Computational Implications Of The Zone Of Dependence Concept For Three Dimensional Boundary Layers On A Spinning Body
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The Role of the Zone of Dependence Concept in Three-dimensional Boundary-layer Calculations
The subject is studied for the general initial-value problem which arises in several applications; e.g., a spinning body at incidence. An exact solution which simulates the essential features of the boundary layer on such a body is used as a test case. The zone of dependence concept places a restriction on the local mesh aspect ratio that may be used. Results from four finite-difference schemes are compared against the exact solution for various wall speeds and mesh aspect ratios. Error growth occurs when the zone of dependence rule is not satisfied. The sensitivity and manner of error growth for the four schemes are different; two of them are relatively insensitive. From stability analyses it is shown that the concepts of stability and zone of dependence are not the same. Our numerical experiments partly contradict the stability analyses.