An adaptive isogeometric analysis framework for two-dimensional steady-state unconfined seepage problems

In addressing seepage problems with free surfaces, conventional moving mesh methods often encounter numerical instability due to mesh distortion, whereas fixed mesh approaches typically fail to deliver high-accuracy solutions with controllable computational cost. To overcome these limitations, this study develops an adaptive isogeometric analysis framework for two-dimensional steady-state unconfined seepage, aiming to achieve efficient and stable numerical solutions. Combining the local refinement capability of truncated hierarchical NURBS with the permeability adjustment strategy, the proposed framework is shown to capture the free surface accurately while avoiding mesh reconstruction required by traditional methods. By introducing an adaptive criterion based on a posteriori error estimator, the system can intelligently identify and refine key regions near the free surface during the iteration process, significantly improving computational efficiency without compromising accuracy. Numerical results demonstrate that the proposed method exhibits excellent robustness under conditions with different seepage properties, and shows exceptionally good agreement with reference solutions. This method also provides a reliable foundation for subsequent multi-physics coupling analysis and seepage simulation in complex engineering scenarios. • A novel method for locating free surface in unconfined seepage problems is proposed. • The fixed-mesh method is ingeniously integrated with local refinement to avoid re-meshing. • A novel error estimator is combined with adaptive strategy for efficiency enhancement. • The proposed method is applied to homogeneous/heterogeneous porous media.