On the Construction of High-Order and Exact Pressure Equilibrium Schemes for Arbitrary Equations of State

Speaker: Nguyen Ly, Analytical Mechanics Associates/NASA Ames Research Center
October 15, 2026

Presentation

Abstract

Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces.

In this presentation, we discuss the construction of a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. As background, we also describe the pressure-equilibrium problem in computational fluid dynamics, past quasi-conservative approaches, and the more recent developments in conservative solutions to maintaining the equilibrium.

Biography

Nguyen Ly is an Aerospace Engineer at Analytical Mechanics Associates (AMA). He is currently working as a contractor in the Computational Aerosciences Branch (Code TNA) at NASA's Ames Research Center. His current research interests are GPU-accelerated numerical schemes for multiphase and reacting flows. He obtained a Ph.D. in Mechanical Engineering at Stanford University, working under the guidance of Professor Matthias Ihme. He was also a recipient of the NSTGRO fellowship. At Stanford, Nguyen’s research interest was the development of advanced numerical models for transcritical multiphase fluid flows.

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