{lambda} elements for singular problems in CFD: Newtonian fluids
- Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering
This paper presents two dimensional {lambda} element formulation for singular problems in steady state, incompressible, Newtonian fluid flow. Treatment of problems with known and unknown strength of singularities is presented. The 2D {lambda} element approximation functions and the corresponding nodal degrees of freedom are derived by taking tensor product of the one dimensional {lambda} approximation functions and the corresponding nodal variable operators in the r coordinate system with the one dimensional p-version approximation functions and the corresponding nodal variable operators in the {Theta} coordinate system. The origin of the local (r, {theta}) coordinate systems 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 with p-version elements in {theta} direction. The {lambda} elements 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 in the singular zone, 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) are recast into a system of first order differential equations using stresses as auxiliary variables. Least squares approach (or Least Squares Finite Element Formulation: LSFEF) is used to construct the integral form (error functional, I) using these equations. The conditions resulting from least squares minimization are satisfied using Newton`s method with line search.
- OSTI ID:
- 376032
- Report Number(s):
- CONF-960154--; ISBN 0-9648731-8-4
- Country of Publication:
- United States
- Language:
- English
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