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 LECHON April 26, 2005 11:20

burger's equation

I would to know better manner in order to solve burger's equation.

thanks.

 ag April 27, 2005 10:56

Re: burger's equation

The best way would be to solve it analytically. This can be done using a Cole-Hopf transformation. Assuming that you actually want a numerical scheme for solving it, the answer is that it depends on what your goal is. A first-order time, upwind space scheme is easy to program but may be too dissipative. And do you want to use a finite volume scheme as a precursor to an unstructured solver, or is structured sufficient? The answer to your question really depends on how you define 'better manner'.

 LECHON April 27, 2005 11:31

Re: burger's equation

first of all, thank you very much.

I'm interensting in resolving the equation with a numerical scheme, whit finite difference for spacial coordinate and a runge kutta for the time. the question is, in order to get good accurancy: the order of the scheme must be high (third-order or more)? What is the influence of CFL in the shock?

bye

Pd.- structured sufficiently.

 Mani April 27, 2005 12:49

Re: burger's equation

I am not sure if it makes sense to use "unstructured" methodology for a 1-D problem, as mentioned earlier. So I agree with your assessment to do it structured. There is a large variety of applicable schemes, but you already decided (or your assignment states) the use of Runge-Kutta. I think the 4-th order R-K is a standard method that's pretty easy to implement, and that's more than sufficient for this problem.

For the spatial discretization I would suggest you experiment a bit in order to get familiar with the issues of diffusion and dispersion, and thus, to learn something (I am assuming this is the purpose of the exercise). You might start with the simplest one: first-order upwinding. The CFL number will first of all have an effect on the stability of your explicit scheme. Besides that, diffusion and dispersion will generally depend on the CFL number, so that your solution is indeed affected. In which way your solution is affected by CFL depends on the spatial discretization. For the linear wave equation, the first-order upwind scheme will give you the exact solution (zero diffusion) at CFL=1. That's not exactly going to be the case with the nonlinear Burger equation, especially since the wave speed is not a uniform quantity any more. Again, I would suggest you experiment with various schemes and CFL numbers to gain some experience.

But before you start programming: You will find information on this standard problem in many CFD textbooks (e.g. Hirsch).

 temp April 27, 2005 13:46

Re: burger's equation

what does 'better manner' mean ?? Anyway, you should take a look in spectral methods e.g. Galerkin, Collocation, ... depending on your particular problem.

 diaw April 27, 2005 19:22

Re: burger's equation

How would one develop the finite element equations for the Burger problem, using a 'Bubnov-Galerkin' approach?

Does anyone have links to a good book?

Thanks, diaw...

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