Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Coupling particle sets of contours and streamline methods for solving convection problems

In this work a particle sets of contours method is coupled with a streamline technique in order to obtain accurate approximations of transport problems. A modified streamline technique is proposed and several bench tests arising in the field of porous media are then simulated to validate the new method.     

Three dimensional non-isentropic subsonic Euler flows in rectangular nozzles

In this paper, we study the existence and uniqueness of three dimensional non-isentropic subsonic Euler flows in rectangular nozzles. This work is an extension of Chen and Xie’s work on isentropic subsonic Euler flows. If, besides small normal component of vorticity, Bernoulli’s function and entropy function with small variations are given on the entrance, the existence and uniqueness of non-isentropic subsonic Euler flows are established.     

Flow past symmetric convex profiles with open wakes

A fixed domain approach and a Baiocchi type transformation in conjunction with a modified Schwarz alternating iteration scheme are used to solve problems of flow past truncated convex shaped profiles between walls in a logarithmic hodograph plane. The flows are such that an open wake or cavity is formed behind the profile. The basic numerical scheme consists of the successive over-relaxation finite difference approach over the whole domain of the problem with the use of a projection operation over only part of the domain. The numerical results that are obtained using this approach for the cases of a truncated circular arc profile and a wedge profile are compared with published results and are found to be in good agreement.     

Water seepage through soils with a sloping surface

An analytical solution is derived for a two-dimensional soil with a sloping surface under steady and water-saturated flow conditions. The soil was assumed to consist of several layers where each layer was horizontally stratified. Moreover, the lower layer was assumed to be bounded by an impermeable barrier, whereas the soil surface was assumed to be of constant slope (terraced type) or of an arbitrary configuration. Each layer was considered anisotropic in nature where the hydraulic conductivity in the vertical and horizontal directions are dissimilar. Potential and stream functions were obtained and several flow nets are presented for two-layered soils with varying degrees of anisotropy. The results shown illustrate the significance of the degree of anisotropy of each soil layer on the water flow pattern, the relative flow rate as well as the volume of water passing through individual soil layers.