Performance and limitations of p-version finite element method for problems containing singularities
- Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering
In this paper, the authors investigate the performance of p-version Least Squares Finite Element Formulation (LSFEF) for a hyperbolic system of equations describing a one-dimensional radial flow of an upper-convected Maxwell fluid. This problem has r{sup 2} singularity in stress and r{sup {minus}1} singularity in velocity at r = 0. By carefully controlling the inner radius r{sub j}, Deborah number DE and Reynolds number Re, this problem can be used to simulate the following four classes of problems: (a) smooth linear problems, (b) smooth non-linear problems, (c) singular linear problems and (d) singular non-linear problems. They demonstrate that in cases (a) and (b) the p-version method, in particular p-version LSFEF is meritorious. However, for cases (c) and (d) p-version LSFEF, even with extreme mesh refinement and very high p-levels, either produces wrong solutions, or results in the failure of the iterative solution procedure. Even though in the numerical studies they have considered p-version LSFEF for the radial flow of the upper-convected Maxwell fluid, the findings and conclusions are equally valid for other smooth and singular problems as well, regardless of the formulation strategy chosen and element approximation functions employed.
- OSTI ID:
- 376020
- Report Number(s):
- CONF-960154-; ISBN 0-9648731-8-4; TRN: IM9642%%108
- 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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Related Subjects
COMPUTERS
INFORMATION SCIENCE
MANAGEMENT
LAW
MISCELLANEOUS
66 PHYSICS
42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES
FINITE ELEMENT METHOD
PERFORMANCE
FLUID MECHANICS
SINGULARITY
GALERKIN-PETROV METHOD
LEAST SQUARE FIT
DIFFERENTIAL EQUATIONS
ACCURACY
ITERATIVE METHODS
THEORETICAL DATA