一种能量稳定、守恒守恒且局部保守的多组分气体流在多孔弹性介质中的数值框架
An Energy-Stable, Bound-Preserving and Locally Conservative Numerical Framework for Multicomponent Gas Flow in Poroelastic Media
AI总结：
本文提出了一种能量稳定、守恒且局部保守的数值框架，用于模拟多孔弹性介质中多组分气体流动，通过稳定离散化方法和自适应时间步长策略提升计算效率与稳定性。
摘要：
本文提出了一种稳健且高效的数值框架，用于模拟多孔弹性介质中的多组分气体流动，重点在于保持基本热力学原理并确保计算可靠性。模型捕捉了多组分传输与固体变形之间的复杂非线性耦合，同时解决了诸如质量守恒、能量稳定性和摩尔密度有界性等关键数值挑战。为此，我们开发了一种稳定的离散化方法，以保证保持原始能量耗散定律，并确保每个气体组分的摩尔密度的有界性。此外，所提出的方法结合了自适应时间步长策略，根据系统动态动态调整时间步长大小，显著提高了计算效率，而不会牺牲稳定性和准确性。在空间离散化方面，采用混合有限元方法结合上游方案用于流体和传输方程，以确保局部质量守恒，同时使用不连续伽辽金（DG）方法对多孔弹性方程的动量方程进行离散化，以有效克服数值锁紧现象。数值实验展示了该方法在各种场景下模拟多组分气体流动的性能、稳健性和适用性。
英文摘要：
In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The model captures the complex nonlinear coupling between multicomponent transport and solid deformation, while addressing critical numerical challenges such as mass conservation, energy stability, and molar density boundedness. To achieve this, we develop a stabilized discretization approach that guarantees the preservation of the original energy dissipation law and ensures the boundedness of each gas component's molar density. Furthermore, the proposed method incorporates an adaptive time-stepping strategy that dynamically adjusts the time step size based on the system's dynamics, significantly enhancing computational efficiency without compromising stability or accuracy. For spatial discretization, a mixed finite element method combined with an upwind scheme is employed for the flow and transport equations to ensure local mass conservation, while a discontinuous Galerkin (DG) method is utilized for discretizing the momentum equation of poroelasticity to effectively overcome numerical locking phenomena. Numerical experiments are presented to demonstrate the performance, robustness, and applicability of the method in simulating multicomponent gas flow under various scenarios.
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