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1. A Data Assimilation Enabled Model for Coupling Dual Porosity Flow with Free Flow

   https://doi.org/10.1109/DCABES.2018.00085  

   Douglas, Craig; Hu, Xiukun; Bai, Baojun; He, Xiaoming; Wei, Mingzhen; Hou, Jiangyong (October 2018, 17th International Symposium on Distributed Computing and Applications for Business Engineering and Science (DCABES))
2. Modeling and a Domain Decomposition Method with Finite Element Discretization for Coupled Dual-Porosity Flow and Navier–Stokes Flow

   https://doi.org/10.1007/s10915-023-02185-7  

   Hou, Jiangyong; Hu, Dan; Li, Xuejian; He, Xiaoming (June 2023, Journal of Scientific Computing)
3. Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

   https://doi.org/10.1002/nme.6158  

   Al Mahbub, Md. Abdullah; He, Xiaoming; Nasu, Nasrin Jahan; Qiu, Changxin; Zheng, Haibiao (July 2019, International Journal for Numerical Methods in Engineering)

   Summary In this paper, we propose and analyze two stabilized mixed finite element methods for the dual‐porosity‐Stokes model, which couples the free flow region and microfracture‐matrix system through four interface conditions on an interface. The first stabilized mixed finite element method is a coupled method in the traditional format. Based on the idea of partitioned time stepping, the four interface conditions, and the mass exchange terms in the dual‐porosity model, the second stabilized mixed finite element method is decoupled in two levels and allows a noniterative splitting of the coupled problem into three subproblems. Due to their superior conservation properties and convenience of the computation of flux, mixed finite element methods have been widely developed for different types of subsurface flow problems in porous media. For the mixed finite element methods developed in this article, no Lagrange multiplier is used, but an interface stabilization term with a penalty parameter is added in the temporal discretization. This stabilization term ensures the numerical stability of both the coupled and decoupled schemes. The stability and the convergence analysis are carried out for both the coupled and decoupled schemes. Three numerical experiments are provided to demonstrate the accuracy, efficiency, and applicability of the proposed methods. 

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4. Dual Porosity-Enhanced Antireflection Coatings with Continuous Gradient

   https://doi.org/10.1021/acsami.3c07254  

   Hwang, Uiseok; Nam, Jae-Do; Lee, Daeyeon (August 2023, ACS Applied Materials & Interfaces)
5. Porosity evolution of mafic crystal mush during reactive flow

   https://doi.org/10.1038/s41467-023-38136-x  

   Gleeson, Matthew L. M.; Lissenberg, C. Johan; Antoshechkina, Paula M. (May 2023, Nature Communications)

   Abstract The emergence of the “mush paradigm” has raised several questions for conventional models of magma storage and extraction: how are melts extracted to form eruptible liquid-rich domains? What mechanism controls melt transport in mush-rich systems? Recently, reactive flow has been proposed as a major contributing factor in the formation of high porosity, melt-rich regions. Yet, owing to the absence of accurate geochemical simulations, the influence of reactive flow on the porosity of natural mush systems remains under-constrained. Here, we use a thermodynamically constrained model of melt-mush reaction to simulate the chemical, mineralogical, and physical consequences of reactive flow in a multi-component mush system. Our results demonstrate that reactive flow within troctolitic to gabbroic mushes can drive large changes in mush porosity. For example, primitive magma recharge causes an increase in the system porosity and could trigger melt channelization or mush destabilization, aiding rapid melt transfer through low-porosity mush reservoirs. 

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