Smoothed particle hydrodynamics: Methodology development and recent achievement

Since its inception, the full Lagrangian meshless smoothed particle hydrodynamics (SPH) has experienced a tremendous enhancement in methodology and impacted a range of multi-physics applications in science and engineering. This review presents a concise survey on latest developments and achievements of the SPH method, including: (1) Brief review of theory and fundamental with kernel corrections, (2) The Riemann-based SPH method with dissipation limiting and high-order data reconstruction by using MUSCL, WENO and MOOD schemes, (3) Particle neighbor searching with particle sorting and efficient dual-criteria time stepping schemes, (4) Total Lagrangian formulation with stablized, dynamics relaxation and hourglass control schemes, (5) Fluid-structure interaction scheme with interface treatments and multi-resolution discretizations, (6) Novel applications of particle relaxation in SPH methodology for mesh and particle generations. Last but not least, benchmark tests for validating computational accuracy, convergence, robustness and efficiency are also supplied accordingly.