# Physical Relaxation Terms for Compressible Two-Phase Systems

@article{Bresch2020PhysicalRT, title={Physical Relaxation Terms for Compressible Two-Phase Systems}, author={Didier Bresch and Cosmin Burtea and Fr{\'e}d{\'e}ric Lagouti{\`e}re}, journal={arXiv: Analysis of PDEs}, year={2020} }

In this note, we propose the first mathematical derivation of a macroscopic Baer-Nunziato type system for compressible two-phase flows allowing two pressure state laws depending on the different phases. By doing so, we extend the results obtained by the first author and M. Hillairet (Annales ENS 2019) to cover this important physical situation. A relaxation term in the mass fraction equation is obtained without closure assumptions contrarily to theoretical-physics literature dedicated to…

## 3 Citations

### Analysis of compressible bubbly flows. Part II: Derivation of a macroscopic model

- Computer Science, Mathematics
- 2022

It is proved that solutions to the microscopic model exist on a timespan independent of the number of bubbles, provided physical parameters scale according to thenumber of bubbles.

### Relaxation limit for a damped one-velocity Baer-Nunziato model to a Kappila model

- Mathematics
- 2021

In this paper we study a singular limit problem in the context of partially dissipative first order quasilinear systems. This problem arises in multiphase fluid mechanics. More precisely, taking into…

### On the overdamping phenomenon for compressible multi-fluid systems with rough coefficients

- Mathematics
- 2022

In this paper we investigate two types of relaxation processes quantitatively in the context of small data global-in-time solutions for compressible one-velocity multi-ﬂuid models. First, we justify…

## References

SHOWING 1-10 OF 28 REFERENCES

### A compressible multifluid system with new physical relaxation terms

- Mathematics
- 2016

In this paper, we rigorously derive a new compressible multifluid system from compressible Navier-Stokes equations with density-dependent viscosity in the one-dimensional in space setting. More…

### Note on the derivation of multi-component flow systems

- Mathematics
- 2015

In this note, we justify rigorously the formal method proposed in (M. Hillairet, J. Math. Fluid Mech. 2007) to derive viscous and compressible multi-component ow equations. We present here a simpler…

### A Multi-Fluid Compressible System as the Limit of Weak Solutions of the Isentropic Compressible Navier–Stokes Equations

- Mathematics
- 2011

This paper mainly concerns the mathematical justification of a viscous compressible multi-fluid model linked to the Baer-Nunziato model used by engineers, see for instance Ishii (Thermo-fluid dynamic…

### A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows

- Computer Science
- 1999

A new model and a solution method for two-phase compressible flows is proposed that provides reliable results, is able to compute strong shock waves, and deals with complex equations of state.

### Propagation of oscillations in the solutions of 1-D compressible fluid equations

- Mathematics
- 1992

We study the propagation of initial osillations in the solutions of one-dimensional inviscid gas dynamic equations and the compressible Navier-Stokes equations. Using Multiple scale analysis, we…

### Multi-fluid Models Including Compressible Fluids

- Mathematics
- 2017

In this chapter, we focus on multi-fluid models including compressible fluids in the isentropic or isothermal case. The main objective of these notes is to present at the level of beginners an…

### Theory of Multicomponent Fluids

- Engineering
- 1998

Preliminaries.- Physical Reality, Corpuscular Models, Continuum Models.- Classical Continuum Theory.- Viscous and Inviscid Fluids and Elastic Solids.- Kinetic Theory.- Classical Theory of Solutions.-…