Smoothed particle hydrodynamics (SPH) is a state-of-the-art numerical simulation method in fluid mechanics. It is a novel approach for modeling and comprehending complex fluid behaviors. In contrast to traditional grid-dependent techniques like finite element and finite difference methods, SPH utilizes a meshless, purely Lagrangian approach, offering significant advantages in fluid simulations. By leveraging a set of arbitrarily distributed particles to represent the continuous fluid medium, SPH enables the precise estimation of partial differential equations. This grid-free methodology effectively addresses many challenges associated with conventional methods, providing a more adaptable and efficient solution framework. SPH’s versatility is evident across a broad spectrum of applications, ranging from advanced computational fluid dynamics (CFD) to complex computational solid mechanics (CSM), and proves effective across various scales—from micro to macro and even astronomical phenomena. Although SPH excels in tackling problems involving multiple degrees of freedom, complex boundaries, and large discontinuous deformations, it is still in its developmental phase and has not yet been widely adopted. As such, a thorough understanding and systematic analysis of SPH’s foundational theories are critical. This paper offers a comprehensive review of the defining characteristics and theoretical foundations of the SPH method, supported by practical examples derived from the Navier–Stokes (N-S) equations. It also provides a critical examination of successful SPH applications across various fields. Additionally, the paper presents case studies of SPH’s application in tunnel and underground engineering based on practical engineering experiences and long-term on-site monitoring, highlighting SPH’s alignment with real-world conditions. The theory and application of SPH have thus emerged as highly dynamic and rapidly evolving research areas. The detailed theoretical analysis and case studies presented in this paper offer valuable insights and practical guidance for scholars and practitioners alike.
