A numerical technique to solve a problem of the fluid motion in a straight plane rigid duct with two axisymmetric rectangular constrictions

Abstract

A second-order numerical technique is developed to study the steady laminar fluid motion in a straight two-dimensional hard-walled duct with two axisymmetric rectangular constrictions. In this technique, the governing relations are solved via deriving their integral analogs, performing a discretization of these analogs, simplifying the obtained (after making the discretization) coupled nonlinear algebraic equations, and the final solution of 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 TVD-scheme and a two-point scheme of discretization of the spatial derivatives, whereas the second one is made on the basis of the implicit three-point asymmetric backward differencing scheme. The above-noted uncoupled linear algebraic equations are solved by an appropriate iterative method, which uses the deferred correction implementation technique and the technique of conjugate gradients, as well as the solvers ICCG and Bi-CGSTAB.