A Numerical Method for Highly Accelerated Laminar Boundary-Layer Flows

Ackerberg, R. C.; Phillips, J. H.

doi:10.1137/0710016

Cited by 5 publications

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An effective numerical integration method for typical stiff systems

Aiken

Lapidus

1974

AIChE Journal

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There is an equivalence between stiff and singularly perturbed systems of ordinary differential equations. This feature is exploited in this paper by numerically employing recent singular perturbation methods to attack troublesome boundary layer stage of the solution in which some variables have very short response times. The numerical method affords a means of essentially determining the thickness of this boundary layer. The algorithm is capable of high stability and accuracy for the commonly occurring stiff system, whether or not it is in singularly perturbed form. Application to a singularly perturbed reaction system and a highly stiff reactor system not in singularly perturbed form demonstrate the effectiveness and utility of this approach. SCOPEMany commonly occurring physical and chemical dynamic systems have widely separated time constants. CONCLUSIONS AND SIGNIFICANCERecognition of the equivalence of stiff and singularly Perturbed equations makes available new tools for the solution of both forms of equations. Jn this study, use is mad9 of sineular perturbation methods to develop a numerical technique capable of high stability and accuracy. A unique feature preTent is the ability to monitor the contribution of the stiff component to assess when Page 368 March, 1974 AlChE Journal (Vol. 20, No. 2)the solution is out of the boundary layer. Thereafter the bulk of the transient may be obtained without the accuracy problems associated with this initial section. me numerical approach is applicable to numerous problems in chemical engineering and other disciplines where currently inadequate solution procedures are employed.

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