This paper presents formulations, computations and investigations of the solutions of class C00 and C11 for two dimensional viscoelastic fluid flows in u, v, p, , with Oldroyd-B constitutive model using p-version Least Squares Finite Element Formulation (LSFEF). The main thrust of the research work presented in the paper is to employ ‘right class of interpolations’ and the best computational strategy to establish: i) when does Oldroyd-B model begins to fail in simulating the correct physics of flow ii) when and why does the proposed computational process fail iii) is there a correlation between i) and ii). Fully developed flow between parallel plates and the stick-slip problems are used as model problems.
The investigations presented in this paper reveal the following. a) The manner in which the stresses are non-dimensionalized significantly influences the performance of the iterative procedure of solving nonlinear algebraic equations. b) Solutions of the class C00 are always the wrong class of solutions of GDEs in variables u, v, p, and and thus spurious. c) C11 class of solutions are the right class of solutions of the GDEs in variables u, v, p, and . d) In the flow domains, containing sharp gradients of the dependent variables, conservation of mass is difficult to achieve at lower p-levels (worse for coarse meshes). e) An augmented form of GDEs are proposed that always ensure conservation of mass at all p-levels regardless of the mesh and the nature of the solution gradients. f) We demonstrate that Oldroyd-B model describes correct physics of dilute polymer solutions of constant viscosity only for a limited range of Deborah numbers. Beyond this range, the computed solutions are not in agreement with the flow physics (thus spurious) even though the proposed computational process works exceptionally well. g) Numerical studies with graded meshes and high p-levels presented in this paper are aimed towards establishing and demonstrating detail behavior of local as well as global nature of the computed 10 solutions, h) Various norms are proposed and tested to judge local and global dominance of elasticity or viscous behavior 1) New definitions are proposed for elongational (extensional) viscosity. The proposed definitions are more in conformity and agreement with the flow physics compared to currently used definitions j) A significant aspect and strength of our work is that we utilize straightforward p-version LSFEF with C00 and C11 type interpolations without linearizing GDEs and that SUPG, SUPG/DC, SUPG/DC/LS operators are neither needed nor used.