The dual reciprocity boundary elements method for the linear and nonlinear two‐dimensional time‐fractional partial differential equations

In this paper, we apply the dual reciprocity boundary elements method for the numerical solution of two‐dimensional linear and nonlinear time‐fractional modified anomalous subdiffusion equations and time‐fractional convection–diffusion equation. The fractional derivative of problems is described in the Riemann–Liouville and Caputo senses. We employ the linear radial basis function for interpolation of the nonlinear, inhomogeneous and time derivative terms. This method is improved by using a predictor–corrector scheme to overcome the nonlinearity which appears in the nonlinear problems under consideration. The accuracy and efficiency of the proposed schemes are checked by five test problems. The proposed method is employed for solving some examples in two dimensions on unit square and also in complex regions to demonstrate the efficiency of the new technique. Copyright © 2016 John Wiley & Sons, Ltd.     

Solution to transient Navier–Stokes equations by the coupling of differential quadrature time integration scheme with dual reciprocity boundary element method

The two‐dimensional time‐dependent Navier–Stokes equations in terms of the vorticity and the stream function are solved numerically by using the coupling of the dual reciprocity boundary element method (DRBEM) in space with the differential quadrature method (DQM) in time. In DRBEM application, the convective and the time derivative terms in the vorticity transport equation are considered as the nonhomogeneity in the equation and are approximated by radial basis functions. The solution to the Poisson equation, which links stream function and vorticity with an initial vorticity guess, produces velocity components in turn for the solution to vorticity transport equation. The DRBEM formulation of the vorticity transport equation results in an initial value problem represented by a system of first‐order ordinary differential equations in time. When the DQM discretizes this system in time direction, we obtain a system of linear algebraic equations, which gives the solution vector for vorticity at any required time level. The procedure outlined here is also applied to solve the problem of two‐dimensional natural convection in a cavity by utilizing an iteration among the stream function, the vorticity transport and the energy equations as well. The test problems include two‐dimensional flow in a cavity when a force is present, the lid‐driven cavity and the natural convection in a square cavity. The numerical results are visualized in terms of stream function, vorticity and temperature contours for several values of Reynolds (Re) and Rayleigh (Ra) numbers. Copyright © 2008 John Wiley & Sons, Ltd.     

单个球形生物质颗粒热解过程的数值模拟

本文对单个球形生物质颗粒的热解过程进行数值模拟．利用双倒易边界元法和四阶龙格-库塔方法分别对非线性的导热方程和化学反应动力学方程组进行求解．讨论了生物质颗粒的大小与环境温度对热解时间和热解产物中相关组分质量分数的影响．     

分析金属熔滴快速凝固过程的双倒易边界元方法

本文发展了非线性边界条件相变传热过程的轴对称双倒易边界元方法,数值模拟了金属熔滴在快速冷却条件下的快速凝固过程。分别研究了在微重力落管和落塔中及喷射成形过程中金属熔滴的快速凝固过程,得到了过冷度,再辉时间,温度变化及相变界面随时间的变化等数值结果。     

The dual reciprocity boundary integral equation technique to solve a class of the linear and nonlinear fractional partial differential equations

In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear and nonlinear time‐fractional partial differential equations (TFPDEs). The main aim of the present paper is to examine the applicability and efficiency of DRBEM for solving TFPDEs. We employ the time‐stepping scheme to approximate the time derivative, and the method of linear radial basis functions is also used in the DRBEM technique. This method is improved by using a predictor–corrector scheme to overcome the nonlinearity that appears in the nonlinear problems under consideration. To confirm the accuracy of the new approach, several examples are presented. The convergence of the DRBEM is studied numerically by comparing the exact solutions of the problems under investigation. Copyright © 2015 John Wiley & Sons, Ltd.     

双倒易边界元拓展于模拟生物组织中热波传播问题

1前言双倒易边界元是一个新发展的纯边界积分数值方法＊，乞今在热波传播问题的应用尚未见到报导。对热波在工程材料中传播的反射和衰减特性已作过一些研究，但它们均局限在快速温度变化及极低温情形．生物组织热波传播问题的研究则尚未见到报导。我们曾用有限差分法考察过一维情况下热波在不同时刻下的演化情况，算例中波形存在锯齿这是由于有限差分误差所致．热波问题的数值模拟，需要对热波及其分解、叠加和反射能进行准确定位与精确捕获。在已发表的有限差分泡括采用了TVD高精度算法）数值解中报道了热波前沿存在严重的数值脉动。边界…     

分析半透明单晶生长传热过程的边界元方法

论文发展了一个能求解带相变运动界面非定常传热和非线性热物理特性问题的双倒易边界元方法。数值模拟了半透明单晶生长中热过程的一个例子。由于方法是纯边界积分方法,计算量与计算内存都大大减少。获得了单晶生长过程瞬态温度场分布和固液相界面形状时间推进的一些结果。     

A computationally efficient solution of the wave equation for the transient response of infinite reservoirs

In this paper, the transient response of an infinite reservoir is analyzed using the dual-reciprocity boundary element method. A vertical and an inclined-face rigid dam are analyzed under a transient loading. Sharan-type boundary-condition transmission is implemented in the formulation. The results are compared with the exact solution and those obtained by using the finite element method. It is seen that the application of the dual-reciprocity boundary element method is simpler and the results are in very good agreement with the exact solution and those obtained by using the finite element method.     

热储能系统中二维多重相变问题第二类边界条件的双倒易边界元解法

本文发展了二维非定常热导热并带有多重相变运动边界问题的双倒易边界元方法．对热储能系统中相变材料的多重相变运动边界问题进行了模拟，得出了温度分布及相变界面随时间的变化，结果表明，双倒易边界元方法能够很好地处理这类问题．     

A Minimal Distance Constrained Adaptive Mesh Algorithm with Application to the Dual Reciprocity Method

We present a new technique for generating error equi-distributing meshes that satisfy both local quasi-uniformity and a preset minimal mesh spacing. This is first done in the one-dimensional case by extending the Kautsky and Nichols method and then in the two-dimensional case by generalizing the tensor product methods to alternating curved line equi-distributions. With the new meshing approach, we have achieved better accuracy in approximation using interpolatory radial basis functions. Furthermore, improved accuracy in numerical results has been obtained when the interpolatory strategy is applied to the dual reciprocity boundary element method for solving a class of linear and nonhomogeneous partial differential equations.