基于SPH方法的间断现象的数值模拟研究-计算机软件与理论专业论文.docxVIP

the final kernel and particle approximations for a function and its derivatives are similar to those in RSPH. The remained part ensures the consistency of the kernel approximation for treating discontinuities. DRSPH remedies the boundary deficiency problem and restores the particle consistency in discontinuous regions without modifying kernel functions. Compared with DCSPM proposed by Liu in 2003, DRSPH does not need the normalization. The function and its first derivatives in DRSPH are calculated by solving the matrix at the same time with 2-order approximation accuracy. Through defining the particle consistency in discontinuous regions, it is demonstrated that DRSPH restores the particle consistency in discontinuous regions more effectively than DCSPM, and has first order particle consistency in approximating the function. DRSPH requires an efficient algorithm of discontinuity detection based on discrete functions in current time step. If an efficient algorithm for discontinuity detection is provided, DRSPH will be very useful in discontinuous regions, especially for the problems in a multi-dimensional space. Key Words: discontinuous phenomena, Smoothed Particle Hydrodynamics, particle inconsistency. 目 录 摘要 ........................................................................ I Abstract ................................................................... II 第 1 章 绪论 ................................................................. 1 1.1 数值模拟 ............................................................ 1 1.2 国内外研究状况 ...................................................... 4 1.3 本文的创新点和主要工作 .............................................. 6 1.4 本文的内容安排 ...................................................... 6 HYPERLINK \l _TOC_250000 第 2 章 SPH 的基本公式和概念 8 2.1 SPH 的基本概念 8 2.2 SPH 方法中必要的公式 8 2.2.1 场函数的核近似法 ............................................... 8 2.2.2 粒子近似法 .................................................... 10 2.2.3 核函数的选取 ..................................