Talk by Boniface Nkonga
Posted on: 28 Aug 2026
Title: Liquid and liquid–gas flows at all speeds
Speaker: Boniface Nkonga, INRIA and Univ. Cote d’Azur
Date: 4 September 2026
Time: 11 AM IST
Venue: TIFRCAM Auditorium and Zoom
Abstract: This work addresses all-speed flows, and in particular low-Mach-number flows, for the numerical approximation of the Kapila et al. [2] multiphase flow model. This model is valid for fluid mixtures evolving in mechanical equilibrium but out of thermal equilibrium and is efficient for computing material interfaces separating miscible and non-miscible fluids. In this context, the interface is treated as a numerically diffused zone that captures all present waves (shocks, expansion waves). The same flow model can be used to solve cavitating and boiling flows [3]. Many applications involving liquid–gas interfaces and cavitating flows span a wide range of Mach numbers, from 10E−3 to supersonic (and even hypersonic) conditions with respect to the mixture sound speed. Therefore, it is important to develop numerical methods free of Mach-number restrictions. To do this, we build a preconditioned Riemann solver and embed it in the Godunov explicit scheme. This method converges to exact solutions but requires very small time steps to be efficient. We then derive an implicit version, first in one dimension and then for 2D unstructured meshes. We then address two-phase flow preconditioning in the framework of the Saurel et al. [4] algorithm. We detail the necessary modifications to the preconditioned Riemann solver. We demonstrate convergence of both single-phase and two-phase numerical solutions using single-phase and two-phase steady nozzle flow solutions. Finally, the method is illustrated by computing real cavitating flows in Venturi nozzles. The model and method reproduce vapor pocket size and instability frequencies without using any adjustable parameter.
References
- S. LeMartelot, B. Nkonga, R. Saurel, Liquid and liquid–gas flows at all speeds, J. Comput. Phys. (2013)
- A. Kapila, R. Menikoff, J. Bdzil, S. Son, D. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations, Phys. Fluids (2001)
- R. Saurel, F. Petitpas, R. Abgrall, Modeling phase transition in metastable liquids: Application to cavitating and flashing flows, J. Fluid Mech. (2008)
- R. Saurel, F. Petitpas, R.A. Berry, Simple and efficient methods for relaxation for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, J. Comput. Phys. (2009)