\(p\)-version least squares finite element formulation for axisymmetric incompressible non-Newtonian fluid flow. (English) Zbl 0846.76045
The paper presents a \(p\)-version least squares finite element formulation for axisymmetric incompressible non-Newtonian fluid flow. The dimensionless form of the equations describing the fluid motion in cast into a set of first order coupled partial differential equations involving non-Newtonian stresses as auxiliary variables. The pressure, velocities (primary variables) and the stresses (auxiliary variables) are interpolated using equal order, \(C^0\) continuous, \(p\)-version hierarchical approximation functions. The least squares functional (or error functional) is constructed using the system of coupled first order nonlinear partial differential equations (integrated sum of squares of the errors resulting from the individual equations for the entire discretization) without linearization, approximations or assumptions. The paper presents an implementation of the power law model for non-Newtonian viscosity.
Keywords:
non-Newtonian stresses; \(p\)-version hierarchical approximation functions; error functional; power law modelReferences:
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