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Old   July 13, 2007, 21:09
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What conditions should I use for the end points of following discretisations.

Derivative operator:

(3F_i - 4F_(i-1) + F_(i-2))/(2*delta_x) (-3F_i + 4F_(i+1) - F_(i+2))/(2*delta_x)

forward difference operator u_i - 2u_(i-1) + u_(i-2)

backward difference operator u_(i+2) -2u_(i+1) + u_i

Roe's averaging:

W = 0.5*(sqrt(rho_i) + sqrt(rho_i))

x_i = 0.5*(sqrt(rho_i)*x_i + sqrt(rho_(i + 1)*x_(i + 1))/W_i;
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