Smoothed Particle Hydrodynamics With Anisotropic Adaptive Spatial Resolution

ABSTRACT Smoothed Particle Hydrodynamics (SPH) has emerged as a promising meshless computational method with applications in diverse fields. However, SPH faces significant challenges in computational efficiency and resolution adaptability. To address these limitations, this study introduces a novel SPH framework with anisotropic adaptive spatial resolution (AASR), which combines the strengths of anisotropic SPH (ASPH) and adaptive spatial resolution (ASR). The proposed method enables directionally anisotropic particle spacing for any single particle, along with gradual resolution transitions between neighboring particles, achieving grid‐like refinement flexibility while preserving the Lagrangian nature of SPH. Several auxiliary SPH techniques, including free surface detection, particle shifting technique and the renormalized density gradient, are improved to match the AASR framework. The framework is further enhanced by coupling with the Finite Particle Method (FPM), which improves numerical stability and accuracy in non‐uniform particle distributions. Numerical validations are conducted in five benchmark cases, including lid‐driven shear cavity flow, Taylor–Green vortex, solitary wave propagation, standing wave dissipation, and wave–floating–breakwater interaction. Results demonstrate that the AASR technique can maintain resolution in any critical regions while coarsening elsewhere. While notably improving computational efficiency, the new method preserves satisfactory numerical accuracy, with about a first‐order convergence rate in the benchmark. In addition, existing SPH enhancements or auxiliary techniques are compatible with the AASR framework after necessary modification. This work advances SPH applicability to large‐scale and multi‐resolution problems, establishing a meshless alternative with comparable resolution control to grid‐based methods.