A self-adaptive numerical method to solve convection-dominated diffusion problems
type: Item
instance of: scholarly article
title: A self-adaptive numerical method to solve convection-dominated diffusion problems
zbMATH Open document ID: 1427.65146
DOI: 10.1155/2017/8379609
author: Zhi-Wei Cao
author: Zhi-Fan Liu
author: Zhifeng Liu
author: Xiaohong Wang
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: Convection-dominated diffusion problems usually develop multiscaled solutions and adaptive mesh is popular to approach high resolution numerical solutions. Most adaptive mesh methods involve complex adaptive operations that not only increase algorithmic complexity but also may introduce numerical dissipation. Hence, it is motivated in this paper to develop an adaptive mesh method which is free from complex adaptive operations. The method is developed based on a range-discrete mesh, which is uniformly distributed in the value domain and has a desirable property of self-adaptivity in the spatial domain. To solve the time-dependent problem, movement of mesh points is tracked according to the governing equation, while their values are fixed. Adaptivity of the mesh points is automatically achieved during the course of solving the discretized equation. Moreover, a singular point resulting from a nonlinear diffusive term can be maintained by treating it as a special boundary condition. Serval numerical tests are performed. Residual errors are found to be independent of the magnitude of diffusive term. The proposed method can serve as a fast and accuracy tool for assessment of propagation of steep fronts in various flow problems.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76M10
zbMATH DE Number: 6972569
Wikidata QID: Q59147830
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/8379609
OpenAlex ID: W2735077220
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description: scientific article; zbMATH DE number 6972569