An implicit rheological model for numerical simulation of generalized Newtonian fluids

Fitting an explicit curve over some discrete data extracted from a rheometer is the usual way of writing a rheological model for generalized Newtonian fluids. These explicit models may not match totally with the extracted data and may ignore some features of the rheological behavior of the fluids. In this paper, a cubicspline curve fitting is used to fit a smooth curve from discrete rheological data. Spline interpolation avoids the problem of Runge's phenomenon, which occurs in interpolating using high degree polynomials. The formulation for applying presented rheological model is described in the context of least squares meshfree technique. One problem is solved to show validity of the scheme: a fluid with rather complex rheology model is considered and solved by both conventional explicit and proposed implicit models to show the advantages of the presented method.