Decomposition Singularity Tolerance - CAESAR II - Help

CAESAR II Users Guide

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CAESAR II
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CAESAR II Version
13

Defines the value used by the software to check the ratio of off-diagonal to on-diagonal coefficients in the row. The default value is 1.0 e+10. If this ratio is greater than the decomposition singularity tolerance, then a numerical error may occur. This problem does not have to be associated with a system singularity. This condition can exist when very small, and/or long pipes are connected to very short, and/or large pipes. These solutions have several general characteristics:

  • When computer precision errors of this type occur, they are very local in nature. They typically affect only a single element or very small part of the model and are readily noticeable upon inspection.

  • The 1E10 limit can be increased to 1E11 or 1E12 and still provide a reasonable check on solution accuracy. Any solution computed after increasing the limit should always be checked closely for reasonableness. At 1E11 or 1E12, the number of significant figures in the local solution is reduced to two or three.

  • Although the 1E10 limit can be increased to 1E20 or 1E30 to get the job to run, it is important to remember that the possibility for a locally errant solution exists when stiffness ratios get this high. Solutions should be carefully checked.