Based on the first chapter , in the second chapter , we will develop an efficient adaptive moving mesh algorithm with local time stepping . the principle idea will be demonstrated by investigat - ing the conservation laws and the convection - dominated problems 以第一部分为基础，在文章的第二部分，我们将针对守恒律和对流占优方程问题，发展一种有效的局部时间步长自适应移动网格算法。
Based on these new techniques , the software with automatically variable irregular space grid and automatically variable time stepsize has been developed , which greatly enhances the computational efficiency for the numerical solution of two - dimension three - temperature equations 在此基础上，针对欲求解的问题构造了一个自动改变空间网格自动改变时间步长的软件，大幅度提高了该问题的计算效率。
No . 2 , a fast simulation technique is proposed to approximate the filtering effects of the implicit method in order to alleviate the heavy computation brought by the implicit integration method . no . 3 , an algorithm to dynamically regulate the time step is detailed 柔体仿真过程中一直存在的瓶颈问题首先是为保证仿真过程的稳定性而不得不采用较小的时间步长，其次是求解微分方程时耗费的计算量过大。
Through caculation example , the factors that will influece the results of seismic soil response including element meshing , intergration step , damping , boundary were studied and the regularity was generalized . in the third part , the pile - soil - superstructure model was constructed and solved 通过算例考察了影响土体地震反应的单元网格划分、积分时间步长、阻尼取值、边界等因素,并对土体地震反应的规律性现象做了总结。
In chapter four , the writer studied and discussed the critical elements that affect the simulation of the collision between ship and pier protective device , and found the feasible way to deal with the conflict between calculation efficiency and precision 第四章对结构碰撞有限元计算的有效性进行了基础性研究，重点探讨单元尺寸、摩擦力、计算时间步长、沙漏控制等因素对仿真计算的影响，得到有用的结论，提高了计算的可靠性和效率。
The finite element model of the thermal conductive equation and the thermo - elastic equation in the system consisting of a transparent coating and a opaque substrate is established based on the analysis of the stability of solution and two important parameters , meshing size and time step 摘要在分析了网格大小和时间步长这两个重要参数和求解稳定性的基础上，采用有限元方法建立了透明薄膜基底系统的热传导方程和热弹性方程的有限元模型。
In order to advance the sst turbulence equations at the same rate as the flow equations , a point - implicit scheme is used . the convection term in turbulence equations is discretized using first - order upwinding scheme to ensure more stability in time integration and the positivity of the turbulent variables Sst湍流方程求解时,使用点隐式格式进行时间推进从而解除了由于源项存在所引起的时间步长的限制,保证湍流方程和流动方程同步推进时的稳定性。
4 . a 2 - d and 3 - d euler equations and n - s equations are solved using the cell - centered finite volume method and four - step runge - kutta scheme on the cartesian grids with standard convergence acceleration techniques such as local time stepping , enthalpy and implicit residual smoothing 使用jameson中心有限体积法和runge - kutta时间推进方法，求解了关于二维、三维复杂流场的euler 、 navier - stokes方程，采用了当地时间步长、隐式残值光顺等多种加速收敛方法。
Compared with the conventional finite - difference method on the fixed grid - size rectangular grids , the new method can be more cost - effective in complex models . numerical tests for both seismic modeling and reverse - time migration are performed on various theoretical models and a physical experiment 用该剖分方法得到的网格在各速度层内的空间步长是不同的，而全区域上的时间步长却近于恒定，因此在复杂模型上，本文方法的计算效率要高于传统的矩形网格差分方法。
The viscid flux is discretized by second - order central difference scheme . baldwin - lomax turbulence model is implemented in navier - stokes flow solver . for steady - state calculations , a four - stage runge - kutta scheme with convergence acceleration techniques such as local - time stepping and implicit residual smoothing is used 其中，定常计算中的时间推进采用四步runge ? kutta方法，并应用了当地时间步长、隐式残值光顺等加速收敛措施；非定常计算中的时间推进采用jameson的隐式双时间方法。
