AI 中文总结
本文针对封闭系统低马赫数实际气体流动，提出质量守恒的低马赫数数值框架，经制造解法及理想、实际流体基准流动验证，适用于跨临界CO₂通道流动，兼具准确性与鲁棒性。
AI 中文摘要
针对由一般非线性状态方程控制的封闭系统实际流体流动，本文提出一种质量守恒的低马赫数框架。该公式确保空间均匀热力学压力、状态方程与全局质量守恒之间的一致性。此外，数值算法采用分步法策略，即先更新热力学状态，再求解动量方程，速度场通过压力修正法推进。该方法通过解耦热力学与动量更新，并保留基于快速傅里叶变换（FFT）的压力修正求解器，实现了高效求解过程。所得公式具有二阶空间精度。首先采用制造解法进行验证，其中热力学状态通过解析密度和热力学压力场规定，可验证非线性状态方程、热力学压力演化及低马赫数散度约束。随后，针对理想流体和实际流体的基准层流与湍流流动（尤其是跨临界CO₂通道流动）对该框架进行验证，证明其在强热力学非线性存在时的准确性与鲁棒性。
英文摘要
A mass-preserving low-Mach-number framework is proposed for closed-system real-fluid flows governed by general nonlinear equations of state. The formulation enforces consistency between the spatially uniform thermodynamic pressure, the equation of state, and global mass conservation. Moreover, the numerical algorithm employs a segregated strategy in which the thermodynamic state is updated before the momentum equations, and the velocity field is advanced using a pressure-correction method. This approach enables an efficient solution procedure by decoupling the thermodynamic and momentum updates and retaining the use of FFT-based solvers for the pressure correction. The resulting formulation is implemented with second-order spatial accuracy. The implementation is first verified using the method of manufactured solutions, in which the thermodynamic state is prescribed through analytical density and thermodynamic-pressure fields, enabling verification of the nonlinear equation of state, thermodynamic-pressure evolution, and the low-Mach-number divergence constraint. The framework is subsequently validated against benchmark laminar and turbulent flows for both ideal and real fluids, particularly transcritical CO$_2$ channel flow, demonstrating its accuracy and robustness in the presence of strong thermodynamic nonlinearities.
