求解Euler方程的区域分解方法与并行算法

将复杂形状区域划分成多块子区域，研究发展了一种多块区域之间迎风守恒型的内边界耦合方法，实现相邻子区域解的光滑过渡，使多区耦合得到总体流场的数值解。对二维翼型跨音速流动和圆板形隆起物超音速流动等进行了分区数值计算，并将计算结果与单区计算结果和实验结果作了比较。并行分区计算引入“先进先出”的同步控制等待机制，实现了高效率并行计算，还分析了影响并行效率的主要因素。

A Lagrangian lattice Boltzmann method for Euler equations

A Lagrangian lattice Boltzmann method for solving Euler equations is proposed. The key step in formulating this method is the introduction of the displacement distribution function. The equilibrium distribution function consists of macroscopic Lagrangian variables at time steps n and n + 1. It is different from the standard lattice Boltzmann method. In this method the element, instead of each particle, is required to satisfy the basic law. The element is considered as one large particle, which results in simpler version than the corresponding Eulerian one, because the advection term disappears here. Our numerical examples successfully reproduce the classical results.

一种易于并行求解Euler方程组的分区技术

在具有复杂边界的计算区域内,求解偏微分方程组时,经常需要分区和并行计算,分区方法直接关系到数值计算的并行化程度,本文在应用时间算子分裂方法求解Euler方程组的过程中,提出了一种非常容易实现并行化计算的分区技术.

二维Euler方程的非结构网格再生成自适应方法

给出了提高二维Euler方程定常解质量的非结构网格自适应方法和模拟结果。计算了无粘激波在固壁上的反射、NAC0012翼型跨声速绕流和马赫数为3的前台阶绕流，自适应效果较好。

Euler方程的双分布函数格子Boltzmann Godunov方法

应用双分布函数系统，通过Ｇｏｄｕｎｏｖ分解，构造了一维Ｅｕｌｅｒ方程的格子Ｂｏｌｔｚｍａｎｎ算法。解决了传统格子气固有的ＧＣ问题与能量方程之间的矛盾，实现了分布函数与宏观物理量之间的一一对应。

基于CE/SE方法的二维Euler型多物质流体弹塑性问题计算

将CE/SE方法推广到二维固体流体弹塑性问题的数值计算,同时结合杂交粒子水平集方法追踪物质界面和合适的边界条件,提出一套完整的二维Euler型流体弹塑性计算方案.通过长钨杆侵彻装甲钢实验的数值模拟,对方法的精度和有效性进行验证.

全机绕流Euler方程多重网格分区计算方法

全机三维复杂形状绕流数值求解只能采用分区求解的方法，本文采用可压缩Euler方程有限体积方法以及多重网格分区方法对流场进行分区计算。数值方法采用改进的van Leer迎风型矢通量分裂格式和MUSCL方法，基于有限体积方法和迎风型矢通量分裂方法，建立一套处理子区域内分界面的耦合条件。各个子区域之间采用显式耦合条件，区域内部采用隐式格式和局部时间步长等，以加快收敛速度。计算结果飞机表面压力分布等气动力特性与实验值进行了比较，二者基本吻合。计算结果表明采用分析“V”型多重网格方法，能提高计算效率，加快收敛速度达到接近一个量级。根据全机数值计算结果和可视化结果讨论了流场背风区域旋涡的形成过程。

Euler Solution Using Adaptive Cartesian Grid With A Gridless Boundary Treatment

A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indicate the developed method is reasonable for complex flows.

CFD study of a sudden-expanding coal combustor using Euler-Euler and Euler-Lagrange models

In this study, the Euler-Euler (E-E) and Euler-Lagrange (E-L) models designed for the same chemical mechanism of heterogeneous reactions were used to predict the performance of a typical sudden-expanding coal combustor. The results showed that the current E-E model underestimated the coal burnout rate because the particle temperature fluctuation on char combustion is not adequately considered. A comparison of the E-E and E-L simulations showed the underestimation of heterogeneous chemical reaction rates by the E-E model. (C) 2010 Elsevier Ltd. All rights reserved.

Numerical Investigation of Richtmyer-Meshkov Instability Driven by Cylindrical Shocks

In this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov(RM) instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied.

Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.