High order implicit collocation method for the solution of two‐dimensional linear hyperbolic equation

In this article, we introduce a high‐order accurate method for solving the two dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivatives of linear hyperbolic equation and collocation method for the time component. The resulted method is unconditionally stable and solves the two‐dimensional linear hyperbolic equation with high accuracy. In this technique, the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method give a very efficient approach for solving the two dimensional linear hyperbolic equation. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

功能梯度厚壁中空圆柱体弹性动力学平面应变响应的解析解

研究了边界表面受均布动压力作用的功能梯度(FGM)厚壁中空圆柱体,给出了其平面应变响应下的弹性动力学解．假设材料性能(除Poisson比外)随厚度按幂律函数变化．为了得到一个精确解,将动力径向位移分为准静力部分和动力部分,导出了每个部分的一个解析解．先由Euler方程得到准静力学部分的解,再由分离变量法和正交展开法得到动力学部分的解．在不同动荷载作用下,对不同的FGM中空圆柱体,画出径向位移和应力图,并对本方法的优点进行了讨论．该解析解适用于中空圆柱体各种组合的FGM,厚度可以是任意的,初始条件也可以是任意的,壁面上均匀分布着任意形式的动压力．     

Pore-Level Investigation of Heavy Oil Recovery During Water Alternating Solvent Injection Process

This study concerns with the microscopic and macroscopic fluid distribution and flow behavior during water alternating solvent (WAS) injection process to heavy oil using micromodel generated from thin section of a real rock which has rarely attended in the available literature. In this study, a one-quarter five-spot glass micromodel was deployed to examine the effect of flow media topology on microscopic displacements as well as macroscopic efficiency of WAS process. The micromodel was initially saturated with the heavy oil, and then the hydrocarbon solvent and water were injected alternately into it. The observations confirmed that WAS injection scheme is an effective method for the recovery of the significant amount of residual oil. Using solvent as the leading batch in WAS scheme can really improve the oil recovery by increasing the amount of microscopic sweep efficiency in flow paths, where the molecular diffusion in solvent–heavy oil system occurs. Presence of connate water in WAS scheme can improve the recovery efficiency especially at higher water saturations. Heterogeneity of the medium caused the water to be distributed better in the medium, but the amount of residual oil in the flow area is going to be increased. Small precipitates of asphaltene particles due to solvent injection and localized entrapment of the oil due to heterogeneity effects, water blockage, and deadend pores were observed mainly in this process. The results of this study reveals the pore scale events in WAS injection process and will be helpful for developing reliable simulation models.     

Optimization of the operational parameters in a fast axial flow CW CO2 laser using artificial neural networks and genetic algorithms

This paper presents an artificial intelligence approach for optimization of the operational parameters such as gas pressure ratio and discharge current in a fast-axial-flow CW CO₂ laser by coupling artificial neural networks and genetic algorithm. First, a series of experiments were used as the learning data for artificial neural networks. The best-trained network was connected to genetic algorithm as a fitness function to find the optimum parameters. After the optimization, the calculated laser power increases by 33% and the measured value increases by 21% in an experiment as compared to a non-optimized case.     

Numerical prediction of flow in a model of a (potential) soft acting peristaltic blood pump

This paper presents a numerical study of the flow field in a novel ‘soft’ acting peristaltic pump. The pump has potential applications wherever pumping of biological or sensitive fluids with reduced damage is required. The application of the device presented is as a blood pump. The model of the pump comprises a cylindrical tube that forms three chambers. The walls of these chambers move radially as a function of time. The pumping action is initiated by applying phased movement between the chambers. The flow is treated as laminar, unsteady, incompressible, Newtonian, and with a moving boundary. The governing equations are solved using a finite element method (FEM). An operating speed of 60 cycle min⁻¹ has been chosen. The results show that a periodic solution can be achieved after four cycles. The velocity field, streamline and shear stress are presented and discussed. The flow has generally a two‐way pulsatile nature, moving forwards and backwards. However, at the outlet, there is a net outflow over one cycle against a zero pressure head. Net flow linearly decreases to zero with increasing pressure head. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical assessment of a shock‐detecting sensor for low dissipative high‐order simulation of shock–vortex interactions

Considering the importance of high‐order schemes implementation for the simulation of shock‐containing turbulent flows, the present work involves the assessment of a shock‐detecting sensor for filtering of high‐order compact finite‐difference schemes for simulation of this type of flows. To accomplish this, a sensor that controls the amount of numerical dissipation is applied to a sixth‐order compact scheme as well as a fourth‐order two‐register Runge–Kutta method for numerical simulation of various cases including inviscid and viscous shock–vortex and shock–mixing‐layer interactions. Detailed study is performed to investigate the performance of the sensor, that is, the effect of control parameters employed in the sensor are investigated in the long‐time integration. In addition, the effects of nonlinear weighting factors controlling the value of the second‐order and high‐order filters in fine and coarse non‐uniform grids are investigated. The results indicate the accuracy of the nonlinear filter along with the promising performance of the shock‐detecting sensor, which would pave the way for future simulations of turbulent flows containing shocks. Copyright © 2014 John Wiley & Sons, Ltd.     

Second-order stochastic dominance constrained portfolio optimization: Theory and computational tests

Due to the definition of second-order stochastic dominance (SSD) in terms of utility theory, portfolio optimization with SSD constraints is of major practical interest. We contribute to the field in two ways: first, we present a self-contained theory with some new results and new proofs of known results; second, we perform a set of tests for computational efficiency. We provide new and simple arguments for the formulation of SSD constraints in a mathematical programming framework. For many individuals, an SSD constraint may seem too severe wherefore various relaxations (ASSD), have been proposed. We introduce yet another relaxation, directional SSD, where a candidate portfolio is admissible if a step from the benchmark in the direction of the candidate yields a dominating portfolio. Optimal step size depends on individual preferences reflected by the objective function. We compare computational efficiency of seven approaches for SD constrained portfolio problems, including SSD and ASSD constrained cases.     

Using generating functions to convert an implicit (3,3) finite difference method to an explicit form on diffusion equation with different boundary conditions

In this article, our main goal is to develop an idea to convert an implicit (3,3) ??-scheme finite difference method to an explicit form for both linear and nonlinear diffusion equations and also for nonlinear advection-diffusion equation with different boundary conditions. Accordingly, we assist power series generating functions which are a routine method in discrete mathematics. Also, the stability analysis of ??–scheme to implement in nonlinear advection–diffusion equation has been investigated. Finally, the new approach has been implemented for Fisher, reaction–diffusion, Burgers and coupled Burgers equations as test problems to verify the ability and efficiency of the method proposed in this paper.     

A new wavelet method for solving the Helmholtz equation with complex solution

The Helmholtz equation which is very important in a variety of applications, such as acoustic cavity and radiation wave, has been greatly considered in recent years. In this article, we propose a new efficient computational method based on the Legendre wavelets (LWs) expansion together with their operational matrices of integration and differentiation to solve this equation with complex solution. Because of the fact that both of the operational matrices of integration and differentiation are used in the proposed method, the boundary conditions are taken into account automatically. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifies the problems. As an applied example, “propagation of plane waves” is investigated to demonstrate the validity and applicability of the presented method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 741–756, 2016     

A Krylov-Schur-like method for computing the best rank-(r1,r2,r3) approximation of large and sparse tensors

Numerical Algorithms - The paper is concerned with methods for computing the best low multilinear rank approximation of large and sparse tensors. Krylov-type methods have been used for this...