Three finite - difference methods , i . e . , stagger grid , implicit and explicit algorithms , are analyzed in detail . multi - grid algorithm is firstly introduced in elastic wave simulation , to solve for the stability problem inherent in stagger grid and implicit algorithm , also for the efficiency problem inherent in explicit algorithm , and the precision , stability and efficiency for simulation of elastic wave arc increased by multi - grid method . phase - delay method is provided to effectively absorb boundary reflection and increase efficiency for wave motion simulation , based on phase delay and amplitude decaying features along wave propagation 在水平分层介质接收函数的波形反演研究的基础上，本文系统阐述了非均匀介质中弹性波传播数值模拟常用的三种有限差分方法：显式差分、隐式差分和交错网格法，首次将多重网格算法应用于弹性波方程的数值模拟问题，克服了交错网格法和显式差分法稳定性差，以及隐式差分法计算效率低的缺点，大大提高了弹性波数值模拟的精度、稳定性和计算效率。
The paper uses a high order method to solve incompressible viscous complex flows based on a domain decomposition and matched method , , the primitive variable and pressure poisson equation formulation are employed for the numerical solutions of the incompressible navier - stokes equations , in tensor forms , on non - staggered grids 本文采用了一种基于分块耦合求解粘性不可压缩复杂流场的高精度计算方法。计算模块采用原始变量和压力poisson方程方法，差分方程为张量形式的粘性不可压缩navier - stokes方程组在非交错网格上离散。
The schemes are numerically tested on a variety of id and 2d problems ; solutions obtained in computation the results of the numerical solutions for euler equation and shallow water equations by gauss schemes presented in the paper under distributed memory parallel multiprocessor are presented . the efficient of parallel computation are satisfied 利用曙光- 1000型分布存储大规模并行机，对我们在交错网格下所构造求解euler方程和浅水方程的高分辨差分格式进行了并行实现，并对并行效率进行了分析，计算结果和并行效率都比较令人满意。
