常压DBD二维流体模型的FCT方法数值模拟

根据常压介质阻挡放电流体模型的物理方程,采用固定网格有限差分算法,分别用四阶和六阶相位误差FCT方法模拟求解二维流体连续方程.在均匀的初始条件下研究放电雪崩过程中电子密度的时空演化,具体分析和比较两种算法的差异.FCT方法模拟求解得出的计算结果与气体放电理论吻合较好,是一种具有较好的准确性和高精度的算法.     

A geometrically-conservative,synchronized, flux-corrected remap for arbitrary Lagrangian–Eulerian computations with nodal finite elements

This article describes a conservative synchronized remap algorithm applicable to arbitrary Lagrangian–Eulerian computations with nodal finite elements. In the proposed approach, ideas derived from flux-corrected transport (FCT) methods are extended to conservative remap. Unique to the proposed method is the direct incorporation of the geometric conservation law (GCL) in the resulting numerical scheme. It is shown here that the geometric conservation law allows the method to inherit the positivity preserving and local extrema diminishing (LED) properties typical of FCT schemes. The proposed framework is extended to the systems of equations that typically arise in meteorological and compressible flow computations. The proposed algorithm remaps the vector fields associated with these problems by means of a synchronized strategy. The present paper also complements and extends the work of the second author on nodal-based methods for shock hydrodynamics, delivering a fully integrated suite of Lagrangian/remap algorithms for computations of compressible materials under extreme load conditions. Extensive testing in one, two, and three dimensions shows that the method is robust and accurate under typical computational scenarios.     

A positivity-preserving ALE finite element scheme for convection–diffusion equations in moving domains

A new high-resolution scheme is developed for convection–diffusion problems in domains with moving boundaries. A finite element approximation of the governing equation is designed within the framework of a conservative Arbitrary Lagrangian Eulerian (ALE) formulation. An implicit flux-corrected transport (FCT) algorithm is implemented to suppress spurious undershoots and overshoots appearing in convection-dominated problems. A detailed numerical study is performed for P₁ finite element discretizations on fixed and moving meshes. Simulation results for a Taylor dispersion problem (moderate Peclet numbers) and for a convection-dominated problem (large Peclet numbers) are presented to give a flavor of practical applications.     

Failsafe flux limiting and constrained data projections for equations of gas dynamics

A new approach to flux limiting for systems of conservation laws is presented. The Galerkin finite element discretization/L² projection is equipped with a failsafe mechanism that prevents the birth and growth of spurious local extrema. Within the framework of a synchronized flux-corrected transport (FCT) algorithm, the velocity and pressure fields are constrained using node-by-node transformations from the conservative to the primitive variables. An additional correction step is included to ensure that all the quantities of interest (density, velocity, pressure) are bounded by the physically admissible low-order values. The result is a conservative and bounded scheme with low numerical diffusion. The new failsafe FCT limiter is integrated into a high-resolution finite element scheme for the Euler equations of gas dynamics. Also, bounded L² projection operators for conservative interpolation/initialization are designed. The performance of the proposed limiting strategy and the need for a posteriori control of flux-corrected solutions are illustrated by numerical examples.     

Explicit and implicit FEM-FCT algorithms with flux linearization

A new approach to the design of flux-corrected transport (FCT) algorithms for continuous (linear/multilinear) finite element approximations of convection-dominated transport problems is pursued. The algebraic flux correction paradigm is revisited, and a family of nonlinear high-resolution schemes based on Zalesak’s fully multidimensional flux limiter is considered. In order to reduce the cost of flux correction, the raw antidiffusive fluxes are linearized about an auxiliary solution computed by a high- or low-order scheme. By virtue of this linearization, the costly computation of solution-dependent correction factors is to be performed just once per time step, and there is no need for iterative defect correction if the governing equation is linear. A predictor–corrector algorithm is proposed as an alternative to the hybridization of high- and low-order fluxes. Three FEM-FCT schemes based on the Runge–Kutta, Crank–Nicolson, and backward Euler time-stepping are introduced. A detailed comparative study is performed for linear convection–diffusion equations.     

