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1D Euler Equation by Finite Difference Scheme

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Old   August 19, 2014, 01:53
Default 1D Euler Equation by Finite Difference Scheme
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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 U_t by using a fifth order WENO scheme. Then I can compute U(x,t+1). However, to compute U(x,t+2) I need to know F(U(x,t+1)). 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.
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Old   August 19, 2014, 04:18
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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
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Old   August 19, 2014, 18:54
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Quote:
Originally Posted by FMDenaro View Post
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 U.
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Old   August 20, 2014, 03:27
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Quote:
Originally Posted by Catkun View Post
Hi FMDenaro,

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

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
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