Minimization of the Truncation Error by Grid Adaptation

A new grid adaptation strategy, which minimizes the truncation error of a pth-order finite difference approximation, is proposed. The main idea of the method is based on the observation that the global truncation error associated with discretization on nonuniform meshes can be minimized if the interior grid points are redistributed in an optimal sequence. The method does not explicitly require the truncation error estimate, and at the same time, it allows one to increase the design order of approximation globally by one, so that the same finite difference operator reveals superconvergence properties on the optimal grid. Another very important characteristic of the method is that if the differential operator and the metric coefficients are evaluated identically by some hybrid approximation, then the single optimal grid generator can be employed in the entire computational domain independently of points where the hybrid discretization switches from one approximation to another. Generalization of the present method to multiple dimensions is presented. Numerical calculations of several one-dimensional and one two-dimensional test examples demonstrate the performance of the method and corroborate the theoretical results.     

自动亮度控制对微光电视系统强光适应性的影响

定量分析了自动亮度控制对微光电视系统强光适应性的影响。结合系统信号响应特性,建立了自动亮度控制作用后强光能量与系统成像对比度的关系模型;充分考虑系统动态范围、增益特性、灰度量化等因素,建立了自动亮度控制电路作用后系统响应特性的定量表征模型。基于上述模型,建立了引入自动亮度控制后强光作用微光系统成像的数字仿真模型,并基于模拟输出图像定量分析了不同能量强光对系统侦察性能的影响。理论分析及实验仿真结果表明：自动亮度控制的引入,能够扩大微光系统的动态范围,增强微光电视系统的适用性,但同时导致系统随着强光光亮度增大,成像灰度及对比度下降,侦察性能下降。     

A Product Theorem for Markov Chains with Application to PF-Queueing Networks

Queueing networks in random environments represent more realistic models of computer and telecommunication systems than classical product form networks. This is due to the fact that network behaviour often depends on human activities which may vary according to daytime dependent behavioural patterns as well as physiological and mental indexes. In this paper we establish a product connection theorem for Markov chains which contains some corresponding results for spatial processes as well as for queueing networks in random environment as special cases. We demonstrate how our results can be applied to construct an adequate model for wireless networks with hook up capacity.     

Adaptation of the Experimental Background (ATEB) Method in Voltammetric Determination of Thujone in Herbal Matrices

In this work, a new baseline correction method, named the Adaptation of The Experimental Background (ATEB), based on the subtraction of the blank sample signal (registered for solution without an analyte, for example a supporting electrolyte), was introduced. However, the method was something more than the simple subtraction of the blank sample signal. An innovation of the algorithm consisted in improving of the blank sample signal through application of the polynomials. Operation of the algorithm was demonstrated in determination of thujone in the synthetic and real samples. The synthetic samples were composed of two different mixtures of the quasi‐absinthe herbal matrices spiked with 0.7–14 mg L⁻¹ of thujone. The measurements were conducted with or without presence of Cu²⁺, which is an interfering agent originating from production of absinthe like alcoholic beverages. The real sample was Rodnik's absinthe, likewise spiked with thujone. Application of the ATEB method enabled calculation of the calibration lines with very good correlation (not lower than 0.997).     

A high‐order flux reconstruction adaptive mesh refinement method for magnetohydrodynamics on unstructured grids

We report our recent development of the high‐order flux reconstruction adaptive mesh refinement (AMR) method for magnetohydrodynamics (MHD). The resulted framework features a shock‐capturing duo of AMR and artificial resistivity (AR), which can robustly capture shocks and rotational and contact discontinuities with a fraction of the cell counts that are usually required. In our previous paper, 36 we have presented a shock‐capturing framework on hydrodynamic problems with artificial diffusivity and AMR. Our AMR approach features a tree‐free, direct‐addressing approach in retrieving data across multiple levels of refinement. In this article, we report an extension to MHD systems that retains the flexibility of using unstructured grids. The challenges due to complex shock structures and divergence‐free constraint of magnetic field are more difficult to deal with than those of hydrodynamic systems. The accuracy of our solver hinges on 2 properties to achieve high‐order accuracy on MHD systems: removing the divergence error thoroughly and resolving discontinuities accurately. A hyperbolic divergence cleaning method with multiple subiterations is used for the first task. This method drives away the divergence error and preserves conservative forms of the governing equations. The subiteration can be accelerated by absorbing a pseudo time step into the wave speed coefficient, therefore enjoys a relaxed CFL condition. The AMR method rallies multiple levels of refined cells around various shock discontinuities, and it coordinates with the AR method to obtain sharp shock profiles. The physically consistent AR method localizes discontinuities and damps the spurious oscillation arising in the curl of the magnetic field. The effectiveness of the AMR and AR combination is demonstrated to be much more powerful than simply adding AR on finer and finer mesh, since the AMR steeply reduces the required amount of AR and confines the added artificial diffusivity and resistivity to a narrower and narrower region. We are able to verify the designed high‐order accuracy in space by using smooth flow test problems on unstructured grids. The efficiency and robustness of this framework are fully demonstrated through a number of two‐dimensional nonsmooth ideal MHD tests. We also successfully demonstrate that the AMR method can help significantly save computational cost for the Orszag‐Tang vortex problem.     