Simulation of Kelvin-Helmholtz Instability with Flux-Corrected Transport Method

The sixth-order accurate phase error flux-corrected transport numerical algorithm is introduced, and used to simulate Kelvin-Helmholtz instability. Linear growth rates of the simulation agree with the linear theories of Kelvin Helmholtz instability. It indicates the validity and accuracy of this simulation method. The method also has good capturing ability of the instability interface deformation.     

An evaluation of the FCT method for high-speed flows on structured overlapping grids

This study considers the development and assessment of a flux-corrected transport (FCT) algorithm for simulating high-speed flows on structured overlapping grids. This class of algorithm shows promise for solving some difficult highly-nonlinear problems where robustness and control of certain features, such as maintaining positive densities, is important. Complex, possibly moving, geometry is treated through the use of structured overlapping grids. Adaptive mesh refinement (AMR) is employed to ensure sharp resolution of discontinuities in an efficient manner. Improvements to the FCT algorithm are proposed for the treatment of strong rarefaction waves as well as rarefaction waves containing a sonic point. Simulation results are obtained for a set of test problems and the convergence characteristics are demonstrated and compared to a high-resolution Godunov method. The problems considered are an isolated shock, an isolated contact, a modified Sod shock tube problem, a two-shock Riemann problem, the Shu–Osher test problem, shock impingement on single cylinder, and irregular Mach reflection of a strong shock striking an inclined plane.     

Improving the Accuracy of the Fast Inverse Square Root by Modifying Newton–Raphson Corrections

Direct computation of functions using low-complexity algorithms can be applied both for hardware constraints and in systems where storage capacity is a challenge for processing a large volume of data. We present improved algorithms for fast calculation of the inverse square root function for single-precision and double-precision floating-point numbers. Higher precision is also discussed. Our approach consists in minimizing maximal errors by finding optimal magic constants and modifying the Newton–Raphson coefficients. The obtained algorithms are much more accurate than the original fast inverse square root algorithm and have similar very low computational costs.     

Optimal tracking control with zero steady-state error for time-delay systems with sinusoidal disturbances

The problem of optimal tracking control with zero steady-state error for linear time-delay systems with sinusoidal disturbances is considered. Based on the internal model principle, a disturbance compensator is constructed such that the system with external sinusoidal disturbances is transformed into an augmented system without disturbances. By introducing a sensitivity parameter and expanding power series around it, the optimal tracking control problem can be simplified into the problem of solving an infinite sum of linear optimal control series without time-delay and disturbance. The obtained optimal tracking control law with zero steady-state error consists of accurate linear state feedback terms and a time-delay compensating term, which is an infinite sum of an adjoint vector series. The accurate linear terms can be obtained by solving a Riccati matrix equation and a Sylvester equation, respectively. The compensation term can be approximately obtained through a recursive algorithm. A numerical simulation shows that the algorithm is effective and easily implemented, and the designed tracking controller is robust with respect to the sinusoidal disturbances.     

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

We numerically investigate the accuracy of two Monte Carlo algorithms originally proposed by Zimmerman [1] and Zimmerman and Adams [2] for particle transport through binary stochastic mixtures. We assess the accuracy of these algorithms using a standard suite of planar geometry incident angular flux benchmark problems and a new suite of interior source benchmark problems. In addition to comparisons of the ensemble-averaged leakage values, we compare the ensemble-averaged material scalar flux distributions. Both Monte Carlo transport algorithms robustly produce physically realistic scalar flux distributions for the benchmark transport problems examined. The base Monte Carlo algorithm reproduces the standard Levermore-Pomraning model [3] and [4] results. The improved Monte Carlo algorithm generally produces significantly more accurate leakage values and also significantly more accurate material scalar flux distributions. We also present deterministic atomic mix solutions of the benchmark problems for comparison with the benchmark and the Monte Carlo solutions. Both Monte Carlo algorithms are generally significantly more accurate than the atomic mix approximation for the benchmark suites examined.     

