Treatment of the Discontinuity in the Spin-up Problem with Impulsive Start.
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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The spin-up equation derived from the Wedemeyer model is considered. For an impulsive start, the boundary conditions prescribe a discontinuity in the velocity on the boundary. The finite difference solution of the spin-up equation is significantly in error unless the discontinuity is treated properly. A solution in the neighborhood of the discontinuity is derived by a direct coordinate expansion, after a stretching transformation is applied. This solution is used as an approximate initial condition the approximation is evaluated and tests show that the error is negligible. The details are given for laminar Ekman layers just the results are given for the turbulent case.
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