An h-adaptive solution of the spherical blast wave problem

Shock waves and contact discontinuities usually appear in compressible flows, requiring a fine mesh in order to achieve an acceptable accuracy of the numerical solution. The usage of a mesh adaptation strategy is convenient as uniform refinement of the whole mesh becomes prohibitive in three-dimensional (3D) problems. An unsteady h-adaptive strategy for unstructured finite element meshes is introduced. Non-conformity of the refined mesh and a bounded decrease in the geometrical quality of the elements are some features of the refinement algorithm. A 3D extension of the well-known refinement constraint for 2D meshes is used to enforce a smooth size transition among neighbour elements with different levels of refinement. A density-based gradient indicator is used to track discontinuities. The solution procedure is partially parallelised, i.e. the inviscid flow equations are solved in parallel with a finite element SUPG formulation with shock capturing terms while the adaptation of the mesh is sequentially performed. Results are presented for a spherical blast wave driven by a point-like explosion with an initial pressure jump of 10⁵ atmospheres. The adapted solution is compared to that computed on a fixed mesh. Also, the results provided by the theory of self-similar solutions are considered for the analysis. In this particular problem, adapting the mesh to the solution accounts for approximately 4% of the total simulation time and the refinement algorithm scales almost linearly with the size of the problem.     

On the impact of anisotropic mesh adaptation on computational wind engineering

This paper addresses the critical issue of the accuracy of CFD predictions for wind engineering. Flows around the Silsoe Cube, a high‐rise building (the Jin Mao Tower), and a low‐rise large‐span building (the Pudong International Airport) are computed with the Navier–Stokes solver FENSAP and compared with measurements. Computations are carried out for two wind directions, by solving the steady‐state ensemble‐averaged Navier–Stokes equations with the Spalart–Allmaras one‐equation turbulence model. Pressure coefficients compare well with wind tunnel experiments and the accuracy of the flow solutions is further improved via an automatic mesh adaptation that dynamically places grid points where the flow physics require them, while keeping the number of unknowns and solution time substantially at the same level. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive finite elements with large aspect ratio for mass transport in electroosmosis and pressure‐driven microflows

A space–time adaptive method is presented for the numerical simulation of mass transport in electroosmotic and pressure‐driven microflows in two space dimensions. The method uses finite elements with large aspect ratio, which allows the electroosmotic flow and the mass transport to be solved accurately despite the presence of strong boundary layers. The unknowns are the external electric potential, the electrical double layer potential, the velocity field and the sample concentration. Continuous piecewise linear stabilized finite elements with large aspect ratio and the Crank–Nicolson scheme are used for the space and time discretization of the concentration equation. Numerical results are presented showing the efficiency of this approach, first in a straight channel, then in crossing and multiple T‐form configuration channels. Copyright © 2009 John Wiley & Sons, Ltd.     

An hp‐adaptive unstructured finite volume solver for compressible flows

The idea of hp‐adaptation, which has originally been developed for compact schemes (such as finite element methods), suggests an adaptation scheme using a mixture of mesh refinement and order enrichment based on the smoothness of the solution to obtain an accurate solution efficiently. In this paper, we develop an hp‐adaptation framework for unstructured finite volume methods using residual‐based and adjoint‐based error indicators. For the residual‐based error indicator, we use a higher‐order discrete operator to estimate the truncation error, whereas this estimate is weighted by the solution of the discrete adjoint problem for an output of interest to form the adaptation indicator for adjoint‐based adaptations. We perform our adaptation by local subdivision of cells with nonconforming interfaces allowed and local reconstruction of higher‐order polynomials for solution approximations. We present our results for two‐dimensional compressible flow problems including subsonic inviscid, transonic inviscid, and subsonic laminar flow around the NACA 0012 airfoil and also turbulent flow over a flat plate. Our numerical results suggest the efficiency and accuracy advantages of adjoint‐based hp‐adaptations over uniform refinement and also over residual‐based adaptation for flows with and without singularities.     

Dynamic adaptation for parabolic equations

A dynamic adaptation method is presented that is based on the idea of using an arbitrary time-dependent system of coordinates that moves at a velocity determined by the unknown solution. Using some model problems as examples, the generation of grids that adapt to the solution is considered for parabolic equations. Among these problems are the nonlinear heat transfer problem concerning the formation of stationary and moving temperature fronts and the convection-diffusion problems described by the nonlinear Burgers and Buckley-Leverette equations. A detailed analysis of differential approximations and numerical results shows that the idea of using an arbitrary time-dependent system of coordinates for adapted grid generation in combination with the principle of quasi-stationarity makes the dynamic adaptation method universal, effective, and algorithmically simple. The universality is achieved due to the use of an arbitrary time-dependent system of coordinates that moves at a velocity determined by the unknown solution. This universal approach makes it possible to generate adapted grids for time-dependent problems of mathematical physics with various mathematical features. Among these features are large gradients, propagation of weak and strong discontinuities in nonlinear transport and heat transfer problems, and moving contact and free boundaries in fluid dynamics. The efficiency is determined by automatically fitting the velocity of the moving nodes to the dynamics of the solution. The close relationship between the adaptation mechanism and the structure of the parabolic equations allows one to automatically control the nodes’ motion so that their trajectories do not intersect. This mechanism can be applied to all parabolic equations in contrast to the hyperbolic equations, which do not include repulsive components. The simplicity of the algorithm is achieved due to the general approach to the adaptive grid generation, which is independent of the form and type of the differential equations.