Error-compensating algorithms in phase-shifting interferometry: a comparison by error analysis

In this paper, two families of phase-shifting algorithms with π/2 phase steps are studied. In family I, three new algorithms are derived by using the averaging technique based on the Surrel six-sample algorithm with phase shifts of π/2. Family II includes four well-known algorithms derived by the averaging technique based on the conventional four-sample algorithm with π/2 phase steps. A polynomial model of phase-shift errors used to describe general expressions for calculation of the correct object phase via the Fourier spectra analysing method as a function of the harmonic order in the fringe signal is presented. The error-compensating properties of the algorithms in families I and II are investigated by the Fourier spectra analysing method. It is found that the averaging technique, when used in any of the algorithm with π/2 phase steps, can improve the phase-shifting algorithm property: it is insensitive to phase-shift error when the fringe signal contains the first harmonic, but it can't be used to enhance the phase-shifting algorithm properties when the fringe signal contains higher order harmonics (n2). P–V (peak–valley) phase errors are calculated by the computer simulation and tables and plots are presented, from which the algorithms in families I and II are compared. It is shown that the algorithms in family I are more insensitive to phase-shift errors when the fringe signal contains the second harmonic and the algorithms in family II are more insensitive to phase-shift errors when the fringe signal is a sinusoidal waveform.     

发射率限定辐射测温原理

辐射测温技术随着辐射测量传感器技术的进步而不断进步,已经由单波长测温发展到多波长和多波段测温,由点温测量发展到二维甚至三维温度场测量。但是在辐射测温更精确反演方面,却很难克服因发射率未知性而引起的模型构建误差。发射率行为难以确定并极大地影响了测温精度,急需发展一种具有通用性,不受发射率具体行为限制,具有较高稳定性的辐射测温方法。双波长测温适用于发射率具有灰体行为的物体温度测量,一系列的发射率补偿算法和波长选择方法均未能很好地实现通用性测量,往往直接单色测量可能误差比比色法更小。多波长测温得到广泛应用,但并不是波长越多越好,发射率模型仍然具有较大局限性。提出了发射率直接限定算法和发射率松驰限定算法来反演温度。在发射率限定条件相同时,这两种方法是等价的。发射率松驰限定算法基于最小二乘算法和松驰因子进行真温求解。推导了松驰限定法的误差传递公式,发现在保证测量信号强度的前提下,λT越小温度误差越小;发射率行为对温度相对误差具有重要影响,在相同的λT条件下,发射率随波长变化越大,在限定区间上覆盖越均匀,测量误差越小。但从直接限定算法可以看出所测波长数越多,测量误差越小。两种方法均可以看出,减少限定区间长度也可以显著地提高测量精度。     

An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

Model error is one of the key factors restricting the accuracy of numerical weather prediction(NWP). Considering the continuous evolution of the atmosphere, the observed data(ignoring the measurement error) can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers’ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.     

High order “ZIP” differencing of convective terms

The ZIP flux form for differencing the term (wv)_x, where w is a convected quantity and v is a convective velocity, is observed to be equivalent to differencing the alternative expression wv_x + wx_v using centered second order finite differences. The advantage of this form is that one class of nonlinear computational instabilities is eliminated. Based on this observation, the extension of the ZIP flux concept to arbitrarily high order accuracy is given. Computational examples show the advantage both of the ZIP flux concept itself and of its higher order forms within the context of flux-corrected transport (FCT) algorithms.     

On optimal solution error covariances in variational data assimilation problems

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters such as distributed model coefficients or boundary conditions. The equation for the optimal solution error is derived through the errors of the input data (background and observation errors), and the optimal solution error covariance operator through the input data error covariance operators, respectively. The quasi-Newton BFGS algorithm is adapted to construct the covariance matrix of the optimal solution error using the inverse Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints. Preconditioning is applied to reduce the number of iterations required by the BFGS algorithm to build a quasi-Newton approximation of the inverse Hessian. Numerical examples are presented for the one-dimensional convection–diffusion model.     

