Multiphase Science and Technology, Vol. 16, Nos. 1-3, pp. 97-100, 2004 TEST-CASE NO 14: POISEUILLE TWO-PHASE FLOW (PA) S. Vincent a1 , J.P. Caltagirone a , O. Lebaigue b a TREFLE - UMR CNRS 8508, ENSCPB Universit´ e Bordeaux 1, 33607 Pessac cedex, France b DER/SSTH/LMDL, CEA/Grenoble, 38054 Grenoble cedex 9, France Abstract. The two-layer laminar Poiseuille flow is suggested as a case test. Two superimposed layers of viscous fluids separated by a flat interface are flowing in a horizontal channels. The analytical solution is provided. 1. PRACTICAL SIGNIFICANCE AND INTEREST OF THE TEST-CASE The two-phase Poiseuille flow is a simple interfacial flow that permits to estimate accu- rately the time and space convergence order of the numerical resolution of the Navier- Stokes equations in their Eulerian two-phase flow formulation. Moreover, this test case allows characterizing the sensitivity of the numerical solution with respect to the aver- ages implemented on the density and the viscosity at the interface in the discretization of the motion equations. To finish with, the Poiseuille flow allows calculating analytically the viscous stress tensor to verify if the continuity of its tangential component is verified numerically at the interface. The present test case is interesting because it possesses a theoretical solution. However, no interface deformation is induced in this problem. Therefore, it represents a necessary test, but certainly not a sufficient reference. 2. DEFINITIONS AND PHYSICAL MODEL DESCRIPTION The horizontal stratified flow of a two fluid between two parallel walls is considered (see figure 1). The gravity and the surface tension forces are neglected. For long times, a steady solution is obtained for the two-phase Poiseuille flow problem which can be described by an analytical solution. If L is the length of the horizontal walls, d is the distance between the bottom horizontal boundary and the interface and H the distance between the two horizontal boundaries, the velocity field, u =(u x , u y ), and the pressure, p, can be calculated by assuming the velocity to be parallel to the x axis and by considering the continuity of the velocity and the viscous stress tensor at the interface. In this way, the 1 Phone: +33 (0)5 40 00 27 07, Fax: +33 (0)5 40 00 66 68, e-mail: vincent@enscpb.fr