Huang et al. (2025) Simulating precipitation-induced karst-stream interactions using a coupled Darcy–Brinkman–Stokes model

Identification

• Journal: Hydrology and earth system sciences
• Year: 2025
• Date: 2025-11-17
• Authors: Fuyun Huang, Yuan Gao, Zizhao Zhang, Xiaonong Hu, Xiaoguang Wang, Shengyan Pu
• DOI: 10.5194/hess-29-6285-2025

Research Groups

• School of Geology and Mining Engineering, Xinjiang University, Urumqi, Xinjiang 830046, China
• School of Water Conservancy and Environment, University of Jinan, Jinan, Shandong 250022, China
• State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu, Sichuan 610059, China
• Tianfu Yongxing Laboratory, Chengdu, Sichuan 610059, China
• State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, Sichuan 610059, China

Short Summary

This study developed a coupled Darcy–Brinkman–Stokes model to simulate precipitation-induced karst-stream interactions, integrating water-air two-phase flow and variably saturated conditions. It found that rainfall intensity is the dominant driver, leading to complex multi-media interactions and shifting discharge contributions, with groundwater stored in porous media significantly influencing subsequent stream levels.

Objective

• To develop and employ a two-phase variably saturated model capable of coupling free flow and seepage flow to reveal the interaction mechanisms between karst aquifer systems and adjacent streams under rainfall infiltration recharge-driven conditions.
• To investigate how groundwater saturation variations in different media (conduits, fractures, matrix) of the karst aquifer system influence inter-media interactions.
• To address the gap in existing numerical methods that struggle to accurately characterize collaborative recharge processes among various media within karst aquifer systems.
• To specifically investigate the impact of precipitation intensity, different water retention models, multi-stage conduit arrangements, and parameter sensitivity on the interaction mechanism.

Study Configuration

• Spatial Scale: A conceptual karst aquifer model adjacent to a stream, with domain dimensions of 200 meters (length) × 200 meters (width) × 30 meters (thickness). The model resolves micro-scale variations in water levels and interfaces within free-flow zones (streams, sinkholes, conduits) and gradually coarsening grids in porous media.
• Temporal Scale: Simulations were conducted for a total duration of 45,000 seconds, analyzing single and multiple consecutive precipitation events.

Methodology and Data

• Models used:
  • Darcy–Brinkman–Stokes (DBS) model: A unified mathematical framework for coupling seepage flow in porous media and free flow in karst conduits and streams, capable of describing immiscible and incompressible two-phase flow.
  • Volume of Fluid (VOF) method: Applied to monitor dynamic changes in aquifer saturation and reconstruct dynamic water-air interfaces.
  • Water Retention Models: Brooks–Corey (BC) model and van Genuchten–Mualem (VGM) model were used to characterize unsaturated seepage and relative permeability in karst media.
  • Comparative Models: MODFLOW-Conduit Flow Process v2 (MODFLOW-CFPv2) and Navier–Stokes (N-S) equations were used for comparison and validation.
• Data sources:
  • Numerical simulations based on a conceptual karst aquifer-stream system.
  • Validation against experimental datasets for unsaturated-unsteady seepage problems from Warrick et al. (1985) (sandy clay loam) and Vauclin et al. (1979) (2D laboratory infiltration).
  • Soil hydraulic properties obtained from the international UNSODA database (Leij et al., 1996).
  • Rainfall infiltration recharge boundary conditions formulated based on previous studies (Huang et al., 2024; Chang et al., 2015).

Main Results

• Precipitation Intensity: Rainfall intensity is the dominant driver of karst-stream interactions. Higher intensities lead to more complex processes, involving multi-media collaborative recharge and shifting discharge contribution ratios. The DBS model captures secondary discharge peaks due to overflow effects, unlike MODFLOW-CFPv2.
• Consecutive Rainfall Events: Groundwater stored in porous media (matrix) significantly influences subsequent stream levels, while conduit storage shows negligible carry-over impact due to rapid drainage. The storage effect primarily occurs in the porous medium.
• Water Retention Characteristics: The choice of water retention model (Brooks–Corey vs. van Genuchten–Mualem) significantly impacts stream hydrographs by altering the water storage and release dynamics of the matrix. The van Genuchten–Mualem model predicts longer groundwater migration distances and is more sensitive in simulating diffusion and infiltration processes.
• Conduit Geometry: Larger conduit radii lead to higher initial discharge peaks and shorter peak arrival times in the stream and karst spring. Square-section conduits exhibit higher peak discharge than circular conduits of the same nominal radius due to larger cross-sectional areas.
• Epikarst Permeability: High epikarst permeability (e.g., 10⁻⁶ m/s) results in rapid, sharp streamflow peaks, reflecting efficient groundwater leakage. Lower permeability leads to diminished peaks and broader discharge curves. Epikarst permeability differences have minimal impact on conduit flow unless it matches porous media permeability.
• Porosity: Lower porosity results in higher streamflow peaks and earlier peak times, as reduced pore space limits groundwater storage capacity, forcing rapid discharge. Porosity has negligible effects on the porous media directly below the conduit (PM III), as its behavior is primarily governed by conduit flow.
• Model Performance: The validated DBS model accurately depicts complex two-phase interactive flows (infiltration, overflow, and recession) controlled by dynamic saturation, successfully revealing dynamic interactions between the epikarst, conduits, matrix, and stream. It provides a more detailed and accurate representation of multi-media interactions compared to MODFLOW-CFPv2.

Contributions

• Developed and validated a robust, unified Darcy–Brinkman–Stokes (DBS) model coupled with the Volume of Fluid (VOF) technique, capable of simulating two-phase (water-air) variably saturated flow and seamlessly coupling seepage and free flow in complex karst aquifer-stream systems.
• Demonstrated the critical necessity of a multi-physics, coupled multi-medium approach to accurately capture the highly non-linear and dynamic hydrological responses of karst systems, addressing limitations of conventional single-phase or simplified models.
• Quantified the dominant role of precipitation intensity as a primary driver, fundamentally altering flow paths and contribution ratios of different media by triggering dynamic saturation, overflow, and synergistic recharge processes.
• Elucidated the distinct hydrological roles and carry-over impacts of different karst media (conduits, matrix, epikarst) during single and consecutive rainfall events, highlighting the significant influence of matrix storage on subsequent stream levels.
• Provided comprehensive insights into how inherent hydrogeological properties (water retention characteristics, conduit geometry, epikarst permeability, and matrix porosity) regulate fluid flow patterns and inter-media interactions, enhancing understanding for improved flood risk assessment, water resource allocation, and contamination vulnerability planning.

Funding

• Doctoral Scientific Research Startup Foundation of Xinjiang University (grant no. 620321004)
• Natural Science Foundation of Xinjiang Uygur Autonomous Region (grant no. 2022D01C40)

Citation

@article{Huang2025Simulating,
  author = {Huang, Fuyun and Gao, Yuan and Zhang, Zizhao and Hu, Xiaonong and Wang, Xiaoguang and Pu, Shengyan},
  title = {Simulating precipitation-induced karst-stream interactions using a coupled Darcy–Brinkman–Stokes model},
  journal = {Hydrology and earth system sciences},
  year = {2025},
  doi = {10.5194/hess-29-6285-2025},
  url = {https://doi.org/10.5194/hess-29-6285-2025}
}