具有通用横截面的管道中两层液气分层流的新模型
A new model for two-layer liquid-gas stratified flows in pipes with general cross sections
AI总结：
本文提出了一种适用于通用横截面管道中两层液气分层流的新模型，通过非保守项连接底层不可压缩流体和顶层可压缩气体，实现了质量、动量和能量守恒，并通过数值测试验证了模型的平衡性和收敛性。
摘要：
本文推导了一个新的模型，用于描述具有通用横截面的管道中不可压缩液体和可压缩气体组成的两层不混溶分层流。底层由基于静水压力的不可压缩流体占据，采用浅水近似法进行流体动力学建模。顶层由遵循理想气体定律的可压缩气体占据，从而实现质量、动量和能量的守恒。两个子系统通过非保守项相互连接，代表层间动量和能量的交换。对所得到模型的超几何性质进行了分析，包括熵不等式的推导以及对应系数矩阵特征值的近似。数值测试用于展示该模型及其数值近似的优点，包括平衡性、黎曼问题、扰动以及向静止状态的收敛性。除了水和空气的模拟（层间密度差异显著）外，还展示了密度差异不那么明显的案例（如气体和液态氢）。
英文摘要：
In this work, we derive a new model for immiscible two-layer gas-liquid stratified flows in pipes with general cross sections. The bottom layer is occupied by an incompressible fluid in liquid phase with hydrodynamics based on a hydrostatic pressure, following a shallow water approximation. The top layer is occupied by a compressible gas, following an ideal gas law leading to conservation of mass, momentum and energy. The two subsystems are linked through non-conservative products, representing momentum and energy exchanges between layers. The hyperbolic properties of the resulting model are analyzed, including the derivation of entropy inequalities, and the approximations of eigenvalues of the corresponding coefficient matrix. Numerical tests are included to demonstrate the merits of the model and the numerical approximations, including well-balancedness, Riemann problems, and perturbations and convergence toward steady states at rest. Besides simulations of water and air where the density difference between layers is significant, a case where such difference is not so pronounced (like gas and liquid hydrogen) is also shown.
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