An adaptive mesh strategy for singularly perturbed convection diffusion problems

Vivek Kumar; Balaji Srinivasan

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An adaptive mesh strategy for singularly perturbed convection diffusion problems

机译：奇异摄动对流扩散问题的自适应网格策略

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摘要

In this paper, a new adaptive mesh strategy has been developed for solving convection dominated, convection-diffusion singularly perturbed problems (SPP) using second order central difference schemes. Our strategy uses a novel, entropy-like variable as the adaptation parameter for convection diffusion SPP. Further, unlike the popular layer adapted meshes mainly by Bakhvalov (B-type) and Shishkin (S-type), no pre-knowledge of the location and width of the layers (boundary as well as interior) is needed. The method is completely free of arbitrary perturbation parameters ∈ (robust) and results in oscillation free solutions to a range of convection-diffusion SPP. Numerical results for various test problems: linear (boundary layers with and without turning points), nonlinear and systems of coupled equations are presented. This method is expected to aid in robust computations of convection dominated SPP.

机译：在本文中，已开发出一种新的自适应网格策略，用于使用二阶中心差分方案来解决对流占优，对流扩散奇异摄动问题（SPP）。我们的策略使用一种新颖的类似熵的变量作为对流扩散SPP的自适应参数。此外，与主要由Bakhvalov（B型）和Shishkin（S型）流行的适用于图层的网格不同，不需要预先知道图层的位置和宽度（边界以及内部）。该方法完全不受任意扰动参数ε（鲁棒）的影响，并导致对流扩散SPP范围的无振荡解。给出了各种测试问题的数值结果：线性（具有和不具有转折点的边界层），非线性和耦合方程组。预期该方法有助于对流主导的SPP的鲁棒计算。

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来源
《Applied Mathematical Modelling》 |2015年第7期|2081-2091|共11页
作者
Vivek Kumar; Balaji Srinivasan;
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作者单位

Delhi Technological University, Dept of Applied Mathematics, Delhi 110042, India;

Indian Institute of Technology, Dept. of Applied Mechanics, Delhi 110016, India;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Central finite difference schemes; Convection dominated singularly perturbed problems; Layer-adaptive meshes;

机译：中央有限差分方案;对流占优势的奇异摄动问题;图层自适应网格;

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1. A Novel Adaptive Mesh Strategy for Singularly Perturbed Parabolic Convection Diffusion Problems [J] . Vivek Kumar, Balaji Srinivasan Differential equations and dynamical systems . 2019,第1a3期

机译：一种单独扰动抛物线对流扩散问题的新型自适应网格策略
2. Richardson Extrapolation Method for Singularly Perturbed Convection-Diffusion Problems on Adaptively Generated Mesh [J] . Pratibhamoy Das, Srinivasan Natesan Computer Modeling in Engineering & Sciences . 2013,第6期

机译：自适应生成网格上奇摄动对流扩散问题的Richardson外推方法
3. A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation [J] . Grigory I. Shishkin 高等学校计算数学学报（英文版） . 2008,第002期

机译：奇摄动抛物线对流扩散方程的先验自适应网格的有限差分格式
4. Improved Scheme on Adapted Locally-Uniform Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Problem [C] . G.I. Shishkin Conference on boundary and interior layers, computational and asymptotic methods . 2011

机译：改进的方案适应局部均匀网格的奇异扰动抛物线对流扩散问题
5. A new stability method for singularly perturbed convection-diffusion equations. [D] . Ramakkagari, Viswanath. 2007

机译：奇摄动对流扩散方程的一种新的稳定性方法。
6. An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods [O] . Zhilin Li, Peng Song -1

机译：浸没边界/接口方法的自适应网格细化策略
7. Fitted mesh method for a weakly coupled system of singularly perturbed reaction–convection–diffusion problems with discontinuous source term [O] . Mahabub Basha Pathan, Shanthi Vembu 2016

机译：具有不连续源项的奇摄动反应-对流-扩散问题的弱耦合系统的拟合网格方法
8. Modeling, Analysis and Simulation: An A Posteriori Adaptive Mesh Technique for Singularly Perturbed Convection-Diffusion Problems with a Moving Interior Layer [R] . Shishkin, G. I., Shishkina, L. P., Hemker, P. W. 2003

机译：建模，分析与仿真：一种具有运动内层的奇摄动对流扩散问题的后验自适应网格技术

An adaptive mesh strategy for singularly perturbed convection diffusion problems

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