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.     

UNSTRUCTURED TETRAHEDRAL MESH GENERATION FOR THREE-DIMENSIONAL VISCOUS FLOWS

A method of generating general tetrahedral meshes suitable for use in viscous flow simulations is proposed. The approach which is followed consists of the initial generation of a number of unstructured layers of highly stretched elements, in the vicinity of solid walls, followed by the discretisation of the remainder of the domain, by a standard advancing front procedure. The numerical performance of the proposed methodology is demonstrated by the generation of meshes suitable for viscous flow analysis over a number of three-dimensional aerodynamic configurations of current practical interest.     

OPTIMIZATION STRATEGIES IN UNSTRUCTURED MESH GENERATION

We propose a new optimization strategy for unstructured meshes that, when coupled with existing automatic generators, produces meshes of high quality for arbitrary domains in 3-D. Our optimizer is based upon a non-differentiable definition of the quality of the mesh which is natural for finite element or finite volume users: the quality of the worst element in the mesh. The dimension of the optimization space is made tractable by restricting, at each iteration, to a suitable neighbourhood of the worst element. Both geometrical (node repositioning) and topological (reconnection) operations are performed. It turns out that the repositioning method is advantageous with respect to both the usual node-by-node techniques and the more recent differentiable optimization methods. Several examples are included that illustrate the efficiency of the optimizer.     

Mesh generation for aerospace applications

In recent years there has been much research activity in the field of compressible flow simulation for aerodynamic applications. In the 1970’s and 1980’s the advances in the numerical solution of the Full Potential and Euler equations made, in principle, the inviscid flow simulation around complex aerodynamic shapes possible. At this stage much attention was focused on methods capable of generating meshes on which such calculations could be performed. In this paper an overview is presented of some techniques which have been developed to generate meshes for aerospace applications. Structured mesh generation techniques are discussed and their application to complicated shapes utilising the multiblock approach is highlighted. Unstructured mesh generation methods are also discussed with particular emphasis given to the Delaunay triangulation method. Finally, the advantages and disadvantages of the structured and unstructured approaches are discussed and new work is presented which attempts to utilise both these approaches in an efficient and flexible manner. An erratum to this article is available at .     

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．