中文摘要：

光滑粒子流体动力学（SPH）由于无需网格生成和拉格朗日特性，对求解带有自由表面和大变形的力学问题有优势。但是该方法存在计算精度不高，计算效率较低等缺点。为此重点对SPH方法的精度提高进行研究。介绍了传统算法的基本公式，根据误差分析指出该算法精度不高的原因，提出了SPH二阶精度算法。通过精度验证分析，证明了该方法的精度的确能够达到二阶。通过二维计算实例，给出传统方法和二阶方法在粒子均匀分布和非均匀分布时函数值以及函数的一、二阶导数的误差分布，证明二阶算法能够克服传统算法的一些缺点，且计算精度有较大提高。

英文摘要：

The smoothed particle hydrodynamics （SPH） is one of mesh-free methods and has been widely developed during these years. This numerical method has many advantages for free surface problems and large deformation problems, because of its mesh-free and Lagrangian characters. But this method still exists some disadvantages at present, like low accuracy of calculation, more computational expense. According to the shortcomings of original SPH method, this paper focuses on the improvement of precision. Firstly, the foundation theory of original SPH method is introduced in brief, according to the precision analysis, the reason of low precision for the traditional method is pointed out, and second order SPH method is introduced. Then though the verification and analysis of accuracy, it is concluded that the precision of this new method achieves second order. Finally, based on the two dimension numerical tests, the error distributions of the function values, first order and second order derivatives are given by the original and modified method, when the particles are arranged at two ways, uniform distribution and non-uniform distribution. The results demonstrate that the second order method can overcome some shortcoming of the traditional method, and the precision can be improved effectively.