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 Grüneisen coefficient $Γ$ and the linearization remainder $E_0$ via two advection equations. At the end of each time step, the evolved $Γ$ 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.
A thermodynamically consistent and robust four-equation model for multi-phase multi-component compressible flows using ENO-type schemes including interface regularization
A Fourth-order Conservative Adaptive Multiresolution Wavelet Upwind Scheme for Compressible Flows
School of Civil Engineering and Mechanics, Lanzhou University（兰州大学土木工程与力学学院）；Key Laboratory of Mechanics on Disaster and Environment in Western China (Lanzhou University), the Ministry of Education, Lanzhou University（兰州大学西部灾害与环境力学教育部重点实验室）；Department of Mechanical Engineering, Institute of Science Tokyo（东京科学大学机械工程系）
