# A Darcy law for the drift velocity in a two-phase flow model

## Abstract

This work deals with the design and numerical approximation of an Eulerian mixture model for the simulation of two-phase dispersed flows. In contrast to the more classical two-fluid or Drift-flux models, the influence of the velocity disequilibrium is taken into account through dissipative second-order terms characterized by a Darcy law for the relative velocity. As a result, the convective part of the model is always unconditionally hyperbolic. We show that this model corresponds to the first-order equilibrium approximation of classical two-fluid models. A finite volume approximation of this system taking advantage of the hyperbolic nature of the convective part of the model and of the particular structural form of the dissipative part is proposed. Numerical applications are presented to assess the capabilities of the model.

- Authors:

- INRIA, B.P. 93, 06902 Sophia Antipolis Cedex (France). E-mail: Herve.Guillard@sophia.inria.fr
- Institut de Radioprotection et de Surete Nucleaire (IRSN), BP3-13115 St. Paul-lez-Durance Cedex (France)

- Publication Date:

- OSTI Identifier:
- 20991582

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 224; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2007.02.025; PII: S0021-9991(07)00076-9; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPUTERIZED SIMULATION; DARCY LAW; FLUIDS; MATHEMATICAL MODELS; MIXTURES; TWO-PHASE FLOW; VELOCITY

### Citation Formats

```
Guillard, H., and Duval, F.
```*A Darcy law for the drift velocity in a two-phase flow model*. United States: N. p., 2007.
Web. doi:10.1016/j.jcp.2007.02.025.

```
Guillard, H., & Duval, F.
```*A Darcy law for the drift velocity in a two-phase flow model*. United States. doi:10.1016/j.jcp.2007.02.025.

```
Guillard, H., and Duval, F. Sun .
"A Darcy law for the drift velocity in a two-phase flow model". United States.
doi:10.1016/j.jcp.2007.02.025.
```

```
@article{osti_20991582,
```

title = {A Darcy law for the drift velocity in a two-phase flow model},

author = {Guillard, H. and Duval, F.},

abstractNote = {This work deals with the design and numerical approximation of an Eulerian mixture model for the simulation of two-phase dispersed flows. In contrast to the more classical two-fluid or Drift-flux models, the influence of the velocity disequilibrium is taken into account through dissipative second-order terms characterized by a Darcy law for the relative velocity. As a result, the convective part of the model is always unconditionally hyperbolic. We show that this model corresponds to the first-order equilibrium approximation of classical two-fluid models. A finite volume approximation of this system taking advantage of the hyperbolic nature of the convective part of the model and of the particular structural form of the dissipative part is proposed. Numerical applications are presented to assess the capabilities of the model.},

doi = {10.1016/j.jcp.2007.02.025},

journal = {Journal of Computational Physics},

number = 1,

volume = 224,

place = {United States},

year = {Sun May 20 00:00:00 EDT 2007},

month = {Sun May 20 00:00:00 EDT 2007}

}