Numerical capture of wing tip vortex improved by mesh adaptation

This paper presents a mesh adaptation procedure linked to a finite volume solver, the goal of which is to increase the precision of the numerical simulation of a wing tip vortex flow. The adaptation scheme is applied to hexahedron meshes and hybrid meshes made up of tetrahedrons and prisms. To evaluate the ability of each type of element to capture the physics of a tip vortex, a specific test case is studied and results obtained numerically from this test case are compared with experimental results. The error estimator of the adaptation scheme is derived from a solution scalar variable. It is shown that the element anisotropy as well as the adaptation algorithms used have an impact on the precision of the solution. Adaptation of hexahedrons allows a better capture of the tip vortex far from the vortex root, even though the adaptation of those hexahedrons barely changes the number of nodes used to achieve a specified precision, contrary to the adaptation of hybrid meshes. Copyright © 2009 John Wiley & Sons, Ltd.     

A Nonconforming Arbitrary Quadrilateral Finite Element Method for Approximating Maxwell＇s Equations

The main aim of this paper is to provide convergence analysis of Quasi-Wilson nonconforming finite element to Maxwell's equations under arbitrary quadrilateral meshes. The error estimates are derived, which are the same as those for conforming elements under conventional regular meshes.     

Convergence and superconvergence analysis of a new quadratic Hermite-type triangular element on anisotropic meshes

A new quadratic Hermite-type triangular finite element is conceived to solve a class of two-dimensional second-order elliptic boundary value problems. Its error estimates on anisotropic meshes are developed. Furthermore, we verify that some conditions set to the meshes contribute to the proof of its superconvergence properties, which can improve the approximation results. Numerical examples are given to confirm our theoretical analysis.     

油气资源数值模拟的变网格交替方向特征有限元格式和分析

石油科学在有机地球化学、石油的生成、运移、聚集研究取得重大进展,在评价油气资源时,对盆地发育史尤其对流体流动规律和受热变化历史的计算是非常重要的.其数学模型是三维空间非线性偶合偏微分方程组的初边值问题.从实际出发,考虑了流体的压缩性和三维问题大规模科学与工程计算的特征, 提出了一类变网格交替方向特征有限元格式,应用变分形式、算子分裂、广义$L^2$投影、能量方法、负模估计、微分方程先验估计的理论和技巧,得到最佳阶$L^2$误差估计. 此方法已成功应用到油气资源评估数值模拟的生产实践中,成功解决了这一重要问题.     

A second order difference scheme with nonuniform rectangular meshes for nonlinear parabolic system

In this paper, a difference scheme with nonuniform meshes is proposed for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in both space and time.     

Exponential splitting time integration for pseudospectral methods on moving meshes

Moving meshes are successfully used in many fields. Here we investigate how a recently proposed approach to combine the Strang splitting method for time integration with pseudospectral spatial discretization by orthogonal polynomials can be extended to include moving meshes. A double representation of a function (by coefficients of polynomial expansion and by values at the mesh nodes associated with a suitable quadrature formula) is an essential part of the numerical integration. Before numerical implementation the original PDE is transformed into a suitable form. The approach is illustrated on the linear heat transfer equation.     

The Fourier-finite-element method with Nitsche mortaring

^** Email: bernd.heinrich{at}mathematik.tu-chemnitz.de The paper deals with a combination of the Fourier-finite-elementmethod with the Nitsche-finite-element method (as a mortar method).The approach is applied to the Dirichlet problem for the Poissonequation in 3D axisymmetric domains with non-axisymmetric data.The approximating Fourier method yields a splitting of the 3Dproblem into 2D problems on the meridian plane of the givendomain. For solving these 2D problems, the Nitsche-finite-elementmethod with non-matching meshes is applied. Some important propertiesof the approximation scheme are derived and the rate of convergencein an H¹-like norm as well as in the L₂-norm is estimated fora regular solution. Finally, some numerical results are presented.     

Feature-sensitive parameterization of polygonal meshes

This paper investigates a parameterization method for polygonal meshes which is able to improve map distortion exploiting local curvature of the surface mesh. Parametrization is an important tool in geometric modelling and computer graphics applications such as, for example, texture mapping, shape morphing, and remeshing. The paper presents a feature-sensitive scheme which is based on a stretch-minimizing strategy which iterates the shape-preserving parameterization taking into account the influence of the curvature on the mesh stretch. In particular, the main goal is to provide a distortion in the parametrization driven by the curvature directions, in such a way that strong distortion correspond to area with mean curvature approaching to zero. Computed examples demonstrate the effectiveness of the proposed method using geometric measures on angle, edge and area stretching, and illustrate the high quality of the mesh parameterizations produced.     

Adaptive variational curve smoothing based on level set method

This paper presents an adaptive method for variational curve smoothing based on level set implementation. A suitable cost functional is minimized via solving the derived Euler–Lagrangian equation, of which the discretization is conducted on unstructured triangular meshes by employing a simple and effective finite volume scheme. Through adaptive refinement of the mesh, the geometry features of the given curve can be well resolved in a cost-effective way. Various numerical experiments demonstrate the effectiveness and efficiency of the proposed approach.