A well deliverability model for non-Darcian flow in geothermal reservoirs

A new numerical algorithm is proposed to estimate the deliverability of a geothermal well. The mathematical model assumes a single-component fluid. The model accounts for both the phase change phenomenon and the non-Darcian behavior of the flow. The contemporaneous presence of both effects has to the authors’ knowledge never been fully taken into account. Provided that the numerical solution is based on a finite differences or finite volumes method, the numerical code we developed (called DNDmultiphase) can be plugged as an additional module into existing codes devoted to simulations of a whole reservoir (such as TOUGH2 or HYDROTHERM).     

Verification of a stochastic diffusion gas model

The advantages of the model under consideration are clear mathematical justification, logical simplicity, and flexibility. A stochastic algorithm for CUDA architecture aimed at the numerical solution of a three-dimensional problem in a phase space for this model is implemented. The validity of conservation laws for the stochastic gas model is shown. The linear and nonlinear problems are compared numerically.     

Solving the Dynamic Optimal Set Partitioning Problem with Arrangement of Centers of Subsets

A mathematical model is presented for the dynamic problem of optimal partitioning of a set from a space Rⁿ with arrangement of centers of subsets under joint constraints on the partition and phase variable. A method is described that solves this problem and synthesizes the essentials of the theory of continuous partitioning problems and optimal control theory for dynamic systems. A numerical algorithm for solving the problem and an analysis of the results of computational experiments are presented.     

The Shock-Wave Structure in a Gas−Particle Mixture with Chaotic Pressure

We consider the propagation of a shock wave in a mixture of a gas and fine solid particles with allowance for the difference in their velocities and the availability of the proper pressure of the phase of particles; here, equations of the Anderson type and others are used. We propose an approximate mathematical model of the flow; in this model, the dependence of the pressure of the first (gaseous) phase from the particles’ volume-concentration can be ignored, but the terms that present the phase volume-concentration multiplied by the pressure gradient of the gas are taken into account. It turns out that with this representation of the equation of state, the mathematical model has the hyperbolic type. For this system of equations of mechanics of heterogeneous media, we carry out the classification of the types of shock waves implemented in the considered mixture. The presented statements about the types are illustrated by numerical computations in stationary and nonstationary formulations; for this purpose, the numerical method of the TVD type is developed.     

Contribution of simulation to the optimization of inspection plans for multi-stage manufacturing systems

In this paper we develop a new mathematical model to optimize inspection plans for multi-stage manufacturing systems with possible misclassification errors. The presented model minimizes total inspection related costs while still assuring a required output quality. Because of the complexity of the proposed mathematical model, a simulation algorithm is presented to model the multistage manufacturing system subject to inspection and to estimate the resulting inspection costs. We use the popular Arena simulation software to implement our simulation algorithm and then we utilize OptQuest, Arena’s built-in optimization package, to find the optimal inspection plan. Finally, a numerical example is presented and simulation experiments are also conducted in order to examine the effects of several model parameters.     

Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics

We deeply researched into the asymptotic behaviour of a numerical method adapted for the solution of mathematical model of hematopoiesis which describes the dynamics of a stem cell population. We investigated the stationary solutions of the original model by their numerical approximation: we proved the existence of a numerical stationary solution that provides a good approximation to the nontrivial equilibrium solution of the problem. Also, we presented a numerical simulation which confirms this behaviour.     

On Reducing Numerical Complexity of Complex Robot Dynamics

An algorithm for the reduction of the numerical complexity of the analytical expressions participating in the dynamic model of robotic mechanism is a necessary part of the process of mathematical modelling of complex robotic mechanisms in symbolic form. Decomposition of the polynomial expressions into the products is a basic part of the algorithm for reducing the number of numerical operations in the analytical expressions of the robotic mechanisms dynamic models. The mathematical background for the data structures as well as the algorithm for decomposition of the polynomial expressions is developed and described in detail. The procedure for the reduction of the numerical complexity is illustrated by an example of the anthropomorphic locomotion configuration with fourteen degrees of freedom, and the obtained results are presented. The emphasis was placed on the procedure for decomposition of the expressions into the products because this procedure gives additional reduction in the number of mathematical operations.     

