How to Recover Oscillation-Free Pressure in Real Fluids: The RFQC Method and Its Liquid-Upwind Anomaly
Abstract
From the perspective of continuum thermodynamics, we revisit the pressure oscillation problem in finite-volume methods for multiphase real fluids and clarify the physical counterpart of the Real Fluid Quasi-Conservative (RFQC) method. The pressure oscillation in conservative finite-volume methods originates from their implicit thermodynamic equilibrium assumption, whereas recovering an oscillation-free pressure requires additional physical information. The RFQC method achieves this by evolving the affine parameters xi and E0 of the isentropic internal-energy-pressure relation along pathlines, while the thermodynamic re-projection converts the deviation from the isentropic trajectory into an internal-energy error, thereby ensuring the thermodynamic consistency and numerical stability of the method. We then investigate the applicability limit of the RFQC method and identify a Liquid-upwind Anomaly (LUA) in extreme phase-change cases. For a Riemann problem involving liquid-vapor phase change, a numerical anomaly may occur if a liquid-upwind translational velocity is initially superimposed. Theoretical analysis reveals that this anomaly is initiated by the jump in the affine slope xi during phase change, which delays pressure rise in the downstream vapor cell. Concurrently, the re-projection removes the positive pressure increment, repeatedly generating large internal-energy errors and trapping the vapor cell in a cycle of delayed pressure recovery. The analysis indicates that the LUA is a start-up anomaly, which can be resolved by introducing a regularization strategy at the initial discontinuity. With the proposed regularization strategy, the RFQC method is equipped with enhanced accuracy and robustness for extreme thermodynamic flows, such as sonic phase-change jets.
Related
- On the Existence of Pressure-Equilibrium-Preserving Numerical Fluxes for Supercritical Fluids
- A Pressure-Free Virtual Element Method for the Surface Stokes Problem
- Different representation learning objectives recover distinct latent structures from the same psychometric data
- When Can World Models Recover Physical Laws?
- Illposedness of incompressible fluids in supercritical Sobolev spaces
BibTeX
@misc{bai2026recover,
title = {{How to Recover Oscillation-Free Pressure in Real Fluids: The RFQC Method and Its Liquid-Upwind Anomaly}},
author = {Haotong Bai and Yixin Yang and Wenjia Xie and Ping Yi and Mingbo Sun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.13996},
eprint = {2607.13996},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.13996},
}
RIS
TY - UNPB
TI - How to Recover Oscillation-Free Pressure in Real Fluids: The RFQC Method and Its Liquid-Upwind Anomaly
AU - Haotong Bai
AU - Yixin Yang
AU - Wenjia Xie
AU - Ping Yi
AU - Mingbo Sun
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2607.13996
UR - https://arxiv.org/abs/2607.13996
AB - From the perspective of continuum thermodynamics, we revisit the pressure oscillation problem in finite-volume methods for multiphase real fluids and clarify the physical counterpart of the Real Fluid Quasi-Conservative (RFQC) method. The pressure oscillation in conservative finite-volume methods originates from their implicit thermodynamic equilibrium assumption, whereas recovering an oscillation-free pressure requires additional physical information. The RFQC method achieves this by evolving the affine parameters xi and E0 of the isentropic internal-energy-pressure relation along pathlines, while the thermodynamic re-projection converts the deviation from the isentropic trajectory into an internal-energy error, thereby ensuring the thermodynamic consistency and numerical stability of the method. We then investigate the applicability limit of the RFQC method and identify a Liquid-upwind Anomaly (LUA) in extreme phase-change cases. For a Riemann problem involving liquid-vapor phase change, a numerical anomaly may occur if a liquid-upwind translational velocity is initially superimposed. Theoretical analysis reveals that this anomaly is initiated by the jump in the affine slope xi during phase change, which delays pressure rise in the downstream vapor cell. Concurrently, the re-projection removes the positive pressure increment, repeatedly generating large internal-energy errors and trapping the vapor cell in a cycle of delayed pressure recovery. The analysis indicates that the LUA is a start-up anomaly, which can be resolved by introducing a regularization strategy at the initial discontinuity. With the proposed regularization strategy, the RFQC method is equipped with enhanced accuracy and robustness for extreme thermodynamic flows, such as sonic phase-change jets.
ER -