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A functionally-analytic method for modeling axial-symmetric flows of ideal fluid

Plaksa Sergiy A.

Demonstratio Mathematica

2019

Vol. 52, nr 1

213--224

We consider axial-symmetric stationary flows of the ideal incompressible fluid as an important case of potential solenoid fields. We use an integral expression of the Stokes flow function via the corresponding complex analytic function for solving a boundary value problem with respect to a steady streamline of the ideal incompressible fluid along an axial-symmetric body. We describe the solvability of the problem in terms of the singularities of the mentioned complex analytic function. The obtained results are illustrated by concrete examples of modelling of steady axial-symmetric flows.

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

Clermont J., Normandin M., Radu D.

Control and Cybernetics

2000

Vol. 29, no 2

535-553

This paper presents new theoretical elements for numerical simulation of two- and three-dimensional flows, based on the concept of streamlines and domain decomposition. The so-called "stream-tube method", considered previously particularly for flows inolving open streamlines, is extended to general streamline comfigurations. It is shown how local transformation functions may be defined in order to simulate flows of complex fluids, notably those requiring evaluation of particle time history. The specific features (for example : mass conservation, simplicity in handling time-dependent constitutive 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 literature data.