An efficient edge based data structure for the compressible Reynolds-averaged Navier–Stokes equations on hybrid unstructured meshes

An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

大口径光学元件装夹转运结构设计及分析

为了实现大口径光学元件的安全装夹、转运,通过光学元件开槽与不开槽两种装夹方式的分析,得出开槽夹紧转运方式将带来微裂纹、应力集中、成本高等缺陷,提出了利用摩擦力克服光学零件的重力和惯性力的低应力装夹转运方案。通过对光学元件低应力夹紧结构设计,并利用有限元分析方法,得到不开槽装夹方式下,光学元件的最大主应力为1.11 MPa,最大切应力为0.73 MPa,远低于光学元件破坏的强度极限,且受力均匀,无应力集中现象。     

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.     

Time-dependent Ginzburg–Landau equations for multi-gap superconductors

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finite-element technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

X射线光刻掩模背面刻蚀过程中的形变仿真

开发了理论模型以验证有限元方法用于X射线光刻掩模刻蚀过程数值仿真的正确性。利用相同的有限元技术，对X射线光刻掩模的背面开窗、Si片刻蚀过程进行数值仿真。结果表明，图形区域的最大平面内形变(IPD)出现在上、下边缘处，最大非平面形变(OPD)出现在左、右边缘处。此外对Si片单载荷步刻蚀和多载荷步刻蚀的仿真进行比较，结果表明图形区域最终的形变量与Si片刻蚀的过程无关。     

基于有限状态的全周期序列混沌映射的研究

在有限长度的数字计算机中，混沌迭代序列是一个有限周期序列，其相关性能远远低于理想序列。基于skew tent映射，提出一种离散化的有限状态混沌映射，它允许精确的数值计算，没有舍入误差，通过选择合适的参数，映射能产生全周期长度的序列。仿真实验表明，归一化的序列平均周期对计算机精度不敏感，生成的二进制序列具有良好的相关性能。     

固体力学有限元体系的结构拓扑变化理论

本文是文[1]的继续.文[1]提出了杆件系统的结构拓扑变化理论和拓扑变化法本文将这一理论和方法推进到连续体有限元体系;且在此基础上揭示出有限元体系的一个新性质,称为基本位移之梯度的正交性定理,从而给出一套设计敏度的显式表达式,可直接用于计算.