EDF Special Workshop (2015)

Abstract:

This paper is concerned with the design of a very simple and efficient Godunov-type method for the so-called two-fluid two-pressure compress- ible model for two-phase flows. It is a contribution to the proceedings of a workshop organized by the EDF R&D French utility company and devoted to the verification of numerical schemes for two-phase flows. The present study focuses on the convective part of the two-fluid two-pressure model and is a short form of a longer paper [1] where the numerical strategy also takes into account additional terms associated with sources, pressure relaxation and drag forces. Numerical simulations and comparisons with other strategies are proposed in the last section.

Keywords :

Paper presented by: Jean-Marc Hérard

Abstract:

The present paper is devoted to a comparison of numerical methods for the convective part of a two-phase flow model. Four explicit schemes are tested using Riemann problems or regular solutions. The main criteria for comparing the methods are: the accuracy for a fixed size of mesh, the convergence, the robustness and the CPU time cost necessary to reach a fixed error. The conclusions of this study are the following. The clas- sical Rusanov scheme is not competitive, as expected. The relaxation scheme seems to be more efficient than the VFROE-ncv method, espe- cially regarding robustness. The staggered scheme, recently investigated for this model, is sometimes less accurate for a fixed size of mesh than the VFROE-ncv and relaxation schemes but is the most acurate for a fixed run time.

Keywords : Baer-Nunziato model, benchmark study, explicit schemes.

Paper presented by: Jean-Marc Hérard

Abstract

We present some verification test cases applied to a code developed at EDF R&D for the simulation of two-phase flows with mass transfer. The aim of this code is to allow the simulation of a wide range of industrial situations by considering all the thermodynamic disequilibria between the phases - pressure, temperature and chemical potential- and by assuming the kinematic equilibrium - a single velocity for both phases. The under- lying homogeneous model [1, 13] is based on the Euler system of equations supplemented by a complex pressure law describing the behaviour of the mixture of the two phases. Different first-order schemes are compared on the basis of two analytical solutions: a classical Riemann problem and a steady-state heated pipe test.

Key words : Homogeneous model, two-phase flows, verification.

Paper presented by: Jean-Marc Hérard