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Code Manual for CONTAIN 2.0 - Federation of American Scientists

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where c is the user-specifiable implicit integration weighting factor “crank”, and Tmdenotes the value<br />

<strong>of</strong> T at timestep n. The default value <strong>of</strong> c = 1 represents a fully implicit treatment. For certain<br />

problems, a value <strong>of</strong> c less than 1 may yield more accurate results. A value <strong>of</strong> 0.5 yields what is<br />

called Crank-Nicholson integration. Fully explicit integration is obtained when c = O. If values less<br />

than 0.5 are used, care should be taken in selecting the cell timestep to ensure that the Courant<br />

stabdity criterion is not violated (the diffhsion length in Equation (10-106) during the cell timestep<br />

must not exceed the node thickness). Extremely large timesteps should also be avoided when using<br />

values between 0.5 and 1.0; such values will always give stable but possibly oscillato~ temperatures.<br />

Note that c = 1 will always give stable, non-oscillatory internal temperatures. However, <strong>for</strong> most<br />

problems, timesteps that give oscillatory behavior or negative temperatures when c

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