Development of time-space adaptive SPH for large deformation and impact

Abstract

<p indent="0mm">A spatially adaptive smoothed particle hydrodynamics (ASPH) method, where the particles can split and merge according to the adaptive criteria, was developed to improve the computational efficiency of the classical smoothed particle hydrodynamics (SPH) method. Recently, the ASPH algorithm has been widely applied to solve complex problems in mechanics. However, the splitting pattern in the current ASPH algorithm may lead to particle disorder when simulating large deformation and impact problems, and a smaller time step should be performed after particle splitting. An adaptive splitting pattern that is based on a relative position vector and velocity interpolation is introduced in this study. Subsequently, this numerical method is combined with the Runge-Kutta Chebyshev method to achieve adaptive time integration. Thus, the time-space adaptive smoothed particle hydrodynamics method (T-S ASPH) is proposed in this study. This algorithm can increase the computational accuracy by eliminating the particle disorder when simulating the large deformation and impact problems while improving the computational efficiency and time integration accuracy. Typical examples are simulated by the classical SPH, current ASPH and developed T-S ASPH methods. The results indicate that, compared with the other two methods, the proposed T-S ASPH method exhibits higher accuracy, efficiency, stability, and order of convergence for the large deformation and impact problems.