# How to solve exactly Riemann problems?

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 September 17, 2004, 21:20 How to solve exactly Riemann problems? #1 Matthew Xu Guest   Posts: n/a Hello, I want to know how to solve exactly Riemann problems of nonstrictly hyperbolic conservation laws, such as the modified Burgers' equation, u_t+(a(x)u^2)_x=0. Can you give me some advices?Many thanks.

 September 17, 2004, 23:06 Re: How to solve exactly Riemann problems? #2 Matthew Xu Guest   Posts: n/a I know the iterate method can solve this problem. Are there any references?

 September 20, 2004, 04:09 Re: How to solve exactly Riemann problems? #3 Tom Guest   Posts: n/a You need to solve the characteristic equations dt/ds = 1, dx/ds = 2au, du/ds = - a'u^2 with, at s=0, t=0, x=X, u = f(X).

 September 20, 2004, 13:28 Re: How to solve exactly Riemann problems? #4 Jarmo Monttinen Guest   Posts: n/a See the following: Toro, E. F. 1997. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer New York. or Godlewski, E. and P.-A. Raviart. 1996. Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer New York. These will tell you everything you need to know. And then some more. -- Jarmo

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