Adaptive ADI numerical analysis of 2D quenching-type reaction diffusion equation with convection Term
Adaptive ADI numerical analysis of 2D quenching-type reaction diffusion equation with convection Term
复制标题
含对流项的二维猝灭型反应扩散方程的自适应ADI数值分析
DOI：
10.1155/2020/8161804
复制
发表时间：
2020
影响因子：
--
通讯作者：
Yongbin Ge
中科院分区：
文献类型：
--
作者：
Xiaoliang Zhu;Yongbin Ge
首次提出了一类带对流项的二维非线性退化奇异反应扩散方程的自适应高阶差分解.在第一和第二中心差分算子分别近似一阶和二阶空间导数之后，通过应用泰勒级数规则离散高阶空间导数，并且通过使用Crank-Nicolson（CN）差分格式离散时间导数。以此方式建立了非均匀网格的交替方向隐式（ADI）格式。同时，精度分析表明，在一定条件下，该方法在时间上为二阶精度，在空间上为四阶精度。在自适应网格上，利用高阶格式演示了奇异抛物方程的猝灭行为，并分析了燃烧室尺寸对猝灭的影响。本文合理地表明，所提出的方案是可行的解决二维淬火型问题。
An adaptive high‐order difference solution about a 2D nonlinear degenerate singular reaction‐diffusion equation with a convection term is initially proposed in the paper. After the first and the second central difference operator approximating the first‐order and the second‐order spatial derivative, respectively, the higher‐order spatial derivatives are discretized by applying the Taylor series rule and the temporal derivative is discretized by using the Crank–Nicolson (CN) difference scheme. An alternating direction implicit (ADI) scheme with a nonuniform grid is built in this way. Meanwhile, accuracy analysis declares the second order in time and the fourth order in space under certain conditions. Sequentially, the high‐order scheme is performed on an adaptive mesh to demonstrate quenching behaviors of the singular parabolic equation and analyse the influence of combustion chamber size on quenching. The paper displays rationally that the proposed scheme is practicable for solving the 2D quenching‐type problem.