{lambda} elements for singular problems in CFD: Viscoelastic fluids
- Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering
This paper presents two dimensional {lambda} element formulation for viscoelastic fluid flow containing point singularities in the flow field. The flow of viscoelastic fluid even without singularities are a difficult class of problems for increasing Deborah number or Weissenburg number due to increased dominance of convective terms and thus increased hyperbolicity. In the present work the equations of fluid motion and the constitutive laws are recast in the form of a first order system of coupled equations with the use of auxiliary variables. The velocity, pressure and stresses are interpolated using equal order C{sup 0} {lambda} element approximations. The Least Squares Finite Element Method (LSFEM) is used to construct the integral form (error functional I) corresponding to these equations. The error functional is constructed by taking the integrated sum of the squares of the errors or residuals (over the whole discretization) resulting when the element approximation is substituted into these equations. The conditions resulting from the minimization of the error functional are satisfied by using Newton`s method with line search. LSFEM has much superior performance when dealing with non-linear and convection dominated problems.
- OSTI ID:
- 376034
- Report Number(s):
- CONF-960154-; ISBN 0-9648731-8-4; TRN: IM9642%%122
- 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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