加工时间可控的炼钢调度问题两阶段模型及优化算法

炼钢-精炼-连铸是钢铁产品的关键生产工序,其有效的调度对生产过程中减少热能消耗、提高生产效率具有重要意义.根据生产过程中工序加工时间可控性和主要工艺约束提出了分散搜索(scattcr scarch,SS)算法和数学规划相结合的两阶段求解算法.第1阶段应用SS算法基于各阶段正常的加工时间,确定炼钢-精炼生产阶段各设备的加工炉次集和各炉次的加工顺序.第2阶段将SS求得的解转化为时间约束网络图,建立了以炉次等待设备时间和设备等待炉次时间及最大完成时间最小为调度目标,工序加工时间可控的混合整数规划模型,应用CPLEX求解模型确定各炉次的加工时间和开始时间.基于国内某钢铁企业炼钢-精炼-连铸生产过程的实绩生成了14个不同规模的测试案例,对钢厂生产实绩效果与本文两阶段求解算法的优化效果进行了对比,分析了不同等待时间权重对两阶段算法性能的影响,并与采用遗传局域搜索(gcnctic local search,GLS)算法与数学规划相结合的求解算法的优化效果进行了比较.实验结果表明本文给出的模型和两阶段求解算法对加工时间可控的炼钢-精炼-连铸调度问题的优化效果很好.     

量子搜索算法的多相位关系研究

假设给定一个总数为N的无序数据库,极其复杂的计算使得几乎不可能建立一个精确的数学公式来描述这个结论:在二维复子空间中,对于一个等幅分布的初始态,存在两个定义在实数域上的相位旋转角集合以使得唯一的目标态能以100%的成功概率找到;文中采取了一种近似的计算方法,通过归纳法推导出了多相位匹配方程.倘若其中一个相位旋转角集合中的元素个数j相对于N(N足够大)较小,则该方程就能保证唯一的目标态以较高的成功概率找到.接着,通过文中推导出的一个递推关系式,对任意给定的j>2,分析了Long算法的计算复杂性.最后,通过一些数值模拟的实例进一步验证了多相位匹配方程的有效性.     

Robust self-tuning control based on discrete-time sliding mode for auto-regressive mathematical model in the presence of unmodelled dynamics

In this paper, we propose a new robust self-tuning control, called the generalized minimum variance αl-equivalent selftuning control (GMVSTC-αl) for the linear timevarying (LTV) systems, which can be described by the discrete-time auto-regressive exogenous (ARX) mathematical model in the presence of unmodelled dynamics. The estimation of the parameters contained in this mathematical model is made on the basis of the proposed modified recursive least squares (m-RLS) parametric estimation algorithm with dead zone and forgetting factor. The stability analysis of the proposed parametric estimation algorithm m-RLS is treated on the basis of a Lyapunov function. A numerical simulation example is used to prove the performances and the effectiveness of the explicit scheme of the proposed robust self-tuning control GMVSTC-αl.     

Numerical simulations of the Boussinesq equation by He's variational iteration method

In this paper, we present a reliable algorithm to study the well-known model of nonlinear dispersive waves proposed by Boussinesq. We solve the Cauchy problem of Boussinesq equation using variational iteration method (VIM). The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that VIM is a powerful mathematical tool for solving nonlinear problems.     

Online hierarchical scheduling: An approach using mathematical programming

This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of m machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize the makespan, i.e., the maximum load of all machines. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both the algorithm and the lower bound are based on solutions of mathematical programming. For any given m, our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any m, and an improved algorithm with better competitive ratios of 2.333 and 2.610 for m=4 and 5, respectively.     

On numerical simulation of flow through oil filters

This paper concerns numerical simulation of flow through oil filters. Oil filters consist of filter housing (filter box), and a porous filtering medium, which completely separates the inlet from the outlet. We discuss mathematical models, describing coupled flows in the pure liquid subregions and in the porous filter media, as well as interface conditions between them. Further, we reformulate the problem in fictitious regions method manner, and discuss peculiarities of the numerical algorithm in solving the coupled system. Next, we show numerical results, validating the model and the algorithm. Finally, we present results from simulation of 3-D oil flow through a real car filter.     

