A Roe scheme for a compressible six-equation two-fluid model
Article first published online: 13 NOV 2012
Copyright © 2012 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Volume 72, Issue 4, pages 478–504, 10 June 2013
How to Cite
Morin, A., Flåtten, T. and Munkejord, S. T. (2013), A Roe scheme for a compressible six-equation two-fluid model. Int. J. Numer. Meth. Fluids, 72: 478–504. doi: 10.1002/fld.3752
- Issue published online: 3 MAY 2013
- Article first published online: 13 NOV 2012
- Manuscript Accepted: 21 OCT 2012
- Manuscript Revised: 11 OCT 2012
- Manuscript Received: 25 JUN 2012
- two-fluid model;
- Roe scheme;
We derive a partially analytical Roe scheme with wave limiters for the compressible six-equation two-fluid model. Specifically, we derive the Roe averages for the relevant variables. First, the fluxes are split into convective and pressure parts. Then, independent Roe conditions are stated for these two parts. These conditions are successively reduced while defining acceptable Roe averages. For the convective part, all the averages are analytical. For the pressure part, most of the averages are analytical, whereas the remaining averages are dependent on the thermodynamic equation of state. This gives a large flexibility to the scheme with respect to the choice of equation of state. Furthermore, this model contains nonconservative terms. They are a challenge to handle right, and it is not the object of this paper to discuss this issue. However, the Roe averages presented in this paper are fully independent from how those terms are handled, which makes this framework compatible with any treatment of nonconservative terms. Finally, we point out that the eigenspace of this model may collapse, making the Roe scheme inapplicable. This is called resonance. We propose a fix to handle this particular case. Numerical tests show that the scheme performs well. Copyright © 2012 John Wiley & Sons, Ltd.