Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: Motivations, current state, and challenges

Incompressible smoothed particle hydrodynamics (SPH) with reduced temporal noise and generalised Fickian smoothing applied to body–water slam and efficient wave–body interaction

This paper presents a comparative study for the weakly compressible (WCSPH) and incompressible (ISPH) smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle. Improved WCSPH and ISPH techniques are used to solve these two bluff body flow
problems. It is shown that both approaches can handle complex geometries using the multiple boundary tangents (MBT) method, and eliminate particle clustering-induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected SPH discretization scheme. WCSPH and ISPH simulation results are compared and validated with those of a finite element method (FEM). The quantitative comparisons of WCSPH, ISPH and FEM results in terms of Strouhal number for the square obstacle test case, and the pressure envelope, surface traction forces, and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the WCSPH method with the suggested implementation produces numerical results as accurate and reliable as those of the ISPH and FEM methods.

A robust weakly compressible SPH method and its comparison with an incompressible SPH

In this article, we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics (SPH) method. Benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries. As well, current SPH boundary approaches do not properly treat curved boundaries in complicated flow domains. These drawbacks have been remedied in a new boundary treatment method presented in this article, called the multiple boundary tangent (MBT) approach. In this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent
treatment produces results that agree with known numerical and experimental solutions. The two benchmark problems chosen are the lid-driven cavity problem, and flow over a cylinder. The SPH solutions using the MBT approach and the results from literature are in very good agreement. These solutions involved
solid boundaries, but the approach presented herein should be extendable to time-evolving, free-surface boundaries.

https://research.sabanciuniv.edu/9801/1/SPH_with_the_multiple_boundary_tangent_method.pdf

SPH with the multiple boundary tangent method

In this article, a two-dimensional transient heat conduction problem is modeled using smoothed particle hydrodynamics (SPH) with a Crank-Nicolson implicit time integration technique. The main feature of this work is that it applies implicit time stepping, an unconditionally stable Crank-Nicolson approach, in the thermal conduction simulation of liquid-phase diffusion (LPD) semiconductor crystal growth. This SPH simulation is compared with the equivalent finite-volume results. As well, two transient thermal conduction test problems are simulated using both explicit and Crank-Nicolson schemes, and their results compared with the analytical solutions. One of the current drawbacks of SPH is that explicit time-stepping algorithms, such as predictor-corrector methods or leapfrog methods, require extremely small time steps for a stable simulation. Using implicit time integration opens SPH up to a much larger class of practical problems in applied mechanics.

Rusty Rook

Papers

SPH with the multiple boundary tangent method

Modeling Transient Heat Transfer Using SPH and Implicit Time Integration

The use of smoothed particle hydrodynamics for simulating crystal growth from solution