High‐order axisymmetric Navier–Stokes code: Description and evaluation of boundary conditions

Abstract

SUMMARYA description is given of a high-order solution algorithm for the solution of the unsteady axisymmetric Navier-Stokes equations. The method consists of a combination of fourth-order and second-order accurate finite difference schemes, where the approximated equations are solved by an alternating direction implicit (ADI) method. Special attention is paid to the boundary conditions. Results are compared with measurements for the cases of rotating flow within a closed cylinder (rotating driven cavity), developing axial flow in a stationary pipe and developing flow in a rotating pipe. KEY WORDS Navier-Stokes equations Boundary conditions Higher order finite difference method

A Resolution Independent Solution for Confined Axisymmetric Vortex Breakdown Flow

“…Also listed in Table 2 are the values measured from the present experiment (denoted "Exp. "), experimental data by Escudier (3) and results from previous computations (6), (20), (21) . Values from previous studies are for Re = 1854 and h = 2.0 except for Ref.…”

“…", values from present experimental visualization ("Exp.") and previous experimental (3) , numerical three-dimensional (20,21) and axisymmetric (6) …”

Early bifurcation in rotating fluid flow with free surface studied by axisymmetric numerical simulations

“…The employed code was developed at LIMSI/CNRS in France ͑see, e.g., Daube et al 21 or So "rensen and Ta Phuoc 16 ͒ and has been tested against experimental observations in different situations ͑al-ways for closed cavity͒, which we mention briefly, for reference. Steady-state stream function isolines have been compared with visualization experiments of Escudier.…”

“…Steady-state stream function isolines have been compared with visualization experiments of Escudier. 1 For example, at Reϭ1854 and ϭ2, it was found 16 that a discretization of 91ϫ71 was acceptably accurate. In addition, calculated velocity profiles have shown to be in good agreement with LDA measurements of Michelsen.…”

“…That is, the temperature is considered the same everywhere. In order to simulate the flow numerically, a previously developed 16 high-order, finite-difference discretization code to solve the axisymmetric Navier-Stokes equations was employed. The computations were carried out on a Cray C92A machine at the UNI-C, DTU.…”