Unconditionally Energy Stable Linear Schemes for the Diffuse Interface Model with Peng–Robinson Equation of State
Unconditionally Energy Stable Linear Schemes for the Diffuse Interface Model with Peng–Robinson Equation of State
复制标题
具有Peng-Robinson状态方程的漫反射界面模型的无条件能量稳定线性方案
DOI：
10.1007/s10915-017-0576-7
复制
发表时间：
2018
影响因子：
2.5
通讯作者：
Qiujin Peng
中科院分区：
文献类型：
--
作者：
Hongwei Li;Lili Ju;Chenfei Zhang;Qiujin Peng
本文研究了描述石油工业中烃类流体真实状态的Peng-Robinson状态方程扩散界面模型的数值解。由于该模型源项的强非线性，如何设计合适的时间离散化以保持系统在离散水平上的能量耗散规律是一个主要的挑战。基于“不变能量二次化”方法和惩罚公式，我们发展了求解单组分两相流体问题的一阶和二阶时间推进格式。在这两种格式中，所得到的时间半离散导致在每个时间步具有对称正定空间算子的线性系统。我们严格证明了它们在时间离散意义下的无条件能量稳定性。文中还给出了二维和三维空间的各种数值模拟，以验证所提出的线性格式的准确性和稳定性，并通过与实验室数据的比较来考察目标模型的物理可靠性。
In this paper, we investigate numerical solution of the diffuse interface model with Peng–Robinson equation of state, that describes real states of hydrocarbon fluids in the petroleum industry. Due to the strong nonlinearity of the source terms in this model, how to design appropriate time discretizations to preserve the energy dissipation law of the system at the discrete level is a major challenge. Based on the “Invariant Energy Quadratization” approach and the penalty formulation, we develop efficient first and second order time stepping schemes for solving the single-component two-phase fluid problem. In both schemes the resulted temporal semi-discretizations lead to linear systems with symmetric positive definite spatial operators at each time step. We rigorously prove their unconditional energy stabilities in the time discrete sense. Various numerical simulations in 2D and 3D spaces are also presented to validate accuracy and stability of the proposed linear schemes and to investigate physical reliability of the target model by comparisons with laboratory data.