Some remarks on the concept of stream tubes for numerical simulations of complex fluid flows - applications

This paper presents new theoretical elements for numerical simulation of tw o- and three-dimensional flows, based on the concept of streamlines and dom ain decomposition. The so-called "stream-tube method" considered previously particularly for flows involving open streamlines, is extended to general streamline configurations. It is shown how local transformation functions m ay be defined in order to simulate flows of complex fluids, notably those r equiring evaluation of particle time history. The specific features (for ex ample: mass conservation, simplicity in handling time-dependent constitutiv e equations) of the stream-tube methods previously investigated numerically are still preserved in the new formulation. An example of calculations is given in the case of the two-dimensional flow of a Newtonian fluid between two eccentric cylinders where results are found to be consistent with liter ature data.