burgers equation. As far as the solution is concerned, they are consistent. But I want to evaluate their accuracy and identify the first order and second-order accurate natures of the solutions.
Are there ways to identify the differences in the solution nature of 1st order and 2nd order accuracy without actually knowing the analytical solutions?
Thanks in advance
You can find a proposal as addressed in the texbook of Peric, Ferziger and Street.
Be aware that you can perform the analysis only until the solution is regular and sufficiently smooth.
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Old   February 12, 2021, 09:38
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Thanks... I'll sure take a look into it.
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Old   February 12, 2021, 13:14
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Thanks... I'll sure take a look into it.



However, the Burgers equation actually has an exact solution, why you don't use it?
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Old   February 12, 2021, 14:01
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However, the Burgers equation actually has an exact solution, why you don't use it?
Yes but I'm looking for a way to check the first order and second-order nature of the solutions without using the analytical solution. The idea is I want to extend my solvers to all Hyperbolic and I'm developing Burgers as a test case.
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Old   February 12, 2021, 14:35
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If you are only interested in the EOC then just use the manufactured solution procedure.

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