Steady-state unconfined seepage in heterogeneous medium using an adaptive multi-patch isogeometric analysis

For seepage problems with free surfaces, traditional approaches use either moving mesh strategies or fixed mesh strategies. Both these approaches have inherent challenges, on one hand, the moving mesh methods often encounter computational instability caused by mesh distortion, whereas the fixed mesh methods face challenges in balancing computational accuracy and efficiency. To overcome these limitations, this paper presents a two-dimensional steady-state unconfined seepage framework based on adaptive multi-patch isogeometric analysis, designed to enable efficient, stable, and precise numerical simulations. The proposed framework incorporates a Zienkiewicz–Zhu error estimator to drive local mesh refinement, and utilizes truncated hierarchical non-uniform rational B-splines (TH-NURBS) for accurate modeling and localized adaptive refinement. The multi-patch technique, integrated with Nitsche’s method, is adopted for the simulation of complex geometries. Validation with several numerical examples shows that the framework provides favorable computational accuracy and efficiency, highlighting its potential for application in complex engineering problems. • An adaptive multi-patch isogeometric analysis for steady-state unconfined seepage is proposed. • Complicated domains are exactly treated by multiple patches coupled with Nitsche’s method. • A Zienkiewicz–Zhu error estimator is developed to perform local refinement. • Fixed-mesh method is ingeniously integrated with local refinement to avoid re-meshing. • Numerical results show the accuracy and effectiveness of the proposed framework.