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Old   July 8, 2007, 06:51
Default MacCormick
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In the MacCormick upwind scheme.

U^(n+1) = U^n - delta_t/delta_x*(f_(i+1) - f_i)

is it f_(i+1) - f_i = A_(i+0.5)*(U_(i+1) - U_i) where A = df/dU

or f = {rho*u, rho*u^2 + P...}^T

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Old   July 9, 2007, 01:22
Default Re: MacCormick
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it appears that the second order upwind schemes doesn't work for the shock tube problem.


U^(n+1) = U^n - delta_t/delta_x*(f_(i+1)^n - f_i^n)


U^(n+2) = 0.5*(U^n + U^(n+1)) - delta_t/delta_x*(f_(i+1)^(n+1) - f_i^(n+1))

However the flux-splitting version does work. Is there anything i am doing wrong?


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