{lambda} elements for one-dimensional singular problems with known strength of singularity
- Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering
This paper presents a new and general procedure for designing special elements called {lambda} elements for one dimensional singular problems where the strength of the singularity is know. The {lambda} elements presented here are of type C{sup 0}. These elements also provide inter-element C{sup 0} continuity with p-version elements. The {lambda} elements do not require a precise knowledge of the extent of singular zone, i.e., their use may be extended beyond the singular zone. When {lambda} elements are used at the singularity, a singular problem behaves like a smooth problem thereby eliminating the need for h, p-adaptive processes all together. One dimensional steady state radial flow of an upper convected Maxwell fluid is considered as a sample problem. Least squares approach (or least squares finite element formulation: LSFEF) is used to construct the integral form (error functional I) from the differential equations. Numerical results presented for radially inward flow with inner radius r{sub i} = 0.1, 0.01, 0.001, 0.0001, 0.00001, and Deborah number of 2 (De = 2) demonstrate the accuracy, faster convergence of the iterative solution procedure, faster convergence rate of the error functional and mesh independent characteristics of the {lambda} elements regardless of the severity of the singularity.
- OSTI ID:
- 376021
- Report Number(s):
- CONF-960154-; ISBN 0-9648731-8-4; TRN: IM9642%%109
- Resource Relation:
- Conference: Energy Week `96: American Society of Mechanical Engineers and American Petroleum Institute energy week conference and exhibition, Houston, TX (United States), 21 Jan - 2 Feb 1996; Other Information: PBD: 1996; Related Information: Is Part Of Energy week `96: Conference papers. Book 5: Composite materials design and analysis; Surana, K.S. [ed.] [Univ. of Kansas, Lawrence, KS (United States)]; Kozik, T.J. [ed.] [Texas A and M Univ., College Station, TX (United States)]; PB: 498 p.
- Country of Publication:
- United States
- Language:
- English
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