An Oscillation-Free Real Fluid Quasi-Conservative Finite Volume Method for Transcritical and Phase-Change Flows

TL;DR

This paper introduces a novel finite volume method for simulating real fluid flows with shock waves and phase changes, eliminating pressure oscillations and ensuring accuracy and robustness in complex transcritical and phase-change scenarios.

Contribution

The paper extends the quasi-conservative method to real fluids with arbitrary equations of state, providing an oscillation-free, thermodynamically consistent simulation approach.

Findings

Successfully suppresses spurious pressure oscillations.

Accurately captures shock waves and phase transitions.

Maintains second-order energy conservation in smooth regions.

Abstract

A new Real Fluid Quasi-Conservative (RFQC) finite volume method is developed to address the numerical simulation of real fluids involving shock waves in transcritical and phase-change flows. To eliminate the spurious pressure oscillations inherent in fully conservative schemes, we extend the classic quasi-conservative method, originally designed for two-phase flows, to real fluids governed by arbitrary equations of state (EoS). The RFQC method locally linearizes the real fluid EoS at each grid point and time step, constructing and evolving the frozen Gr\"uneisen coefficient $\Gamma$ and the linearization remainder $E_0$ via two advection equations. At the end of each time step, the evolved $\Gamma$ and $E_0$ are utilized to reconstruct the oscillation-free pressure field, followed by a thermodynamic re-projection applied to the conserved variables. Theoretical analysis demonstrates that, in smooth regions, the energy conservation error introduced by the RFQC method is a second-order small term dominated by the time-step. In discontinuous regions, this error is determined by the entropy increase rate, thereby maintaining consistency with the inherent truncation error of shock-capturing methods. A series of numerical tests verifies that the method can robustly simulate complex flow processes with only minor energy conservation errors, including transcritical flows, phase transitions, and shock-interface interactions. The RFQC method is proven to be both accurate and robust in capturing shock waves and phase transitions.