Abstract： A second-order Godunov-scheme SPH method is proposed to achieve higher accuracy and steeper representation of wave fronts than that calculated by first-order Godunov-scheme SPH method. The distribution of physical variables inside each particle is represented with linear functions in new method. Therefore physical values at particle boundaries which are calculated through linear interpolation are used as initial values of Riemann problem between interacting particles. Riemann solvers and Taylor series are then introduced into the SPH method. One-dimensional problems of stress wave propagation are simulated by both first-order and second-order Godunov-scheme SPH methods. The results show that the new method has effectively improved the solution accuracy and is stable both in tension and compression.
2011, Vol. 30 
