Analysis of the anisotropy of group velocity error due to spatial finite difference schemes from the solution of the 2D linear Euler equations

Numerical differencing schemes are subject to dispersive and dissipative errors, which in one dimension, are functions of a wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of the wave. For the Euler equations, the direction of flow and flow velocity are also important. Spectral analysis was used to predict the error in magnitude and direction of the group velocity of vorticity–entropy and acoustic waves in the solution of the linearised Euler equations in a two‐dimensional Cartesian space. The anisotropy in these errors, for three schemes, were studied as a function of the wavenumber, wave direction, mean flow direction and mean flow Mach number. Numerical experiments were run to provide confirmation of the developed theory. Copyright © 2012 John Wiley & Sons, Ltd.     

Discrete filter operators for large‐eddy simulation using high‐order spectral difference methods

The combination of a high‐order unstructured spectral difference (SD) spatial discretization scheme with sub‐grid scale (SGS) modeling for large‐eddy simulation is investigated with particular focus on the consistent implementation of a structural mixed model based on the scale similarity hypothesis. The difficult task of deriving a consistent formulation for the discrete filter within the SD element of arbitrary order led to the development of a new class of three‐dimensional constrained discrete filters. The discrete filters satisfy a set of selected criteria and are completely local within the SD element. Their weights can be automatically computed at run time from the number of solution points within each element and the expected filter cutoff length scale. The novel discrete filters can be applied to any SGS model involving explicit filtering and to a broad class of high‐order discontinuous finite element numerical schemes. The code is applied to the computation of turbulent channel flows at three Reynolds numbers, namely Re_τ = 180, 395, and 590 (based on the friction velocity u_τ and channel half‐width δ). Results from computations with and without the SGS model are compared against results from direct numerical simulation. The numerical experiments suggest that the results are sensitive to the use of the SGS model, even when a high‐order numerical scheme is used, especially when the grid resolution is kept relatively low and mostly in terms of resolved Reynolds stresses. Results obtained using existing filters based on the projection of the solution over lower‐order polynomial bases are also shown and demonstrate that these filters are inadequate for SGS modeling purposes, mostly because of their inability to enforce the selected cutoff length scale with sufficient accuracy. The use of the similarity mixed formulation proved to be particularly accurate in reproducing SGS interactions, confirming that its well‐known potential can be realized in conjunction with state‐of‐the‐art high‐order numerical schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Liouville–Green (WKB) asymptotics for almost-diagonal linear second-order matrix difference equations

A Liouville–Green (or WKB) asymptotic approximation theory is developed for a class of almost-diagonal (‘asymptotically diagonal’) linear second-order matrix difference equations. Rigorous and explicitly computable bounds for the error terms are obtained, the asymptotics being made with respect to both, the index and some parameter affecting the equation. The case of the associated inhomogeneous equations is also considered in detail. Some examples and a number of applications are presented for the purpose of illustration.     

三阶柯西差分方程在几类群上的解

在几类群上讨论了三阶柯西差分方程解的存在性问题,将二阶柯西差分方程的已有结论进一步推广到三阶的情况,并给出在不同群上的一般解.     

New classes of second order difference equations solvable by factorization method

Under some assumptions we find a general solution of the factorization problem for a family of second order difference equations.     

Computational modelling of multi-material energetic materials and systems

ABSTRACT

In this paper, we present a systematic roadmap for developing a robust and parallel multi-material reactive hydrodynamic solver that integrates historically stable algorithms with new and current modern methods to solve explosive system design problems. The Ghost Fluid Method and Riemann solvers were used to enforce appropriate interface boundary conditions. Improved performance in terms of computational work and convergence properties was achieved by modifying a local node sorting strategy that decouples ghost nodes, allowing us to set material boundary conditions via an explicit procedure, removing the need to solve a coupled system of equations numerically. The locality and explicit nature of the node sorting concept allows for greater levels of parallelism and lower computational cost when populating ghost nodes. Non-linear numerical issues endemic to the use of real Equations of State in hydro-codes were resolved by using more thermodynamically consistent forms allowing us to accurately resolve large density gradients associated with high energy detonation problems at material interfaces. Pre-computed volume tables were implemented adding to the robustness of the solver base.     

生产率差异与企业对外直接投资进入模式选择

基于企业异质性视角,借鉴演化博弈理论探究企业通过OFDI“走出去”时的跨国并购方和标的方在全要素生产率上的差异对企业OFDI进入策略选择的影响机制。利用Hotelling模型构造资本密集型企业与劳动密集型企业OFDI进入策略选择博弈模型,讨论两类企业OFDI进入方式决策在并购双方生产率差异变化之下的变迁机理。研究发现:当并购方和被并购方生产率差异较小时,市场达到两类企业都倾向于跨国并购策略的演化稳定状态;当并购双方生产率差异较大时,企业的生产要素密集度及其结构对其OFDI进入模式决策具有重要的作用,知识或技术密集度较高的资本密集型企业与综合实力强势的部分劳动密集型企业采取跨国并购战略,而另一部分劳动密集型企业选择绿地新建方式进入国际市场。即企业OFDI进入策略选择因其所属的行业生产要素密集度及其结构不同而具有差异性。研究结论在一定程度上弥补了现有研究的不足,为以后的研究工作提供一定的理论参考。     

任意高差的多档输电线动刚度理论建模

针对目前多档输电线动力特性研究中存在的不足,将任意一档导线视为子结构并基于现有的索振动理论获得了其动张力;利用相邻两档导线的动张力建立了悬垂绝缘子串绕其悬挂点摆动的动力学方程;综合每一档导线的振动方程以及悬垂绝缘子串的摆动方程建立了两档及三档输电线的动力学方程,求解得到由端部位移激励产生的动刚度;通过对动刚度进行分析得到了多档输电线的固有频率以及模态的理论表达形式;建立了小高差的两档及三档导线的有限元模型,理论分析结果与有限元结果一致,验证了理论公式的正确性。本文提出的动刚度理论对于研究多档输电线的动态响应具有重要的应用价值。