On the optimisation of viscoplastic constitutive modelling using a numerical feedback damping algorithm

The authors propose a mathematical model that, in the presence of a constant time step algorithm and a smooth evolution of a state variable, increases the performance of the numerical process, forces the convergence of the numerical solution and, consequently, improves the overall quality of the results. This method reduces the total number of time steps of a simulation process and minimizes the necessary CPU time. The proposed algorithm is based on the mathematical adjustment of the evolution of a chosen state variable. The resulting numerical signals are analysed and properly characterised. Several numerical signals, obtained from different non-linear simulation examples and conditions, are studied. Based on the characterisation of the numerical signals and considering that the numerical results reflect the behaviour of a vibratory system—the numerical code—with its own intrinsic mass, spring and dashpot elements, the authors develop a numerical damping algorithm and present its implementation. The algorithm is applied and tested with a non-linear finite element example, using a viscoplastic constitutive model. The authors also present a set of numerical validation tests consisting of the simulation of the development of residuals stresses that arise from the fabrication process of particle reinforced metal matrix composites (MMC). The cooling down stage of an AlSiC_p 20% vol. MMC is simulated. In order to evaluate the performance of the algorithms, some results, obtained with and without the application of the optimisation algorithm, are presented and thoroughly compared. The numerical damper algorithm proves to be very efficient.     

Image-based color ink diffusion rendering

This paper proposes an image-based painterly rendering algorithm for automatically synthesizing an image with color ink diffusion. We suggest a mathematical model with a physical base to simulate the phenomenon of color colloidal ink diffusing into absorbent paper. Our algorithm contains three main parts: a feature extraction phase, a Kubelka-Munk (KM) color mixing phase, and a color ink diffusion synthesis phase. In the feature extraction phase, the information of the reference image is simplified by luminance division and color segmentation. In the color mixing phase, the KM theory is employed to approximate the result when one pigment is painted upon another pigment layer. Then, in the color ink diffusion synthesis phase, the physically-based model that we propose is employed to simulate the result of color ink diffusion in absorbent paper using a texture synthesis technique. Our image-based ink diffusing rendering (IBCIDR) algorithm eliminates the drawback of conventional Chinese ink simulations, which are limited to the black ink domain, and our approach demonstrates that, without using any strokes, a color image can be automatically converted to the diffused ink style with a visually pleasing appearance     

Thermomechanical Model of an Impermeable Porous Medium with a Chemically Active Filler

A self-consistent mathematical model describing the thermomechanical behavior of an elastic medium, which contains voids filled with a chemically active substance, is considered. The behavior of the medium is described by thermomechanical equations. Processes in the pores are described by a lumped model which allows for energy release, chemical reactions, and conditions of phase equilibrium. The model makes it possible to take into account an arbitrary number of components, which can be in solid and three mobile phases (liquid gaseous, liquid hydrocarbon, and aqueous phases). The distribution of components between phases is obtained using a thermodynamically consistent technique under assumption that any mobile component can be present in any mobile phase. In order to describe the thermodynamic behavior of the components with allowance for phase transitions, cubic equations of state are used, which are rather common in engineering practice. An algorithm based on a combination of domain decomposition method and physical splitting approach is proposed for the numerical solution of the model system of equations.     

Phase equilibrium calculation of multi-component gas separation of supersonic separator

A mathematical model for phase equilibrium prediction of multi-component gas separation process inside a supersonic separator is established and an efficient numerical solution method is designed. The model and the numerical method are then used to predict the phase equilibrium characteristics and the separation performance of a field test natural gas supersonic purification separator. The predicted results are generally in good agreement with the field test measurements, which proves that the phase equilib...     

Numerical simulation of solitary wave generation in a wind-water annular tunnel

We briefly describe laboratory experiments demonstrating wind-water solitary wave generation in a wind-water annular tunnel. A mathematical model of this phenomenon is constructed in the context of a shallow-water approximation. The finite-difference algorithm for solving the system is based on regularized shallow-water equations. For the first time, we obtain a numerical solution of the wind-water solitary wave that is qualitatively consistent with the experimental data.