A novel hybrid approach for accurate simulation of compressible multi-component flows across all-Mach number

TL;DR

The paper introduces a novel all-Mach-number solver for compressible multi-component flows by merging a density-based Godunov-type flux (AUSM SLAU2) with a projection-like pressure update via a pressure Helmholtz equation. It relies on a four-equation homogeneous model with NASG EOS and employs a homogeneous ROUND reconstruction to sharply resolve interfaces without oscillations. The method integrates surface tension and phase-transition physics, enabling accurate simulation of both high-speed shocks and incompressible multiphase dynamics, including boiling and cavitation phenomena. Validations across rising bubbles, shock–bubble interactions, shock tubes with phase changes, nucleate boiling, and Richtmyer–Meshkov instability demonstrate robustness, accuracy, and versatility across Mach regimes. The framework, implemented in OpenFOAM, holds promise for complex engineering applications such as lithium boiling tanks, where coupled pressure-density and pressure-velocity effects are simultaneously important.

Abstract

Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics. Thus, this work presents a novel approach that combines the Godunov-type scheme for high-speed flows with the projection solution procedure for incompressible flows to address this challenge. The proposed hybrid approach begins by splitting the inviscid flux into the advection part and the pressure part. The solution variables are first updated to their intermediate states by solving the advection part with the all-speed AUSM (Advection Upwind Splitting Method) Riemann solver. The advection flux in AUSM is modified to eliminate the pressure flux term that deteriorates the accuracy at the low Mach region. To prevent the advection flux from causing spurious velocities when surface tension is present, the pressure-velocity coupling term is modified to ensure it vanishes at material interfaces. Then, we derive the pressure Helmholtz equation to solve the final pressure and update the intermediate states to the solution variables at the next time step. The proposed hybrid approach retains the upwind property of the AUSM scheme for high Mach numbers while recovering central schemes and the standard projection solution for low Mach limits. To accurately resolve the complex flow structures including shock waves and material interfaces without numerical oscillations, a newly proposed homogenous ROUND (Reconstruction Operator on Unified Normalised-variable Diagram) reconstruction strategy is employed in this work. By simulating high-speed compressible multiphase flows and incompressible multiphase flows, this study demonstrates the ability of the proposed method to accurately handle flow regimes across all Mach numbers.

Figures (11)

• Figure 1: Interface topological changes at different time instants for the case 1 rising bubble problem. The solid black lines show the interface. The circle symbols at the final time instant are the reference solution from hysing2009quantitative.
• Figure 2: Evolution of the centre of mass (a) and rising velocity (b) for the case 1 rising bubble problem. The present solution is plotted using the black solid lines. The reference solution from hysing2009quantitative is represented by the blue triangle. The solution from manzanero2020entropy is shown by the red lines.
• Figure 3: Interface topological changes at different time instants for the case 2 rising bubble problem. The solid black line shows the interface calculated by the proposed method with mesh size $h=6.25\times 10^{-3}$. The circle symbols at the final time instant are the reference solution calculated by the MULES method with $h=1.5625\times 10^{-3}$gamet2020validation.
• Figure 4: Evolution of mass center (a) and rising velocity (b) for the case 2 rising bubble problem. The present solution is plotted in the black solid lines. The reference solution from gamet2020validation is marked by the blue squares. The solution from manzanero2020entropy is in red lines.
• Figure 5: Numerical solution of the magnitude of the density gradient fields (right panel) and experimental results of haas1987interaction (left panel) for air helium shock bubble interaction problem. The snapshots at $t=102 \mu \text{s}$, $t=245 \mu \text{s}$, $t=427 \mu \text{s}$ and $t=674 \mu \text{s}$ are presented from top to bottom.

Theorems & Definitions (1)

• proof