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Old   May 16, 2008, 22:55
Default Yees upwind/symmetric scheme
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I want to use Yees upwind/symmetric TVD scheme to solve the Navier-Stokes equations in cylindrical r-z coordinates. In the paper (J.Comput.Phys. 68:151-179)its given in x-y form. How should I modify for the source flux that appears as a result of splitting the divergence convective term in the r direction.

i.e. dQ/dt = dF/dr + dG/dz + (1/r)H

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Old   May 17, 2008, 20:58
Default Re: Yees upwind/symmetric scheme
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I applied to a 2-D cylindrical C.V. and got the following expression

dQ/dt_(ij) =

[E_(i, j+0.5) * r_(i,j+0.5)/r_ij - E_(i, j-0.5) * r_(i, j-0.5)/r_ij]/delta_r

+ [F_(i+0.5, j) - F_(i-0.5, j)]/delta_z

Q = transpose[rho, rho*u, rho*v, E] E = transpose[rho*v, rho*u*v, rho*v*v + P, (E + P)v] F = transpose[rho*u, rho*u*u + p, rho*u*v, (E + P)u]

i,j are in z and r axis with velocity components u, v rspectively.

How to deal with r_(i, j-0.5)/r_ij at r_ij(0, 0)??


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