非线性对流扩散方程的逆风型差分格式

§1 对流扩散方程可以用来描述水中和大气中污染物质的分布、流体流动和流体中的传热等,以上均有对流扩散的特征。数值求解对流扩散方程很重要,近年来工作不少,如[1,2]。我们考虑二维非线性对流扩散方程的初边值问题     

非线性对流扩散方程的逆风型差分格式

§1 对流扩散方程可以用来描述水中和大气中污染物质的分布、流体流动和流体中的传热等,以上均有对流扩散的特征。数值求解对流扩散方程很重要,近年来工作不少,如[1,2]。我们考虑二维非线性对流扩散方程的初边值问题     

基于Gegenbauer多项式求解分数阶对流扩散方程

<正>1引言对流扩散方程是一种重要的运动方程,包括对流项和扩散项,用于描述质量、热量、能量等流动系统的质量传递规律.许多自然过程都可用对流扩散方程来模拟,如烟雾或灰尘对大气污染物的输送、地下水的污染、有机溶剂中化学溶质的扩散、河流系统的热污染等.但异常扩散现象在自然界中无处不在,从某种意义上说正常扩散和异常扩散的根本区别在于速度.对于异常扩散,情况变得复杂,     

对流-扩散方程的一类交替分组方法

1 引 言 对流-扩散方程是措述流体运动某些物理现象的一类重要数学模型,在热传导、粒子扩散、渗流力学等方面有广泛应用,因此,研究对流-扩散方程的数值计算方法有重要的科学意义和应用价值,开展并行差分法的研究也已成为偏微分方程数值分析的重要内容之一.对于扩散方程和对流-扩散方程的并行差分方法的研究已有许多工作[1-10].本文给出了对流-     

对流扩散方程的经济差分格式

１．引言 对流扩散方程是一类基本的运动方程,它可描述质量、热量的输运过程以及反应扩散过程等众多物理现象．寻找稳定、快速实用的数值方法,有着重要的理论和实际意义．标准的差分方法或有限元方法对它常常失效,根本原因在于“对流项”的存在．［１］提出了解对流扩散方程的特征线修正技术,这一方法考虑沿着特征线（流动方向）的离散,利用了对流扩散问题的物理力学性质,可以有效地克服数值振荡,保证数值解的稳定,尤其对“对流占优”的问题,这一方法有突出的优越性．这方面已有大量的理论和应用研究成果［２,３,７］．对大规模…     

一维定常型对流占优扩散方程的一类迎风有限体积格式

本文针对一维定常型对流占优扩散方程提出了一类迎风有限体积格式 .该格式对对流项具有二阶精度 ,对扩散项保持一阶精度 ,符合对流占优扩散问题强对流、弱扩散的特点 .     

对流扩散方程有限混合分析格式

介绍了对流扩散方程的混合有限分析法 ,得出了求解对流扩散方程隐式格式、离散算子 ,并且证明了这些格式解的存在性 ,分析了格式的截断误差     

对流扩散方程的QC3无网格法

对流扩散方程作为偏微分运动方程的分支,在流体力学、气体动力学等领域有着重要应用.为解决对流扩散方程难以通过解析法得到解析解的难题,采用二阶一致3点积分(Quadratically Consistent 3-Point Integration,简称QC3)提高无网格法的计算效率,通过对积分点上形函数导数的修正,改善无网格法的精度和收敛性.本文将QC3无网格法拓展到对流扩散方程问题中,时域离散采用广义特征线Galerkin法,空间离散采用QC3法.数值结果表明,应用QC3无网格法得到的对流扩散问题数值解与解析解十分接近,验证了QC3无网格法解决对流扩散问题的可行性.     

对流扩散方程的四阶紧凑迎风差分格式

§1.引言 流动和传热传质的基本方程均是对流扩散型的.对流扩散方程的高阶紧凑差分格式,作为提高计算可靠性和节省计算量的一条有效途径,已引起相当的重视.作为该领域的一大进展,新近由Dennis推出的对流扩散方程四阶紧凑格式,在二维情形下呈九点式且勿须引入中间变量,只涉及对流扩散量本身,能在较粗网格下获取较为准确的数值结果.从本质上说,该格式系指数型四阶紧凑格式的多项式型翻版.它与指数型紧凑格     

求解变系数线性对流扩散方程的AGE方法

1、引言 对流扩散方程是描述粘性流体运动的非线性方程的线性化模型方程,而且它本身也描述了许多自然现象,例如在水中或大气中污染物质浓度的扩散,沿海盐度,温度扩散等等．因此求解对流扩散方程的计算方法特别是并行解法引起了充分的重视。     

Numerical treatment of two‐parameter singularly perturbed parabolic convection diffusion problems with non‐smooth data

In the present work, we consider a parabolic convection‐diffusion‐reaction problem where the diffusion and convection terms are multiplied by two small parameters, respectively. In addition, we assume that the convection coefficient and the source term of the partial differential equation have a jump discontinuity. The presence of perturbation parameters leads to the boundary and interior layers phenomena whose appropriate numerical approximation is the main goal of this paper. We have developed a uniform numerical method, which converges almost linearly in space and time on a piecewise uniform space adaptive Shishkin‐type mesh and uniform mesh in time. Error tables based on several examples show the convergence of the numerical solutions. In addition, several numerical simulations are presented to show the effectiveness of resolving layer behavior and their locations.     

