The present paper proposes a new scheme for identifying free surface particles in an improved SPH (Smoothed Particle Hydrodynamics). With the development of the SPH, free surface identification becomes a key challenge in free surface flow simulations, especially for violent breaking water waves. According to numerical tests, existing free surface identified schemes are not reliable for weakly compressible SPH when violent waves are modeled. The new free surface identification scheme suggested here considers changes in density ratio and three auxiliary functions. Although this new scheme originates from a scheme for another meshfree method (MLPG_R method), it includes several improvements, especially developed for the improved SPH. The limited numerical tests have indicated that the scheme does not significantly increase CPU time required, but it considerably improves the identification of free surface particles.
Smoothed Particle Hydrodynamics (SPH) is a Lagrangian meshless particle method. However, its low accuracy of kernel approximation when particles are distributed disorderly or located near the boundary is an obstacle standing in the way of its wide application. Adopting the Taylor series expansion method and solving the integral equation matrix, the second order kernel approximation method can be obtained, namely K2_SPH, which is discussed in this paper. This method is similar to the Finite Particle Method. With the improvement of kernel approximation, some numerical techniques should be adopted for different types of boundaries, such as a free surface boundary and solid boundary, which are two key numerical techniques of K2_SPH for water wave simulation. This paper gives some numerical results of two dimensional water wave simulations involving standing wave and sloshing tank problems by using K2_SPH. From the comparison of simulation results, the K2_SPH method is more reliable than standard SPH.
