摘要：近年来,国外许多学者对求解双曲守恒律组的高分辨率、高精度差分格式进行了深入的研究.例如MUSCL方法、TVD格式、PPM方法、各种限流的方法以及ENO格式等等.将这些方法应用于流体力学方程组,其数值实践的结果表明,在消除波后振荡、提高激波间断分辨率、提高计算精度等方面有明显的效果.在设计这些计算格式时,通常都是研究单个标量方程的计算格式,再推广到方程组的情形.同时,或者对数值解的总变差提出某种要求(不增或基本不增),或者采用修正数值流措施,或者采用插值或重构的方法,在网格内部用线性分布和更高阶的分布取代Godunov方法中的常数分布,以及处理相应的小范围的解的算法.

摘要：流体力学方程求解的应用程序已成为众多重大工程理论研究与设计的重要工具,其应用程序的正确性验证已成为研究的重要问题.人为解验证技术是基于偏微分方程建模与模拟、很难解析求解的复杂工程应用程序正确性验证的重要手段.文章对流体力学方程组人为解构造方法及在应用程序正确性验证方面的研究进行了综述总结.利用李群约化理论得到流体力学方程几类精确解,给出了人为解构造的准则及流程,三维理想流体力学方程组的人为解,二维平面、柱坐标系下流体方程组的人为解及在欧氏应用程序验证中的应用,流体力学拉氏方程组人为解及在拉氏应用程序验证中的应用.

摘要：To optimize the design and improve the performance of wastewater treatment bioreactors,the review concerning the hydrodynamics explored by theoretical equations,process experiments,modeling of the hydrodynamics and flow field measurement is presented. Results of different kinds of experiments show that the hydrodynamic characteristics can affect sludge characteristics,mass transfer and reactor performance significantly. Along with the development of theoretical equations,turbulence models including large eddy simulation models and Reynolds-averaged Navier-Stokes (RANS) models are widely used at present. Standard and modified k-ε models are the most widely used eddy viscosity turbulence models for simulating flows in bioreactors. Numerical simulation of hydrodynamics is proved to be efficient for optimizing design and operation. The development of measurement techniques with high accuracy and low intrusion enables the flow filed in the bioreactors to be transparent. Integration of both numerical simulation and experimental measurement can describe the hydrodynamics very well.

摘要：成娟,舒其望.可压缩流体力学高精度拉格朗日格式及其保正性质[J].计算数学,2020,42(3):261-278.摘要:本文对可压缩流体力学高精度拉格朗日格式及其保正性质近年来的发展给出回顾与综述文中分别介绍了一维、二维可压缩流体力学方程中心型拉格朗日格式的设计步骤,回顾了高精度拉格朗日格式以及高精度保正拉格朗日格式的研究进展.