Flow modelling in a straight rigid-walled duct with two rectangular axisymmetric narrowings. Part 2. An alternative approach

Abstract

A second-order technique is suggested to study fluid motion in a two-dimensional hard-walled duct with two abrupt constrictions. In this technique, the governing relationships are integrated via their rewriting in a non-dimensional form, deriving their integral analogues, performing a discretization of the derived integral relationships, simplifying the obtained (after making the discretization) coupled non-linear algebraic equations, and final solving the resulting (after making the simplification) uncoupled linear ones. The discretization consists of the spatial and temporal parts. The first of them is performed with the use of the total variation diminishing scheme and the two-point scheme of discretization of the spatial derivatives, whereas the second one is made on the basis of the implicit three-point non-symmetric backward differencing scheme. The noted uncoupled linear algebraic equations are solved by an appropriate iterative method.