A conservative discrete compatibility-constraint low-Mach pressure-correction algorithm for time-accurate simulations of variable density flows

In this paper, we develop the discrete compatibility-constraint pressure-correction algorithm for transient simulations of variable density flows at low-Mach numbers. The constraint for the velocity field is constructed from a combination of the discrete equations of continuity and scalar (e.g. energy) transport, imposing that the newly predicted state must be compatible, in agreement with the equation of state. This way, mass and scalar conservation are guaranteed and the equation of state is exactly fulfilled at every time step. For comparison reasons, two other types of well-known pressure-correction algorithms are also used. The first class, denoted as continuity-constraint pressure-correction, is based on a constraint for the velocity field that is derived solely from the continuity equation. The second class, denoted as analytical compatibility-constraint pressure-correction, constructs the constraint from an analytical combination of the material derivative of the equation of state and the continuity and scalar equations. The algorithms are tested for three example fluid configurations: a single-fluid ideal gas, a two-fluid inert mixture and a two-fluid reacting mixture. The latter is special in the sense that the equation of state is non-linear and not everywhere differentiable. The continuity-constraint pressure-correction algorithm yields unstable solutions if density ratios are high. The analytical compatibility-constraint pressure-correction algorithm yields stable results, but the predicted states do not correspond to the equation of state. The discrete compatibility-constraint pressure-correction algorithm performs well on all test cases: the simulation results are stable and exactly match the equation of state.     

Optimal UAV Formation Tracking Control with Dynamic Leading Velocity and Network-Induced Delays

With the rapid development of UAV technology, the research of optimal UAV formation tracking has been extensively studied. However, the high maneuverability and dynamic network topology of UAVs make formation tracking control much more difficult. In this paper, considering the highly dynamic features of uncertain time-varying leader velocity and network-induced delays, the optimal formation control algorithms for both near-equilibrium and general dynamic control cases are developed. First, the discrete-time error dynamics of UAV leader–follower models are analyzed. Next, a linear quadratic optimization problem is formulated with the objective of minimizing the errors between the desired and actual states consisting of velocity and position information of the follower. The optimal formation tracking problem of near-equilibrium cases is addressed by using a backward recursion method, and then the results are further extended to the general dynamic case where the leader moves at an uncertain time-varying velocity. Additionally, angle deviations are investigated, and it is proved that the similar state dynamics to the general case can be derived and the principle of control strategy design can be maintained. By using actual real-world data, numerical experiments verify the effectiveness of the proposed optimal UAV formation-tracking algorithm in both near-equilibrium and dynamic control cases in the presence of network-induced delays.     

Rayleigh-Taylor和Richtmyer-Meshkov不稳定性的FCT方法数值模拟

介绍了二维流体力学不稳定性程序的FCT数值方法,数值模拟Rayleigh-Taylor和Richt-myer-Meshkov流体不稳定性,在线性阶段,与线性理论符合很好;在非线性阶段,与俄罗斯激波管实验的计算结果符合很好。计算结果表明:FCT方法有较高计算精度,给出了不稳定性发展的好的图象,适合于ICF烧蚀和内爆流体不稳定性问题的计算。     

计算机控制光学抛光驻留时间求解中两类优化算法的分析

建立了基于矩阵计算的驻留时间计算模型,根据实际加工要求建立了最小二乘和最佳一致逼近最优化求解数学模型,总结了两类优化问题的求解方法。根据自研数学解法器,利用数值计算分析了这两类算法的计算特点。仿真结果显示,两种自研算法具有较高的计算精度,最小二乘逼近算法计算效率有待提高,对外界扰动和计算模型等误差不敏感,最佳一致逼近算法计算效率较高,但对误差比较敏感。实际加工时,如果面形精度已经比较高时,建议多采用最小二乘逼近算法。     

3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wire-plate ESP

The present study attempts to develop a detailed numerical approach and a simulation procedure to predict the motion of gas, ions and particles inside a simple parallel plate channel containing a single corona wire. A hybrid Finite Element (FEM)-Flux Corrected Transport (FCT)-Finite Volume (FVM) method is used: the FEM–FCT numerical algorithm is applied for modeling the steady-state corona discharge, while the turbulent gas flow and the particle motion under electrostatic forces are modeled using the commercial CFD code FLUENT. Calculations for the gas flow are carried out by solving the Reynolds-averaged Navier–Stokes equations and turbulence is modeled using the k–? turbulence model. An additional source term is added to the gas flow equation to include the effect of the electric field, obtained by solving a coupled system of the electric field and charge transport equations using User-Defined Functions (UDFs). The particle phase is simulated based on the Lagrangian approach, where a large number of particles is traced with their motion affected by the gas flow and electrostatic forces using the Discrete Phase Model (DPM) in FLUENT. The developed model is useful to gain insight into the particle collection phenomena that take place inside an ESP.