An ALE mesh movement scheme for long‐term in‐flight ice accretion

The rather irregular shapes that glaze ice may grow into while accreting over the surface of an aircraft represent a major difficulty in the numerical simulation of long periods of in‐flight icing. There is a constant need for remeshing: a wasteful procedure. In the framework of ALE formulations, a mesh movement scheme is presented, in which frame and elasticity analogies are loosely coupled. The resulting deformed mesh preserves the quality of elements, especially in the near‐wall region, where accurate prediction of heat flux and shear stresses is required. The proposed scheme handles mesh deformation in a computationally efficient manner by localizing the mesh deformation. The 2D problem of ice accretion over single and multi‐element airfoils is considered here as a numerical experiment. Experimentally measured glaze ice shapes were used to evaluate the performance of the present approach. Copyright © 2011 John Wiley & Sons, Ltd.     

An ALE approach to mechano‐chemical processes in fluid–structure interactions

Mathematical modeling and simulation of fluid–structure interaction problems are in the focus of research already for a longer period. However, taking into account also chemical reactions, leading to structural changes, including changes of mechanical properties of the solid phase, is rather new but for many applications is highly important area. This paper formulates a model system for reactive flow and transport in a vessel system, the penetration of chemical substances into the solid wall. Inside the wall, reactions take place that lead to changes of volume and of the mechanical properties of the wall. Numerical algorithms are developed and used to simulate the dynamics of such a mechano‐chemical fluid–structure interaction problem. As a proof of concept scenario, plaque formation in blood vessels is chosen. The arbitrary Lagrangian Eulerian approach (ALE) is chosen to solve the systems numerically. Temporal discretization of the fully coupled monolithic model is accomplished by backward Euler scheme and spatial discretization by stabilized finite elements. The numerical approach is verified by numerical tests, and effective methods to maintain mesh qualities under large deformations are described. For realistic system parameters, the simulations show that the plaque formation in blood vessel is a long‐time effect. The time scale of the formation is in the simulation of comparable order as in reality. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulation of liquid sloshing in curved‐wall containers with arbitrary Lagrangian–Eulerian method

There are many challenges in the numerical simulation of liquid sloshing in horizontal cylinders and spherical containers using the finite element method of arbitrary Lagrangian–Eulerian (ALE) formulation: tracking the motion of the free surface with the contact points, defining the mesh velocity on the curved wall boundary and updating the computational mesh. In order to keep the contact points slipping along the curved side wall, the shape vector in each time advancement is defined to modify the kinematical boundary conditions on the free surface. A special function is introduced to automatically smooth the nodal velocities on the curved wall boundary based on the liquid nodal velocities. The elliptic partial differential equation with Dirichlet boundary conditions can directly rezone the inner nodal velocities in more than a single freedom. The incremental fractional step method is introduced to solve the finite element liquid equations. The numerical results that stemmed from the algorithm show good agreement with experimental phenomena, which demonstrates that the ALE method provides an efficient computing scheme in moving curved wall boundaries. This method can be extended to 3D cases by improving the technique to compute the shape vector. Copyright © 2007 John Wiley & Sons, Ltd.     

A stability analysis of an oscillating body located in fluid flow using automatic differentiation

This paper presents a stability analysis of an oscillating body subjected to fluid forces located in a transient incompressible viscous flow. If the body is supported by elastic springs, oscillation will begin. If the characteristic period of the body and the excited oscillating period due to fluid forces match each other, resonance can occur. Stability analysis is therefore needed to determine the nonlinear behavior of the body. This paper presents an analysis of the changing stability of bodies by the numerical computation. To implement the computation, the motion of fluid around a body is expressed by the Navier–Stokes equation described in the arbitrary Lagrangian–Eulerian form. The fluid influence on the body is discretized by the finite element method based on a mixed interpolation by the bubble function in space. The motion of the body is assumed to be expressed by the equations of motion. To evaluate stability, stability function is defined by the total energy of the oscillating body. The stability is judged according to a stability index, obtained by the use of the automatic differentiation (AD) of the stability function. AD is a derivative computation method that gives high accuracy. By the use of AD, the second‐order derivative matrix, which is needed to compute the stability index, can be obtained exactly. For the numerical studies, analyses of one degree of freedom and two degrees of freedom (2DOF) for a circular cylinder and 2DOF for a rectangular cylinder are carried out. A combination of a cylinder and supporting elastic spring can produce stable, neutral and unstable states. It is shown that the stability of the cylinder can be determined by the stability index. This paper shows new possibilities for stability analysis of bodies located in a fluid flow. Copyright © 2008 John Wiley & Sons, Ltd.     

一类自适应运动网格的ALE方法

从积分形式的二维Lagrange流体力学方程组出发,使用ENO高阶插值多项式,推广了四边形结构网格下的一阶有限体积格式,构造一类结构网格下的高精度有限体积格式.结合有效的守恒重映方法,发展一类高精度的ALE方法,并结合自适应运动网格技术,进行ALE方法的数值模拟,得到预期的效果.     

基于ALE方程的动网格膛口流场数值研究

基于ALE(Arbitrary Lagrangian-Eulerian Equation)方程的有限体积法,采用高精度Roe方法及结构化动网格,利用嵌入网格技术及动边界条件,对弹丸由膛内高压气体推动射出到完全飞高初始流场的整个过程进行了数值模拟.根据数值结果绘制了膛口流场密度和压力分布的时序图,形象地再现了膛口流场中初始激波、弓形激波及膛口冲击波,以及接触闻断、漩涡和剪切层等的动力学发展过程.结果基本反映了膛口流场的典型变化特征,为进一步研究真实膛口流场(如带化学反应、湍流等)奠定了基础.     

SALE速度重映算法的改进

在一维交错网格上基于SALE算法的速度重映策略,提出了3种动量通量的改进算法:①采用迎风斜率加修补的SUR目的;②采用minmod斜率限制器的SM目的和③采用一种新的斜率限制器加修补的SLR目的.3种目的具有二阶守恒保界的性质,同时继承了SALE算法简单高效的特点,可以直接推广到二维情况.     

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.     

On stabilized space‐time FEM for anisotropic meshes: Incompressible Navier–Stokes equations and applications to blood flow in medical devices

In complex applications, such as the analysis of hydraulic performance of blood pumps (ventricular assist devices), the Navier–Stokes equations have to be discretized on very anisotropic meshes. If stabilized finite element formulations are applied, standard definitions of the stabilization parameter are usually not appropriate to handle elements with a high aspect ratio. If, in addition, rotating objects, moving meshes, or turbulence has to be considered in the simulation, further modifications of the stabilization procedure have to be applied. In this paper, we present stabilized space‐time finite element formulations of the incompressible Navier–Stokes equations that show very good convergence properties on complex anisotropic meshes and lead to reasonable numerical accuracy in complex flows when compared with experimental data. Copyright © 2017 John Wiley & Sons, Ltd.