## 1 Introduction  
In China, coal remains the predominant energy source despite the potential acceleration of renewable energy under the \"dual carbon\" objectives [1]. It is anticipated that coal will continue to be the primary source of energy for the foreseeable future, playing a crucial role in the nation's energy strategy [2]. However, the geological conditions of China's coal reserves are notably complex, with over half (53%) of these reserves situated at depths exceeding 1 km [3]. As shallow coal resources become increasingly depleted, owing to rising energy demands, deep coal mining emerges as a critical strategy to sustain energy supply [4]. The coal resources in the Shanxi Formation, which has simpler hydrogeological conditions, are nearly exhausted, leading to a shift to the deeper seams, predominantly within the Taiyuan Formation [5]. As the mining depth increases, deep coal extraction confronts numerous technical challenges, such as coal and gas outbursts, rock bursts, water inrush, and thermal hazards. Among these, groundwater control is crucial [6; 7; 8]. Deep mining activities considerably affect the integrity of coal seam floors, exacerbating the complexity of the Ordovician and Taiyuan limestone aquifers [9]. Therefore, developing a dynamic model of karst water that considers these intricate hydrogeological conditions is imperative to prevent water inrush from coal seam floors and ensure the safe extraction of coal. The establishment of dynamic models for karst water cannot be achieved without the integration of mathematical modeling and computer technology. The combination of these two elements has led to continuous innovation in hydrogeological modeling. In the 1990s, [PERSON] established a standardized set of procedures for numerical simulation, ranging from the development of conceptual models to model redesign, serving as a reference for numerous scholars [10]. [PERSON] highlighted critical considerations in groundwater modeling, notably the impact of discretization methods on the accuracy of simulation results [11]. [PERSON] et al. elucidated the mechanistic causes underlying groundwater flow and transport behaviors across different scales [12]. Advancements in model data input have also been noted; [PERSON] demonstrated the utility of mixed models in quantifying hydrological, geological, and geophysical data, thereby enhancing data integration and model identification [13]. Further innovations in model interpolation and uncertainty analysis have considerably improved simulation accuracy [14; 15]. Furthermore, scholarly work has expanded modeling across various dimensions, showing that three-dimensional (3D) boundary conditions provide superior adaptability compared to two-dimensional approaches [16; 17]. In recent years, the exploration of transport simulation in multiphase media has advanced. For instance, [PERSON] developed a two-dimensional coupled water-gas flow numerical model for porous media using the finite-element method [18]. This model analyses the influence of pore gas on groundwater infiltration patterns in the vadose zone. [PERSON] introduced a coupled surface water-groundwater model framework to simulate the transition zone, assisting in assessing pollution risks to sediments and surface water from upstream sources [19]. The Groundwater Modeling System (GMS), a collaborative development between the Environmental Modeling Research Laboratory at Brigham Young University and the U.S. Army Corps of Engineers, offers a distinct graphical interface for groundwater simulations and has seen increasing application in scientific research. For example, [PERSON] utilized the GMS to develop an integrated 3D groundwater flow model for the Erbil Basin, thereby enhancing the management of groundwater resources in the region [20]. Similarly, [PERSON] applied the GMS to model and predict contaminant transport in groundwater, providing a theoretical basis for protecting drinking-water sources [21].