非线性对流扩散方程的三层隐-显hp-局部间断Galerkin有限元方法

使用Arnold等人提出的求解椭圆方程的间断有限元的一般框架及新的处理非线性对流项的方法,得到了非线性对流扩散方程的三层隐-显hp-LDG方法的误差估计.对Burgers方程进行了数值计算,计算结果验证了文中得到的理论结果.     

Least squares moving finite elements

The moving finite element (MFE) method, when applied to purelyhyperbolic partial differential equation, moves nodes with approximatelycharacteristic speeds, which makes the method useless for steady-stateproblems. We introduce the least squares MFE method (LSMFE)for steady-state pure convection problems which corrects thisdefect. We show results for a steady-state pure convection problemin one dimension in which the nodes are no longer swept downstreamas in MFE. The method is then extended to two dimensions andthe grid aligns automatically with the flow, thereby yieldingfar greater accuracy than the corresponding fixed node leastsquares results, as is shown in two-dimensional numerical trials.     

A fast numerical method for solving coupled Burgers' equations

A new fast numerical scheme is proposed for solving time‐dependent coupled Burgers' equations. The idea of operator splitting is used to decompose the original problem into nonlinear pure convection subproblems and diffusion subproblems at each time step. Using Taylor's expansion, the nonlinearity in convection subproblems is explicitly treated by resolving a linear convection system with artificial inflow boundary conditions that can be independently solved. A multistep technique is proposed to rescue the possible instability caused by the explicit treatment of the convection system. Meanwhile, the diffusion subproblems are always self‐adjoint and coercive at each time step, and they can be efficiently solved by some existing preconditioned iterative solvers like the preconditioned conjugate galerkin method, and so forth. With the help of finite element discretization, all the major stiffness matrices remain invariant during the time marching process, which makes the present approach extremely fast for the time‐dependent nonlinear problems. Finally, several numerical examples are performed to verify the stability, convergence and performance of the new method.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1823–1838, 2017     

Block‐centered upwind multistep difference method and convergence analysis for numerical simulation of oil reservoir

The three‐dimensional displacement of two‐phase flow in porous media is a preliminary problem of numerical simulation of energy science and mathematics. The mathematical model is formulated by a nonlinear system of partial differential equations to describe incompressible miscible case. The pressure is defined by an elliptic equation, and the concentration is defined by a convection‐dominated diffusion equation. The pressure generates Darcy velocity and controls the dynamic change of concentration. We adopt a conservative block‐centered scheme to approximate the pressure and Darcy velocity, and the accuracy of Darcy velocity is improved one order. We use a block‐centered upwind multistep method to solve the concentration, where the time derivative is approximated by multistep method, and the diffusion term and convection term are treated by a block‐centered scheme and an upwind scheme, respectively. The composite algorithm is effective to solve such a convection‐dominated problem, since numerical oscillation and dispersion are avoided and computational accuracy is improved. Block‐centered method is conservative, and the concentration and the adjoint function are computed simultaneously. This physical nature is important in numerical simulation of seepage fluid. Using the convergence theory and techniques of priori estimates, we derive optimal estimate error. Numerical experiments and data show the support and consistency of theoretical result. The argument in the present paper shows a powerful tool to solve the well‐known model problem.     

Block Pulse算子矩阵法求解变系数时间分数阶对流扩散方程（英文）

The numerical technique based on two-dimensional block pulse functions(2D-BPFs) is proposed for solving the time fractional convection diffusion equations with variable coeficients(FCDEs).We introduce the block pulse operational matrices of the fractional order differentiation.Furthermore,we translate the original equation into a Sylvester equation by the proposed method.Finally,some numerical examples are given and numerical results are shown to demonstrate the accuracy and reliability of the above-mentioned algorithm.     

Simulation of planar ionization wave front propagation on an unstructured adaptive grid

The paper deals with the numerical solution of a basic 2D model of the propagation of an ionization wave. The system of equations describing this propagation consists of a coupled set of reaction–diffusion-convection equations and a Poissons equation. The transport equations are solved by a finite volume method on an unstructured triangular adaptive grid. The upwind scheme and the diamond scheme are used for the discretization of the convection and diffusion fluxes, respectively. The Poisson equation is also discretized by the diamond scheme. Numerical results are presented. We deal in more detail with numerical tests of the grid adaptation technique and its influence on the numerical results. An original behavior is observed. The grid refinement is not sufficient to obtain accurate results for this particular phenomenon. Using a second order scheme for convection is necessary.     

Numerical simulations of water–gas flow in heterogeneous porous media with discontinuous capillary pressures by the concept of global pressure

We present an approach and numerical results for a new formulation modeling immiscible compressible two-phase flow in heterogeneous porous media with discontinuous capillary pressures. The main feature of this model is the introduction of a new global pressure, and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion–convection one (the saturation equation) with nonlinear transmission conditions at the interfaces that separate different media. The resulting system is discretized using a vertex-centred finite volume method combined with pressure and flux interface conditions for the treatment of heterogeneities. An implicit Euler approach is used for time discretization. A Godunov-type method is used to treat the convection terms, and the diffusion terms are discretized by piecewise linear conforming finite elements. We present numerical simulations for three one-dimensional benchmark tests to demonstrate the ability of the method to approximate solutions of water–gas equations efficiently and accurately in nuclear underground waste disposal situations.