{lambda} elements for singular problems in CFD: Non-Newtonian fluids
- Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering
This paper presents two dimensional {lambda} element formulation for steady state, isothermal, generalized Newtonian fluid flow. The paper presents specific details and numerical studies for power law fluids. The {lambda} element formulations for problems with known strength of singularity as well as for those with unknown strength of singularity are treated in the paper. The 2D element approximation functions and the corresponding nodal variables are derived using tensor product of the one dimensional {lambda} element approximation functions and the corresponding nodal variable operators in the r coordinate system with the one dimensional p-version approximation functions and nodal variables operators in the {Theta} coordinate system. The origin of the local (r, {theta}) coordinate system is located at the singularity (r=0). The {lambda} elements presented here are of C{sup 0} type and provide interelement C{sup 0} continuity in the {theta} direction with the p-version elements in ({xi}, {eta}) coordinate system. The {lambda} elements presented here do not require a precise knowledge of the extent of the singular zone, i.e., their use can 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. The equations of fluid motion (Navier-Stokes equations) with power law viscosity are recast into a system of first order differential equations using stresses as auxiliary variables. The least squares approach is used to construct the integral form (error functional I) using these equations. The condition resulting from least squares minimization are satisfied using Newton`s method with line search.
- OSTI ID:
- 376033
- Report Number(s):
- CONF-960154-; ISBN 0-9648731-8-4; TRN: IM9642%%121
- 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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