POSITIVELY CONSERVATIVE HIGH-RESOLUTION CONVECTION SCHEMES FOR UNSTRUCTURED ELEMENTS

Despite their geometric flexibility, unstructured mesh schemes for compressible gas dynamics do not usually resolve captured shocks and contact discontinuities as well as corresponding structured mesh schemes. The main reason for this appears to be the difficulty in constructing analogous extensions to higher-order accuracy. This issue is addressed in some detail and a new, compact stencil, Maximum Limited Gradient (MLG) reconstruction technique is presented for unstructured elements. The MLG reconstruction turns out to be a multidimensional analogue of the one-dimensional Superbee slope. We then describe a simple and robust extension to systems of equations, which does not require any diagonalization of flux Jacobian matrices. An application to a blast wave hazard prediction problem is presented using the wave-by-wave extension of the MLG limiter to the Euler equations.     

粘弹流动的间断有限元模拟

针对传统有限元法求解Oldroyd-B本构方程时需加入稳定化方案的缺点,本文基于非结构网格给出了统一间断有限元求解框架．该框架包含采用IPDG(interior penalty discontinuous Galerkin)求解质量方程和动量方程,与采用RKDG(Runge-Kutta discontinuous Galerkin)求解本构方程这两个核心．数值结果表明：该方法在求解Oldroyd-B本构方程时无需加入稳定化方案,实施比有限元法简便,且具有较高的计算精度,可有效地模拟包含应力奇异点的复杂粘弹流动问题,进而揭示非牛顿粘弹流动的基本特征．     

UNIFIED CONSTRUCTION OF FINITE ELEMENT AND FINITE VOLUME DISCRETIZATIONS FOR COMPRESSIBLE FLOWS

A framework for the construction of node-centred schemes to solve the compressible Euler and Navier–Stokes equations is presented. The metric quantities are derived by exploiting some properties of C⁰ finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated.     

基于通量非结构网格有限体积法的Level Set方程求解

在非结构网格上,采用基于通量的格心有限体积法求解Level Set方程,并给出了其数值离散格式.对Zalesak圆盘、旋转收缩圆及圆面剪切三个经典界面运动问题进行了数值模拟,其质量盈亏量与收敛阶的计算结果表明,该方法克服了传统数值方法造成的质量不守恒的缺点,能准确有效地求解拓扑结构发生变化的复杂运动界面问题,且计算量较格点格式大为减少.     

Anisotropic mesh optimization and its application in adaptivity

The construction of solution-adapted meshes is addressed within an optimization framework. An approximation of the second spatial derivative of the solution is used to get a suitable metric in the computational domain. A mesh quality is proposed and optimized under this metric, accounting for both the shape and the size of the elements. For this purpose, a topological and geometrical mesh improvement method of high generality is introduced. It is shown that the adaptive algorithm that results recovers optimal convergence rates in singular problems, and that it captures boundary and internal layers in convection-dominated problems. Several important implementation issues are discussed. © 1997 John Wiley & Sons, Ltd.     

Nucleation Crystallography of Ni Grains on CrFeNb Inoculants Investigated by Edge‐to‐Edge Matching Model in an IN718 Superalloy

In this work, the nucleation crystallography of CrFeNb intermetallic particles as a grain refiner for Ni‐based IN718 superalloys is studied using Edge‐to‐Edge Matching model. Three distinguishable orientation relationships between CrFeNb intermetallic particles and Ni grains are well predicted: , (111)_Ni 1.28° from (0004)_CrFeNb, , (111)_Ni 1.32° from _CrFeNb, and _Ni//[0001]_CrFeNb, (111)_Ni 0.72° from _CrFeNb. The results indicate that CrFeNb intermetallic particles have a strong nucleation potency as an effective grain refiner for Ni‐based superalloy and the existence of semi‐coherent interfaces between the CrFeNb intermetallic particles and Ni grains. Furthermore, the IN718 superalloy is used to experimentally validate the grain refinement effect of CrFeNb intermetallic particles, showing that its grain size is obviously refined from 8.60 to 1.23 mm. And, the corresponding heterogeneous nucleation mechanism of grain refinement at the atomic level is further identified.

     

非结构网格上多介质可压缩流模拟的RKDG方法

针对一般方法模拟具有运动界面的多介质可压缩流动问题计算量大、实施复杂的缺点,本文发展了一种基于非结构网格的数值模拟方法.该方法采用RKDG(RungeKutta Discontinuous Galerkin)方法的弱形式求解Euler方程,用强形式求解可压缩流场模拟中的Level Set方程,并用Simple Fix方法耦合两套方程的数值求解.二维多介质可压缩流的模拟表明:该方法成功地抑制了界面附近的非物理振荡,计算量小、实施简单,并可有效求解具有运动界面的多介质可压缩流动问题.