# 1D Euler Equation by Finite Difference Scheme

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 August 19, 2014, 01:53 1D Euler Equation by Finite Difference Scheme #1 New Member   Cat Join Date: Aug 2014 Posts: 6 Rep Power: 11 Hi guys, I have been writing some code to numerically solve 1D Euler's equation by using the WENO scheme. Supposed we are given the initial condition, I can compute the by using a fifth order WENO scheme. Then I can compute . However, to compute I need to know . I don't know how to obtain those value. Could anyone tell me how to obtain them or give me a good reference? Thanks a lot.

 August 19, 2014, 04:18 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,806 Rep Power: 72 from the intial condition U(x,t0) you reconstruct numerically the flux F[U(x,t0)], right? Hence, the same you have to do when U(x,t0+dt) is available Catkun likes this.

August 19, 2014, 18:54
#3
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Cat
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Quote:
 Originally Posted by FMDenaro from the intial condition U(x,t0) you reconstruct numerically the flux F[U(x,t0)], right? Hence, the same you have to do when U(x,t0+dt) is available
Hi FMDenaro,

Sorry for not making the problem clear. My actual question is how to reconstruct the flux given the .

August 20, 2014, 03:27
#4
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Filippo Maria Denaro
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Quote:
 Originally Posted by Catkun Hi FMDenaro, Sorry for not making the problem clear. My actual question is how to reconstruct the flux given the .

There is no unique answer, it depends on the scheme you wanto to use.
As reference, have a look to the book of Leveque on hyperbolic systems