静态场中插值函数条件的研究

将质点形式SPH方程应用于静态场，被估质点既可以为初设质点，亦可位于初设质点之间。通过分析，得到了合适的插值函数应该满足的3个条件，8个插值函数的分析结果表明了3个条件的适用性。最后，利用一个函数的估值实例，证实了3个条件可以用于评价插值函数的优劣。分析结果表明，Gaussian和五次样条插值函数是最佳的插值函数。

Study on the Criterions for SPH Kernels in Stable Field

The SPH interpolation equations with a summation form are applied in a stable field. The position of estimated particle can either be the initial setting particles or the particles between the initial setting ones. Three criterions for determining suitable kernels are developed. 8 kernels are used to demonstrate the application of the criterions. Finally, for a given function, the estimation results of three kernels are evaluated to verify the feasibility of the three criterions. Through analysis, it is found that the three criterions developed in this study are feasible to evaluate kernels. The Gaussian and the Q-spline kernels can be regarded as the best kernels.